[
  {
    "name": "simulated_schools",
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "lme4": "2.0.6",
      "statsmodels": "0.15.0",
      "PHP": "8.5.10",
      "Python": "3.14.7"
    },
    "R": {
      "coefficients": [
        46.65518658102517,
        1.6139078946454086,
        0.24543063302324322
      ],
      "covariance": [
        [
          4.8579127529874055,
          0.13899062877260648,
          -0.06974343644872319
        ],
        [
          0.13899062877260648,
          0.025679175854565875,
          -0.005167669927211247
        ],
        [
          -0.06974343644872319,
          -0.005167669927211247,
          0.0017399760296578724
        ]
      ],
      "std_errors": [
        2.204067320429983,
        0.16024723353170836,
        0.04171301990575452
      ],
      "z_statistics": [
        21.167768401885013,
        10.07136197659264,
        5.883789607603664
      ],
      "p_values": [
        1.893116048612982e-99,
        7.394689044390862e-24,
        4.009775023303381e-09
      ],
      "conf_int": [
        [
          42.3352940134807,
          50.97507914856964
        ],
        [
          1.299829088301081,
          1.9279867009897362
        ],
        [
          0.16367461632156205,
          0.3271866497249244
        ]
      ],
      "fixed_fitted": [
        84.3233908527064,
        63.70150162386945,
        82.1713861802642,
        63.770609771433485,
        66.85464202631557,
        73.04702321507861,
        62.88496196710182,
        70.83256488387113,
        83.25100477769125,
        75.12013843564368,
        65.51899681049046,
        61.325637108479775,
        82.14022968074349,
        72.6103830726007,
        83.29889891606176,
        74.5667670635339,
        75.3287493421409,
        69.06687243549628,
        66.36720067053,
        62.27004760501314,
        85.68158785725562,
        60.8391613566249,
        67.45683208814617,
        67.91987617192584,
        64.0154213182632,
        70.49641064120887,
        84.86311186105408,
        68.10307439891471,
        77.47553842461214,
        58.061269029546764,
        84.6376226559832,
        62.864296714239885,
        61.01505673133992,
        70.49717038712627,
        68.16300855306037,
        82.80839956247006,
        79.72771175641441,
        81.46081906958584,
        72.12273585880186,
        80.47964529382446,
        64.38984958099692,
        67.12850379622662,
        74.80269771169179,
        59.46274314239887,
        70.65854578187317,
        57.94226520588891,
        80.9103408898493,
        77.85046925952454,
        78.60236174435423,
        73.33815085388086,
        56.63805780903226,
        78.43184314562423,
        68.8084911179115,
        70.79442790410471,
        67.95784321468682,
        69.54414491665123,
        78.35099169645044,
        79.23088541762465,
        85.08162058587925,
        68.1545496335602,
        60.09611536161291,
        69.47257733118441,
        84.78517261838998,
        82.99076771367959,
        77.66809084516993,
        78.7487556395347,
        73.73491840359917,
        75.99015486478011,
        69.69742330435275,
        80.30939775139713,
        68.40237450619684,
        67.06892129139067,
        74.00060770503035,
        83.72929266634863,
        82.4320108145934,
        79.18277515809577,
        77.53569896306125,
        71.76007655554062,
        71.56047845644773,
        65.13534988233914,
        63.55603892376554,
        59.30521990022963,
        77.47679047956314,
        76.81251380299459,
        75.31374218471174,
        66.64979754781643,
        78.42028004416501,
        85.28934648145281,
        66.40468928682132,
        80.33623393501563,
        80.27003286238875,
        65.27545633274822,
        79.78133945165217,
        77.9260091310027,
        73.3129989675301,
        80.94745219896818,
        70.98980680659261,
        63.05921258497578,
        67.85847384167083,
        72.15240365592302,
        81.37083467957405,
        61.02823893177747,
        63.768501982840405,
        67.60716899205643,
        67.29895206509468,
        66.38688492474361,
        79.62306159513807,
        81.36801332921648,
        75.91518789534257,
        74.92766660809293,
        75.83812340045704,
        71.85646852375753,
        82.63013560600439,
        81.22445617911121,
        77.09413994477778,
        76.18163543053744,
        67.10736011689502,
        78.88602534486856,
        78.25050066506223,
        65.93108362652096,
        78.06791639269436,
        86.5687089692692,
        86.83273811914167,
        55.79832313163797,
        78.61673080145337,
        79.40084650903167,
        78.39490690508333,
        79.16849695714875,
        78.60264819537453,
        67.9094757814192,
        77.969814469347,
        80.13492074921972,
        66.88834368831864,
        77.60324294679126,
        70.07323401861626,
        82.54669945392158,
        72.08689199935161,
        66.10290559592741,
        75.0659275752202,
        61.51657043005923,
        63.12047938707946,
        64.08223121393851,
        74.61075411418246,
        61.20882679799459,
        77.25867445662803,
        64.61603846526837,
        82.48963645370524,
        66.97326341122844,
        79.46205837599105,
        73.16384530086262,
        78.52524744589694,
        58.569375638194266,
        71.7063990567311,
        60.159695810322944,
        62.92838486670114,
        65.20599653587448,
        65.06731872114811,
        60.40178199451976,
        76.78749744479516,
        73.1575681192363,
        75.99214100778578,
        77.21053340766389,
        67.70986228760867,
        58.68243491539903,
        69.15859243850127,
        71.74291180594663,
        84.7836135861285,
        63.86251510616156,
        65.36417840466392,
        73.12423350126058,
        67.99909312740365,
        55.90830901631897,
        79.27722052373366,
        76.84375602709487,
        75.71912470837172,
        82.01529157377765,
        75.32576680576925,
        74.02468773658066,
        77.17737537041987,
        73.68800013230444,
        72.06806196662636,
        64.43000862477683,
        58.35659533866382,
        79.75844627676346,
        66.33039633872161,
        67.77789858037225,
        75.59138064576595,
        81.55871513491992,
        56.90386724389714,
        80.54657532293348,
        64.50859623091603,
        81.54449700068974,
        70.13642689700877,
        67.92317081718052,
        73.99025198652292,
        65.32849573122773,
        67.22481003986394,
        67.51707835117487,
        73.88695499949479,
        59.49126000386626,
        75.95340546811602,
        64.53010695427497,
        85.74354407541477,
        68.25679016050552,
        65.43186817969034,
        73.26184610491275,
        81.42002192547592,
        82.42783115841506,
        84.60763248683391,
        71.65372670227892,
        56.52240869734593,
        72.40978858014184,
        76.50313567723397,
        57.65681618880963,
        62.608520625854304,
        61.05396885174139,
        65.52876272008592,
        72.51208555438517,
        81.11723670964348,
        67.16954271935764,
        64.68834888978125,
        81.33091741481523,
        62.509830405748694,
        76.75559659407469,
        73.18806086056425,
        68.12146192617813,
        84.57750678953327,
        67.5110480801422,
        63.4499154548073,
        81.5224236384353,
        75.07759541539548,
        82.16687540106635,
        72.52234528516793,
        69.80428599293822,
        80.75027248519768,
        76.15144453494743,
        60.80712497775309,
        63.466205456622724,
        66.12272537829234,
        64.77099601866509,
        81.0933574045339,
        58.81125083280526,
        62.119600830814285,
        74.4277119416351,
        69.93653208375046,
        58.31181926481629,
        62.85022950287868,
        73.0838583363223,
        59.8804931854347,
        71.78501745230557
      ],
      "fitted": [
        84.45752388513235,
        63.8356346562954,
        82.30551921269014,
        63.904742803859435,
        66.98877505874152,
        73.18115624750456,
        63.01909499952777,
        70.96669791629708,
        83.3851378101172,
        75.25427146806963,
        65.65312984291641,
        61.459770140905725,
        82.27436271316944,
        72.74451610502665,
        83.43303194848771,
        74.70090009595984,
        75.46288237456685,
        69.20100546792223,
        67.97589818772308,
        63.87874512220622,
        87.2902853744487,
        62.44785887381798,
        69.06552960533925,
        69.52857368911891,
        65.62411883545627,
        72.10510815840195,
        86.47180937824716,
        69.71177191610779,
        79.08423594180522,
        59.66996654673984,
        86.24632017317627,
        64.47299423143296,
        62.623754248533,
        72.10586790431935,
        69.77170607025344,
        84.41709707966314,
        81.33640927360749,
        83.06951658677892,
        73.73143337599494,
        82.08834281101754,
        65.99854709819,
        68.7372013134197,
        73.01802925575633,
        57.67807468646342,
        68.87387732593771,
        56.15759674995346,
        79.12567243391383,
        76.06580080358908,
        76.81769328841877,
        71.5534823979454,
        54.85338935309681,
        76.64717468968877,
        67.02382266197604,
        69.00975944816925,
        66.17317475875136,
        67.75947646071576,
        76.56632324051498,
        73.66652068427133,
        79.51725585252593,
        62.59018490020688,
        54.531750628259594,
        63.908212597831096,
        79.22080788503666,
        77.42640298032627,
        72.10372611181661,
        73.18439090618139,
        68.17055367024585,
        70.4257901314268,
        64.13305857099944,
        74.74503301804381,
        62.83800977284352,
        61.50455655803735,
        68.43624297167703,
        78.16492793299533,
        76.86764608124008,
        73.61841042474245,
        71.97133422970795,
        66.1957118221873,
        65.99611372309441,
        65.38442007250661,
        63.80510911393301,
        59.554290090397096,
        77.72586066973061,
        77.06158399316206,
        75.56281237487921,
        66.8988677379839,
        78.66935023433248,
        85.53841667162028,
        66.6537594769888,
        80.5853041251831,
        80.51910305255622,
        65.52452652291568,
        80.03040964181965,
        78.17507932117017,
        73.56206915769758,
        81.19652238913565,
        71.23887699676008,
        63.30828277514325,
        68.1075440318383,
        74.40884260973029,
        83.62727363338131,
        63.28467788558473,
        66.02494093664767,
        69.86360794586369,
        69.55539101890194,
        68.64332387855087,
        81.87950054894533,
        83.62445228302374,
        78.17162684914983,
        77.1841055619002,
        78.0945623542643,
        74.11290747756478,
        84.88657455981165,
        83.48089513291846,
        79.35057889858504,
        78.43807438434472,
        69.36379907070229,
        81.14246429867582,
        80.50693961886951,
        68.18752258032822,
        80.3243553465016,
        88.82514792307646,
        89.08917707294893,
        58.05476208544523,
        80.87316975526063,
        81.65728546283893,
        88.72614496055043,
        89.49973501261584,
        88.93388625084162,
        78.2407138368863,
        88.3010525248141,
        90.46615880468681,
        77.21958174378574,
        87.93448100225835,
        80.40447207408336,
        92.87793750938867,
        82.4181300548187,
        76.4341436513945,
        85.3971656306873,
        71.84780848552633,
        73.45171744254657,
        74.41346926940561,
        84.94199216964954,
        71.54006485346169,
        87.58991251209513,
        59.51133928022436,
        77.38493726866123,
        61.86856422618443,
        74.35735919094705,
        68.0591461158186,
        73.42054826085293,
        53.464676453150254,
        66.60169987168709,
        55.05499662527893,
        57.823685681657125,
        60.101297350830464,
        59.9626195361041,
        55.29708280947575,
        71.68279825975114,
        68.05286893419228,
        70.88744182274176,
        72.10583422261988,
        62.60516310256466,
        53.577735730355016,
        64.05389325345726,
        66.63821262090262,
        86.88636113790177,
        65.96526265793483,
        67.4669259564372,
        75.22698105303385,
        70.10184067917693,
        58.01105656809224,
        81.37996807550694,
        78.94650357886815,
        77.82187226014501,
        84.11803912555092,
        77.42851435754253,
        76.12743528835394,
        79.28012292219314,
        75.79074768407772,
        74.17080951839965,
        66.53275617655011,
        58.92567645070149,
        80.32752738880113,
        66.89947745075928,
        68.34697969240992,
        76.16046175780362,
        82.12779624695759,
        57.472948355934804,
        81.11565643497114,
        65.07767734295369,
        82.11357811272741,
        70.70550800904644,
        68.49225192921818,
        74.55933309856059,
        65.8975768432654,
        67.7938911519016,
        68.08615946321254,
        74.45603611153247,
        60.060341115903924,
        76.52248658015368,
        65.09918806631264,
        86.31262518745244,
        68.82587127254318,
        66.000949291728,
        73.83092721695041,
        81.98910303751359,
        82.50686383577346,
        84.68666516419229,
        71.7327593796373,
        56.60144137470433,
        72.48882125750022,
        76.58216835459237,
        57.73584886616803,
        62.6875533032127,
        61.133001529099786,
        65.6077953974443,
        72.59111823174356,
        81.19626938700189,
        67.24857539671605,
        64.76738156713965,
        81.40995009217362,
        62.58886308310709,
        76.83462927143309,
        73.26709353792265,
        68.20049460353653,
        84.65653946689167,
        67.5900807575006,
        63.528948132165695,
        81.6014563157937,
        70.20088869949693,
        77.29016868516779,
        67.64563856926938,
        64.92757927703967,
        75.87356576929912,
        71.27473781904888,
        55.93041826185455,
        58.58949874072418,
        61.246018662393816,
        59.894289302766545,
        76.21665068863535,
        53.934544116906714,
        57.24289411491574,
        69.55100522573655,
        65.05982536785193,
        53.43511254891775,
        57.97352278698014,
        68.20715162042374,
        55.00378646953616,
        66.90831073640702
      ],
      "residuals": [
        -6.200523885132341,
        3.406365343704607,
        5.917480787309856,
        4.641257196140572,
        -6.851775058741524,
        -1.034156247504555,
        -2.6640949995277765,
        -1.2966979162970773,
        -0.9431378101172072,
        -3.125271468069627,
        -3.8531298429164167,
        2.2472298590942756,
        -5.882362713169442,
        4.333483894973355,
        7.603968051512297,
        -0.24390009595984452,
        0.572117625433151,
        3.560994532077771,
        1.1981018122769314,
        -4.827745122206217,
        4.792714625551298,
        1.9691411261820235,
        -2.0005296053392527,
        11.274426310881083,
        2.6168811645437273,
        -6.477108158401947,
        -0.2358093782471542,
        0.9732280838922094,
        0.35776405819477475,
        -1.589966546739845,
        2.478679826823722,
        0.3950057685670316,
        -4.986754248532996,
        3.4181320956806474,
        -6.531706070253442,
        -0.277097079663136,
        1.4565907263925197,
        -1.3545165867789137,
        -8.235433375994944,
        -3.3703428110175366,
        3.949452901809991,
        7.259798686580297,
        -0.14102925575633662,
        -1.8490746864634175,
        -6.256877325937715,
        -3.52159674995346,
        3.9893275660861605,
        -10.08180080358909,
        7.159306711581237,
        -5.910482397945401,
        -6.554389353096809,
        3.386825310311238,
        5.289177338023961,
        3.6862405518307497,
        0.36182524124863846,
        7.8065235392842425,
        0.13667675948502733,
        -9.920520684271331,
        4.423744147474068,
        -9.788184900206879,
        -2.6727506282595925,
        -6.763212597831092,
        3.8541921149633396,
        -4.469402980326279,
        4.470273888183385,
        -4.887390906181395,
        3.742446329754145,
        5.762209868573208,
        9.069941429000565,
        5.642966981956192,
        -7.08800977284352,
        -4.043556558037352,
        4.981757028322974,
        -1.201927932995332,
        0.5423539187599147,
        -2.9414104247424433,
        0.04966577029205155,
        0.811288177812699,
        2.6328862769055945,
        2.9165799274933875,
        3.7578908860669955,
        0.9137099096029075,
        3.903139330269397,
        -1.9075839931620635,
        -0.14781237487920862,
        8.564132262016088,
        -0.8753502343324868,
        -0.5424166716202876,
        2.582240523011208,
        -4.651304125183103,
        -5.273103052556223,
        3.165473477084319,
        -0.28540964181964057,
        1.8929206788298245,
        -8.33306915769758,
        5.812477610864349,
        -7.930876996760084,
        0.8707172248567545,
        -4.083544031838301,
        7.086157390269719,
        5.760726366618698,
        -2.5746778855847268,
        -3.5469409366476654,
        -1.2886079458636885,
        4.891608981098059,
        -9.136323878550876,
        -8.158500548945327,
        -4.319452283023736,
        9.395373150850162,
        -3.3361055619001974,
        -6.320562354264297,
        -10.115907477564775,
        -1.5415745598116501,
        6.318104867081544,
        -5.947578898585036,
        5.8869256156552865,
        -5.448799070702286,
        -8.19046429867582,
        -3.974939618869513,
        4.613477419671781,
        4.474644653498402,
        7.773852076923546,
        -3.042177072948931,
        6.00923791455476,
        3.543830244739368,
        14.348714537161072,
        -3.7631449605504343,
        1.295264987384158,
        7.261113749158369,
        -6.970713836886304,
        -0.0440525248140915,
        -1.5941588046868134,
        -0.3585817437857344,
        6.060518997741653,
        -3.997472074083362,
        0.09806249061132633,
        4.879869945181298,
        2.923856348605497,
        6.779834369312709,
        11.00319151447367,
        -4.676717442546561,
        1.204530730594385,
        1.5950078303504682,
        -1.4920648534616845,
        -5.735912512095126,
        -0.8223392802243623,
        -1.9869372686612365,
        -1.1015642261844292,
        -3.505359190947047,
        -4.958146115818607,
        5.193451739147079,
        -0.8526764531502522,
        -3.2946998716870866,
        3.9750033747210693,
        5.570314318342874,
        -3.702297350830463,
        5.629380463895899,
        4.6319171905242555,
        -13.388798259751141,
        -4.233868934192273,
        2.8795581772582324,
        -3.6958342226198795,
        1.1068368974353433,
        -0.021735730355018745,
        3.5901067465427445,
        1.8387873790973828,
        2.2016388620982212,
        8.727737342065168,
        5.910074043562801,
        2.127018946966146,
        -13.932840679176934,
        0.6029434319077538,
        -10.46696807550694,
        2.255496421131852,
        -8.308872260145009,
        4.137960874449078,
        8.54648564245747,
        4.496564711646059,
        -3.045122922193144,
        4.105252315922286,
        -1.1738095183996506,
        -3.238756176550112,
        -2.5246764507014845,
        -1.5425273888011333,
        1.6795225492407155,
        3.6340203075900774,
        -6.745461757803611,
        -0.19579624695758469,
        -0.09594835593480155,
        9.005343565028852,
        3.622322657046311,
        2.358421887272584,
        -2.054508009046444,
        -4.056251929218178,
        -1.2603330985605794,
        -3.4195768432653963,
        6.049108848098399,
        -2.6001594632125347,
        -0.6730361115324683,
        2.801658884096078,
        2.0555134198463207,
        -0.377188066312641,
        -8.250625187452442,
        -2.3238712725431867,
        0.40905070827199097,
        1.2080727830495874,
        4.093896962486411,
        -0.11286383577345305,
        -0.2666651641922897,
        -2.3927593796372975,
        1.4635586252956685,
        8.774178742499785,
        -1.1781683545923727,
        5.214151133831976,
        -9.5485533032127,
        6.357998470900213,
        -2.026795397444303,
        6.207881768256442,
        -10.733269387001897,
        2.703424603283949,
        1.9966184328603447,
        -2.4609500921736185,
        -1.0998630831070955,
        -4.801629271433086,
        -0.3350935379226456,
        -2.435494603536526,
        5.463460533108332,
        -2.689080757500605,
        -3.0179481321656922,
        5.028543684206298,
        -2.8708886994969305,
        1.0958313148322105,
        -14.378638569269377,
        2.302420722960335,
        4.1364342307008855,
        1.0512621809511131,
        2.913581738145453,
        -1.7414987407241824,
        1.7429813376061816,
        2.1997106972334564,
        5.411349311364646,
        -0.9845441169067115,
        2.7261058850842588,
        -1.27000522573654,
        -2.7258253678519253,
        0.019887451082247765,
        3.04447721301986,
        -2.5001516204237504,
        -4.317786469536159,
        -2.6843107364070136
      ],
      "marginal_residuals": [
        -6.066390852706391,
        3.5404983761305573,
        6.051613819735806,
        4.775390228566522,
        -6.717642026315573,
        -0.9000232150786047,
        -2.5299619671018263,
        -1.162564883871127,
        -0.809004777691257,
        -2.991138435643677,
        -3.7189968104904665,
        2.381362891520226,
        -5.748229680743492,
        4.467616927399305,
        7.738101083938247,
        -0.10976706353390853,
        0.7062506578591012,
        3.6951275645037214,
        2.80679932947001,
        -3.219047605013138,
        6.401412142744377,
        3.5778386433751024,
        -0.3918320881461739,
        12.883123828074162,
        4.225578681736806,
        -4.868410641208868,
        1.3728881389459247,
        2.5819256010852882,
        1.9664615753878536,
        0.01873097045323391,
        4.087377344016801,
        2.0037032857601105,
        -3.3780567313399175,
        5.026829612873726,
        -4.923008553060363,
        1.3316004375299428,
        3.0652882435855986,
        0.2541809304141651,
        -6.626735858801865,
        -1.7616452938244578,
        5.55815041900307,
        8.868496203773375,
        -1.9256977116917966,
        -3.6337431423988704,
        -8.041545781873175,
        -5.306265205888906,
        2.2046591101507005,
        -11.86646925952455,
        5.3746382556457775,
        -7.695150853880861,
        -8.339057809032262,
        1.602156854375778,
        3.5045088820885013,
        1.9015720958952897,
        -1.4228432146868215,
        6.021855083348768,
        -1.6479916964504326,
        -15.484885417624646,
        -1.1406205858792475,
        -15.352549633560194,
        -8.237115361612908,
        -12.327577331184408,
        -1.7101726183899757,
        -10.033767713679595,
        -1.09409084516993,
        -10.45175563953471,
        -1.8219184035991702,
        0.1978451352198931,
        3.5055766956472496,
        0.07860224860287701,
        -12.652374506196836,
        -9.607921291390667,
        -0.5826077050303411,
        -6.766292666348633,
        -5.022010814593401,
        -8.505775158095759,
        -5.5146989630612495,
        -4.753076555540616,
        -2.9314784564477208,
        3.16565011766086,
        4.006961076234461,
        1.162780099770373,
        4.15220952043687,
        -1.658513802994591,
        0.10125781528826394,
        8.81320245218356,
        -0.6262800441650143,
        -0.29334648145281506,
        2.8313107131786808,
        -4.40223393501563,
        -5.024032862388751,
        3.4145436672517775,
        -0.03633945165216801,
        2.141990868997297,
        -8.083998967530107,
        6.061547801031821,
        -7.681806806592611,
        1.11978741502422,
        -3.834473841670828,
        9.34259634407698,
        8.01716532042596,
        -0.3182389317774721,
        -1.2905019828404036,
        0.9678310079435732,
        7.148047934905321,
        -6.879884924743614,
        -5.902061595138065,
        -2.0630133292164743,
        11.651812104657424,
        -1.0796666080929356,
        -4.064123400457035,
        -7.859468523757528,
        0.7148643939956116,
        8.574543820888792,
        -3.691139944777774,
        8.143364569462562,
        -3.192360116895024,
        -5.934025344868559,
        -1.718500665062237,
        6.869916373479043,
        6.731083607305649,
        10.030291030730808,
        -0.7857381191416692,
        8.265676868362021,
        5.80026919854663,
        16.605153490968334,
        6.568093094916662,
        11.626503042851255,
        17.592351804625466,
        3.3605242185807924,
        10.287185530653005,
        8.737079250780283,
        9.972656311681362,
        16.39175705320875,
        6.333765981383735,
        10.429300546078423,
        15.211108000648395,
        13.255094404072594,
        17.111072424779806,
        21.334429569940767,
        5.6545206129205425,
        11.535768786061482,
        11.92624588581755,
        8.839173202005412,
        4.59532554337197,
        -5.9270384652683745,
        -7.091636453705249,
        -6.206263411228441,
        -8.610058375991045,
        -10.06284530086262,
        0.08875255410306693,
        -5.957375638194264,
        -8.399399056731099,
        -1.1296958103229429,
        0.4656151332988614,
        -8.806996535874475,
        0.5246812788518866,
        -0.47278199451975667,
        -18.493497444795167,
        -9.3385681192363,
        -2.22514100778578,
        -8.800533407663892,
        -3.997862287608669,
        -5.126434915399031,
        -1.5145924385012677,
        -3.2659118059466294,
        4.304386413871498,
        10.830484893838438,
        8.012821595336078,
        4.229766498739423,
        -11.830093127403657,
        2.7056909836810306,
        -8.364220523733664,
        4.358243972905129,
        -6.206124708371718,
        6.240708426222355,
        10.649233194230746,
        6.5993122634193355,
        -0.9423753704198674,
        6.207999867695563,
        0.9289380333736403,
        -1.136008624776835,
        -1.9555953386638194,
        -0.9734462767634682,
        2.2486036612783806,
        4.2031014196277425,
        -6.176380645765946,
        0.3732848650800804,
        0.47313275610286354,
        9.574424677066517,
        4.191403769083976,
        2.9275029993102493,
        -1.4854268970087787,
        -3.4871708171805125,
        -0.6912519865229143,
        -2.8504957312277313,
        6.618189960136064,
        -2.0310783511748696,
        -0.10395499949478904,
        3.370739996133743,
        2.624594531883986,
        0.19189304572502408,
        -7.681544075414777,
        -1.7547901605055216,
        0.9781318203096561,
        1.7771538950872525,
        4.6629780745240765,
        -0.033831158415054574,
        -0.18763248683390543,
        -2.313726702278913,
        1.542591302654067,
        8.85321141985817,
        -1.0991356772339742,
        5.293183811190374,
        -9.469520625854301,
        6.437031148258612,
        -1.9477627200859189,
        6.2869144456148405,
        -10.654236709643484,
        2.7824572806423618,
        2.075651110218743,
        -2.3819174148152342,
        -1.020830405748697,
        -4.7225965940746875,
        -0.25606086056424715,
        -2.3564619261781274,
        5.542493210466731,
        -2.6100480801422066,
        -2.9389154548072938,
        5.107576361564696,
        -7.74759541539548,
        -3.7808754010663534,
        -19.255345285167927,
        -2.574285992938215,
        -0.7402724851976785,
        -3.8254445349474366,
        -1.9631249777530897,
        -6.618205456622725,
        -3.133725378292347,
        -2.6769960186650863,
        0.5346425954660958,
        -5.861250832805254,
        -2.150600830814284,
        -6.14671194163509,
        -7.602532083750461,
        -4.856819264816295,
        -1.8322295028786826,
        -7.3768583363223,
        -9.194493185434702,
        -7.561017452305563
      ],
      "random_effects": [
        0.13413303242595281,
        1.6086975171930762,
        -1.784668455935453,
        -5.564364733353317,
        0.24907019016746823,
        2.2564389538072582,
        10.331238055467102,
        -5.1046991850440095,
        2.102747551773279,
        0.5690811120376655,
        0.07903267735839632,
        -4.876706715898545
      ],
      "residual_variance": 25.355429333476824,
      "random_intercept_variance": 18.105139011022015,
      "sigma": 5.03541749346336,
      "icc": 0.41658771849249715,
      "log_likelihood": -775.3741989085033,
      "aic": 1560.7483978170067,
      "df_residual": 247
    },
    "Python": {
      "coefficients": [
        46.65518657849815,
        1.6139078945768133,
        0.24543063307253452
      ],
      "covariance": [
        [
          4.857912716971337,
          0.13899062893221278,
          -0.06974343652791233
        ],
        [
          0.13899062893221278,
          0.025679175884654494,
          -0.005167669933204526
        ],
        [
          -0.06974343652791233,
          -0.005167669933204526,
          0.0017399760316439163
        ]
      ],
      "std_errors": [
        2.2040673122596184,
        0.16024723362559024,
        0.04171301992956056
      ],
      "z_statistics": [
        21.167768479206323,
        10.071361970264208,
        5.8837896054274035
      ],
      "p_values": [
        1.893112943230698e-99,
        7.394689520257244e-24,
        4.009775076054903e-09
      ],
      "conf_int": [
        [
          42.335294026967304,
          50.975079130029
        ],
        [
          1.2998290880484804,
          1.9279867011051461
        ],
        [
          0.16367461632419433,
          0.3271866498208747
        ]
      ],
      "fixed_fitted": [
        84.32339085319674,
        63.70150162370558,
        82.17138618093499,
        63.77060977088685,
        66.85464202612519,
        73.04702321568811,
        62.884961966758254,
        70.8325648841537,
        83.25100477804085,
        75.12013843554634,
        65.51899680957627,
        61.32563710838464,
        82.14022968126272,
        72.61038307304003,
        83.29889891647203,
        74.56676706425617,
        75.32874934221503,
        69.06687243554991,
        66.36720067027315,
        62.27004760452252,
        85.68158785805015,
        60.8391613564949,
        67.45683208826524,
        67.9198761721811,
        64.01542131837445,
        70.49641064113723,
        84.86311186173529,
        68.10307439875906,
        77.47553842474434,
        58.06126902859181,
        84.63762265637955,
        62.864296713629045,
        61.01505673115884,
        70.49717038665028,
        68.16300855317989,
        82.80839956303316,
        79.72771175668083,
        81.46081907032207,
        72.12273585873874,
        80.47964529365281,
        64.38984958029974,
        67.12850379556892,
        74.8026977119627,
        59.4627431419571,
        70.65854578177913,
        57.942265205090706,
        80.91034088971308,
        77.85046925930398,
        78.60236174473238,
        73.33815085373982,
        56.63805780807031,
        78.43184314550079,
        68.80849111816066,
        70.79442790396726,
        67.95784321401894,
        69.54414491625874,
        78.35099169651498,
        79.23088541817614,
        85.08162058657685,
        68.15454963318318,
        60.09611536098415,
        69.47257733130381,
        84.7851726189652,
        82.990767714134,
        77.66809084531725,
        78.74875563923536,
        73.7349184038402,
        75.99015486480643,
        69.69742330409709,
        80.30939775139157,
        68.40237450550828,
        67.0689212909684,
        74.00060770458641,
        83.72929266690423,
        82.4320108147628,
        79.18277515840984,
        77.53569896338621,
        71.76007655583274,
        71.56047845622456,
        65.13534988214121,
        63.55603892330148,
        59.30521989979156,
        77.47679048000585,
        76.8125138027423,
        75.31374218437443,
        66.64979754812688,
        78.42028004493073,
        85.28934648213323,
        66.40468928645417,
        80.33623393532963,
        80.27003286292117,
        65.27545633288474,
        79.78133945180763,
        77.92600913137855,
        73.31299896773352,
        80.94745219885905,
        70.98980680646298,
        63.05921258479681,
        67.85847384116364,
        72.15240365604258,
        81.3708346801194,
        61.02823893113955,
        63.768501982933486,
        67.60716899146738,
        67.29895206483644,
        66.38688492511122,
        79.62306159557198,
        81.36801332963952,
        75.91518789533026,
        74.9276666078234,
        75.83812340078664,
        71.85646852395118,
        82.6301356063314,
        81.22445617994528,
        77.09413994519078,
        76.18163543135233,
        67.10736011678289,
        78.88602534517015,
        78.25050066544041,
        65.9310836260312,
        78.06791639300444,
        86.56870897021832,
        86.8327381200103,
        55.79832313025603,
        78.61673080145347,
        79.40084650913819,
        78.39490690614636,
        79.1684969574246,
        78.60264819603157,
        67.90947578137391,
        77.9698144697395,
        80.134920749132,
        66.88834368786404,
        77.60324294679202,
        70.0732340183261,
        82.54669945397262,
        72.08689199918311,
        66.10290559495377,
        75.06592757493524,
        61.51657042954689,
        63.120479387329084,
        64.08223121348195,
        74.61075411408883,
        61.20882679712982,
        77.25867445652818,
        64.61603846409038,
        82.48963645422397,
        66.97326341114828,
        79.46205837603526,
        73.16384530006604,
        78.52524744599648,
        58.569375637573074,
        71.70639905651367,
        60.15969580991903,
        62.928384866641196,
        65.20599653588317,
        65.0673187204299,
        60.401781994105555,
        76.78749744522118,
        73.1575681191925,
        75.99214100836625,
        77.21053340810418,
        67.70986228743688,
        58.68243491448635,
        69.15859243811383,
        71.7429118058465,
        84.78361358663273,
        63.862515106128214,
        65.36417840494002,
        73.12423350160282,
        67.99909312742741,
        55.90830901525366,
        79.27722052427484,
        76.84375602670747,
        75.71912470872849,
        82.01529157405972,
        75.32576680603523,
        74.02468773656571,
        77.17737537054325,
        73.68800013225722,
        72.06806196679969,
        64.43000862414664,
        58.356595337984174,
        79.75844627656872,
        66.33039633819817,
        67.77789858059114,
        75.59138064537444,
        81.55871513513779,
        56.90386724297286,
        80.54657532291665,
        64.50859623092211,
        81.54449700123072,
        70.13642689734003,
        67.92317081687486,
        73.99025198652855,
        65.3284957310843,
        67.22481003939444,
        67.5170783512,
        73.88695499930294,
        59.49126000262119,
        75.95340546836667,
        64.5301069538573,
        85.74354407613143,
        68.25679016071064,
        65.43186817971691,
        73.26184610470925,
        81.42002192535568,
        82.4278311589567,
        84.60763248767586,
        71.65372670246327,
        56.52240869634112,
        72.40978858081185,
        76.50313567658573,
        57.65681618809941,
        62.60852062538453,
        61.053968851187186,
        65.52876272046969,
        72.51208555421174,
        81.11723670979232,
        67.1695427190852,
        64.68834888999231,
        81.3309174148224,
        62.50983040519233,
        76.7555965943647,
        73.18806086053051,
        68.12146192558632,
        84.577506790487,
        67.51104808031928,
        63.44991545415305,
        81.52242363858304,
        75.07759541533278,
        82.16687540108039,
        72.52234528509081,
        69.80428599298678,
        80.75027248548095,
        76.15144453564236,
        60.807124977153244,
        63.466205455912835,
        66.12272537827701,
        64.77099601841755,
        81.09335740481933,
        58.811250831867405,
        62.119600830049954,
        74.42771194176784,
        69.93653208354675,
        58.31181926421799,
        62.850229502535996,
        73.08385833642078,
        59.88049318514359,
        71.78501745194683
      ],
      "fitted": [
        84.45752388523809,
        63.83563465574693,
        82.30551921297634,
        63.9047428029282,
        66.98877505816654,
        73.18115624772946,
        63.0190949987996,
        70.96669791619505,
        83.3851378100822,
        75.25427146758769,
        65.65312984161761,
        61.45977014042599,
        82.27436271330407,
        72.74451610508137,
        83.43303194851337,
        74.70090009629752,
        75.46288237425638,
        69.20100546759126,
        67.97589818504434,
        63.87874511929372,
        87.29028537282134,
        62.4478588712661,
        69.06552960303644,
        69.5285736869523,
        65.62411883314564,
        72.10510815590843,
        86.47180937650649,
        69.71177191353026,
        79.08423593951554,
        59.66996654336301,
        86.24632017115074,
        64.47299422840024,
        62.623754245930044,
        72.10586790142148,
        69.77170606795109,
        84.41709707780436,
        81.33640927145203,
        83.06951658509327,
        73.73143337350993,
        82.088342808424,
        65.99854709507093,
        68.73720131034011,
        73.01802926043085,
        57.67807469042526,
        68.87387733024728,
        56.15759675355887,
        79.12567243818124,
        76.06580080777213,
        76.81769329320053,
        71.55348240220798,
        54.85338935653847,
        76.64717469396895,
        67.02382266662882,
        69.00975945243542,
        66.1731747624871,
        67.7594764647269,
        76.56632324498314,
        73.66652069397752,
        79.51725586237822,
        62.590184908984554,
        54.531750636785524,
        63.908212607105185,
        79.22080789476658,
        77.42640298993537,
        72.10372612111863,
        73.18439091503673,
        68.17055367964157,
        70.4257901406078,
        64.13305857989846,
        74.74503302719295,
        62.83800978130965,
        61.50455656676978,
        68.43624298038779,
        78.1649279427056,
        76.86764609056418,
        73.61841043421121,
        71.97133423918758,
        66.19571183163411,
        65.99611373202593,
        65.38442007181453,
        63.8051091129748,
        59.55429008946488,
        77.72586066967916,
        77.06158399241562,
        75.56281237404775,
        66.8988677378002,
        78.66935023460405,
        85.53841667180654,
        66.65375947612749,
        80.58530412500295,
        80.51910305259449,
        65.52452652255806,
        80.03040964148094,
        78.17507932105187,
        73.56206915740684,
        81.19652238853237,
        71.2388769961363,
        63.30828277447013,
        68.10754403083696,
        74.40884260663209,
        83.62727363070891,
        63.28467788172906,
        66.024940933523,
        69.86360794205689,
        69.55539101542595,
        68.64332387570073,
        81.8795005461615,
        83.62445228022904,
        78.17162684591977,
        77.18410555841291,
        78.09456235137615,
        74.11290747454069,
        84.8865745569209,
        83.48089513053479,
        79.35057889578029,
        78.43807438194185,
        69.3637990673724,
        81.14246429575967,
        80.50693961602992,
        68.18752257662071,
        80.32435534359395,
        88.82514792080784,
        89.08917707059982,
        58.05476208084554,
        80.87316975204298,
        81.6572854597277,
        88.72614494209466,
        89.4997349933729,
        88.93388623197987,
        78.24071381732222,
        88.3010525056878,
        90.4661587850803,
        77.21958172381235,
        87.93448098274033,
        80.40447205427441,
        92.87793748992092,
        82.41813003513141,
        76.43414363090207,
        85.39716561088355,
        71.8478084654952,
        73.45171742327739,
        74.41346924943025,
        84.94199215003715,
        71.54006483307813,
        87.58991249247649,
        59.51133928804381,
        77.3849372781774,
        61.86856423510171,
        74.3573591999887,
        68.05914612401948,
        73.42054826994992,
        53.4646764615265,
        66.60169988046711,
        55.054996633872456,
        57.82368569059462,
        60.1012973598366,
        59.96261954438332,
        55.29708281805898,
        71.68279826917461,
        68.05286894314594,
        70.88744183231968,
        72.10583423205762,
        62.605163111390304,
        53.57773573843978,
        64.05389326206726,
        66.63821262979994,
        86.8863611336883,
        65.96526265318379,
        67.46692595199559,
        75.22698104865839,
        70.10184067448299,
        58.01105656230923,
        81.37996807133041,
        78.94650357376304,
        77.82187225578406,
        84.11803912111529,
        77.4285143530908,
        76.12743528362128,
        79.28012291759882,
        75.79074767931279,
        74.17080951385526,
        66.53275617120221,
        58.92567644931196,
        80.3275273878965,
        66.89947744952595,
        68.34697969191892,
        76.16046175670222,
        82.12779624646556,
        57.47294835430064,
        81.11565643424443,
        65.07767734224988,
        82.1135781125585,
        70.7055080086678,
        68.49225192820263,
        74.55933309785632,
        65.89757684241208,
        67.79389115072222,
        68.08615946252777,
        74.45603611063072,
        60.06034111394897,
        76.52248657969444,
        65.09918806518507,
        86.3126251874592,
        68.82587127203841,
        66.00094929104469,
        73.83092721603703,
        81.98910303668346,
        82.50686383623531,
        84.68666516495446,
        71.73275937974188,
        56.60144137361972,
        72.48882125809045,
        76.58216835386433,
        57.73584886537802,
        62.68755330266313,
        61.13300152846579,
        65.60779539774829,
        72.59111823149034,
        81.19626938707093,
        67.2485753963638,
        64.76738156727092,
        81.409950092101,
        62.58886308247094,
        76.83462927164331,
        73.26709353780912,
        68.20049460286492,
        84.65653946776561,
        67.59008075759789,
        63.528948131431655,
        81.60145631586164,
        70.20088870842409,
        77.2901686941717,
        67.64563857818212,
        64.92757928607809,
        75.87356577857226,
        71.27473782873366,
        55.93041827024455,
        58.58949874900414,
        61.24601867136832,
        59.89428931150886,
        76.21665069791064,
        53.93454412495871,
        57.24289412314126,
        69.55100523485915,
        65.05982537663806,
        53.435112557309296,
        57.973522795627304,
        68.20715162951208,
        55.0037864782349,
        66.90831074503814
      ],
      "residuals": [
        -6.200523885238084,
        3.406365344253075,
        5.917480787023663,
        4.641257197071809,
        -6.851775058166538,
        -1.034156247729456,
        -2.664094998799605,
        -1.2966979161950434,
        -0.9431378100822059,
        -3.1252714675876803,
        -3.8531298416176156,
        2.247229859574013,
        -5.882362713304076,
        4.333483894918629,
        7.603968051486632,
        -0.24390009629752285,
        0.5721176257436156,
        3.560994532408742,
        1.1981018149556633,
        -4.827745119293716,
        4.792714627178654,
        1.9691411287339022,
        -2.0005296030364406,
        11.274426313047698,
        2.6168811668543555,
        -6.477108155908425,
        -0.23580937650648082,
        0.9732280864697458,
        0.3577640604844561,
        -1.589966543363012,
        2.478679828849252,
        0.3950057715997559,
        -4.986754245930044,
        3.418132098578525,
        -6.5317060679510845,
        -0.2770970778043562,
        1.4565907285479796,
        -1.3545165850932648,
        -8.235433373509935,
        -3.370342808423999,
        3.9494529049290605,
        7.259798689659888,
        -0.14102926043085517,
        -1.8490746904252617,
        -6.256877330247285,
        -3.5215967535588675,
        3.9893275618187545,
        -10.08180080777214,
        7.15930670679947,
        -5.910482402207975,
        -6.554389356538472,
        3.3868253060310565,
        5.289177333371185,
        3.68624054756458,
        0.3618252375129032,
        7.806523535273101,
        0.1366767550168646,
        -9.920520693977515,
        4.423744137621782,
        -9.788184908984555,
        -2.6727506367855227,
        -6.7632126071051815,
        3.854192105233423,
        -4.469402989935375,
        4.470273878881372,
        -4.8873909150367325,
        3.7424463203584253,
        5.7622098593922,
        9.069941420101543,
        5.642966972807059,
        -7.088009781309651,
        -4.04355656676978,
        4.981757019612218,
        -1.201927942705609,
        0.5423539094358176,
        -2.941410434211207,
        0.04966576081241669,
        0.8112881683658912,
        2.6328862679740723,
        2.9165799281854703,
        3.757890887025205,
        0.9137099105351254,
        3.9031393303208404,
        -1.9075839924156242,
        -0.14781237404774572,
        8.564132262199792,
        -0.8753502346040563,
        -0.5424166718065493,
        2.582240523872514,
        -4.651304125002952,
        -5.273103052594493,
        3.1654734774419353,
        -0.28540964148093906,
        1.8929206789481299,
        -8.33306915740684,
        5.812477611467628,
        -7.930876996136298,
        0.870717225529873,
        -4.083544030836961,
        7.0861573933679125,
        5.760726369291092,
        -2.574677881729059,
        -3.546940933522997,
        -1.2886079420568848,
        4.891608984574049,
        -9.136323875700732,
        -8.158500546161491,
        -4.319452280229029,
        9.395373154080218,
        -3.3361055584129105,
        -6.320562351376154,
        -10.115907474540691,
        -1.5415745569209065,
        6.318104869465216,
        -5.947578895780282,
        5.886925618058157,
        -5.4487990673723985,
        -8.190464295759668,
        -3.9749396160299284,
        4.613477423379294,
        4.474644656406056,
        7.773852079192167,
        -3.04217707059982,
        6.009237919154451,
        3.5438302479570183,
        14.348714540272297,
        -3.7631449420946694,
        1.2952650066271048,
        7.261113768020124,
        -6.9707138173222205,
        -0.04405250568780161,
        -1.594158785080296,
        -0.35858172381234965,
        6.060519017259679,
        -3.997472054274411,
        0.09806251007907463,
        4.87986996486859,
        2.9238563690979333,
        6.779834389116459,
        11.003191534504793,
        -4.676717423277381,
        1.2045307505697451,
        1.5950078499628546,
        -1.4920648330781319,
        -5.735912492476487,
        -0.822339288043807,
        -1.9869372781774075,
        -1.101564235101705,
        -3.505359199988689,
        -4.958146124019478,
        5.193451730050086,
        -0.8526764615264995,
        -3.294699880467107,
        3.9750033661275452,
        5.570314309405376,
        -3.7022973598365994,
        5.629380455616676,
        4.63191718194102,
        -13.388798269174615,
        -4.233868943145936,
        2.8795581676803153,
        -3.6958342320576207,
        1.106836888609699,
        -0.02173573843978005,
        3.590106737932743,
        1.838787370200066,
        2.201638866311697,
        8.727737346816212,
        5.910074048004404,
        2.1270189513416113,
        -13.93284067448299,
        0.6029434376907687,
        -10.466968071330413,
        2.2554964262369595,
        -8.308872255784053,
        4.137960878884712,
        8.54648564690919,
        4.496564716378714,
        -3.0451229175988175,
        4.105252320687214,
        -1.1738095138552609,
        -3.238756171202212,
        -2.5246764493119542,
        -1.5425273878964987,
        1.6795225504740472,
        3.6340203080810767,
        -6.745461756702213,
        -0.19579624646556226,
        -0.09594835430063853,
        9.005343565755567,
        3.622322657750118,
        2.3584218874414944,
        -2.05450800866781,
        -4.056251928202627,
        -1.2603330978563179,
        -3.419576842412077,
        6.049108849277786,
        -2.6001594625277704,
        -0.6730361106307186,
        2.8016588860510296,
        2.0555134203055587,
        -0.37718806518508075,
        -8.250625187459207,
        -2.323871272038417,
        0.4090507089553057,
        1.208072783962976,
        4.0938969633165385,
        -0.11286383623530583,
        -0.26666516495446047,
        -2.392759379741875,
        1.4635586263802765,
        8.774178741909552,
        -1.1781683538643364,
        5.214151134621986,
        -9.54855330266313,
        6.357998471534209,
        -2.0267953977482875,
        6.207881768509665,
        -10.733269387070933,
        2.7034246036361935,
        1.996618432729079,
        -2.460950092101001,
        -1.0998630824709394,
        -4.801629271643307,
        -0.3350935378091151,
        -2.435494602864921,
        5.463460532234393,
        -2.6890807575978926,
        -3.017948131431652,
        5.028543684138356,
        -2.87088870842409,
        1.0958313058282982,
        -14.378638578182112,
        2.3024207139219186,
        4.1364342214277485,
        1.0512621712663304,
        2.9135817297554496,
        -1.741498749004144,
        1.7429813286316787,
        2.1997106884911446,
        5.411349302089363,
        -0.9845441249587097,
        2.726105876858739,
        -1.2700052348591413,
        -2.7258253766380562,
        0.019887442690702528,
        3.044477204372697,
        -2.5001516295120894,
        -4.3177864782349005,
        -2.6843107450381325
      ],
      "marginal_residuals": [
        -6.0663908531967365,
        3.5404983762944227,
        6.051613819065011,
        4.775390229113157,
        -6.717642026125191,
        -0.9000232156881083,
        -2.5299619667582576,
        -1.1625648841536957,
        -0.8090047780408582,
        -2.9911384355463326,
        -3.718996809576268,
        2.3813628916153604,
        -5.748229681262728,
        4.467616926959977,
        7.7381010835279795,
        -0.10976706425617522,
        0.7062506577849632,
        3.6951275644500896,
        2.806799329726857,
        -3.2190476045225154,
        6.401412141949848,
        3.5778386435051033,
        -0.3918320882652466,
        12.883123827818892,
        4.225578681625549,
        -4.868410641137231,
        1.3728881382647131,
        2.5819256012409397,
        1.96646157525565,
        0.018730971408189134,
        4.087377343620446,
        2.00370328637095,
        -3.3780567311588428,
        5.026829613349719,
        -4.923008553179891,
        1.3316004369668377,
        3.0652882433191735,
        0.25418092967792916,
        -6.626735858738741,
        -1.7616452936528049,
        5.5581504197002545,
        8.868496204431082,
        -1.9256977119626981,
        -3.6337431419570976,
        -8.041545781779128,
        -5.306265205090703,
        2.2046591102869115,
        -11.866469259303983,
        5.374638255267627,
        -7.695150853739818,
        -8.339057808070308,
        1.6021568544992135,
        3.5045088818393424,
        1.9015720960327371,
        -1.4228432140189398,
        6.021855083741258,
        -1.6479916965149783,
        -15.484885418176141,
        -1.1406205865768442,
        -15.35254963318318,
        -8.237115360984149,
        -12.327577331303807,
        -1.7101726189652027,
        -10.033767714134001,
        -1.094090845317254,
        -10.451755639235358,
        -1.8219184038402005,
        0.1978451351935746,
        3.505576695902917,
        0.07860224860843346,
        -12.652374505508277,
        -9.607921290968406,
        -0.5826077045864082,
        -6.766292666904235,
        -5.022010814762808,
        -8.505775158409833,
        -5.514698963386209,
        -4.753076555832735,
        -2.9314784562245535,
        3.165650117858789,
        4.0069610766985235,
        1.162780100208444,
        4.152209519994159,
        -1.6585138027423056,
        0.10125781562557279,
        8.81320245187311,
        -0.6262800449307377,
        -0.2933464821332308,
        2.8313107135458324,
        -4.402233935329633,
        -5.024032862921175,
        3.414543667115254,
        -0.03633945180762055,
        2.1419908686214484,
        -8.083998967733521,
        6.0615478011409465,
        -7.68180680646298,
        1.1197874152031915,
        -3.8344738411636428,
        9.342596343957425,
        8.017165319880604,
        -0.3182389311395468,
        -1.2905019829334847,
        0.9678310085326274,
        7.148047935163561,
        -6.87988492511122,
        -5.902061595571979,
        -2.0630133296395172,
        11.65181210466973,
        -1.0796666078233983,
        -4.064123400786642,
        -7.859468523951179,
        0.7148643936686057,
        8.574543820054728,
        -3.69113994519077,
        8.14336456864767,
        -3.1923601167828863,
        -5.934025345170156,
        -1.7185006654404162,
        6.869916373968806,
        6.731083606995568,
        10.03029102978168,
        -0.7857381200103077,
        8.265676869743963,
        5.8002691985465304,
        16.60515349086181,
        6.5680930938536335,
        11.626503042575408,
        17.592351803968427,
        3.3605242186260824,
        10.287185530260501,
        8.737079250868007,
        9.972656312135967,
        16.391757053207982,
        6.333765981673892,
        10.429300546027378,
        15.211108000816893,
        13.255094405046236,
        17.111072425064762,
        21.33442957045311,
        5.654520612670922,
        11.535768786518048,
        11.926245885911172,
        8.839173202870185,
        4.595325543471816,
        -5.92703846409038,
        -7.091636454223973,
        -6.206263411148278,
        -8.610058376035255,
        -10.062845300066044,
        0.08875255400351989,
        -5.957375637573072,
        -8.399399056513673,
        -1.1296958099190277,
        0.4656151333588028,
        -8.806996535883172,
        0.5246812795701032,
        -0.4727819941055529,
        -18.49349744522118,
        -9.338568119192502,
        -2.2251410083662506,
        -8.800533408104187,
        -3.997862287436874,
        -5.126434914486353,
        -1.514592438113823,
        -3.2659118058464998,
        4.3043864133672685,
        10.830484893871784,
        8.012821595059975,
        4.229766498397183,
        -11.830093127427418,
        2.70569098474634,
        -8.364220524274842,
        4.358243973292531,
        -6.206124708728481,
        6.240708425940284,
        10.649233193964761,
        6.599312263434285,
        -0.942375370543246,
        6.207999867742785,
        0.9289380332003105,
        -1.1360086241466405,
        -1.955595337984171,
        -0.9734462765687226,
        2.2486036618018233,
        4.203101419408853,
        -6.1763806453744365,
        0.3732848648622138,
        0.47313275702714463,
        9.574424677083343,
        4.191403769077894,
        2.9275029987692704,
        -1.4854268973400337,
        -3.487170816874851,
        -0.6912519865285418,
        -2.850495731084301,
        6.618189960605562,
        -2.0310783511999944,
        -0.1039549993029425,
        3.370739997378813,
        2.624594531633335,
        0.1918930461426953,
        -7.681544076131431,
        -1.754790160710641,
        0.9781318202830818,
        1.777153895290752,
        4.662978074644315,
        -0.0338311589567013,
        -0.18763248767585594,
        -2.3137267024632706,
        1.542591303658881,
        8.853211419188156,
        -1.0991356765857319,
        5.29318381190059,
        -9.469520625384526,
        6.437031148812814,
        -1.947762720469683,
        6.28691444578827,
        -10.654236709792329,
        2.782457280914798,
        2.0756511100076835,
        -2.3819174148223965,
        -1.020830405192335,
        -4.722596594364703,
        -0.2560608605305106,
        -2.3564619255863164,
        5.5424932095129975,
        -2.610048080319288,
        -2.9389154541530473,
        5.10757636141696,
        -7.747595415332782,
        -3.7808754010803938,
        -19.255345285090804,
        -2.5742859929867734,
        -0.7402724854809435,
        -3.8254445356423616,
        -1.9631249771532424,
        -6.618205455912836,
        -3.1337253782770134,
        -2.6769960184175474,
        0.5346425951806708,
        -5.861250831867402,
        -2.150600830049953,
        -6.146711941767833,
        -7.602532083546748,
        -4.8568192642179895,
        -1.832229502535995,
        -7.376858336420781,
        -9.194493185143592,
        -7.5610174519468245
      ],
      "random_effects": [
        0.13413303204134597,
        1.6086975147712008,
        -1.7846684515318372,
        -5.5643647241986285,
        0.24907018967331845,
        2.2564389505895104,
        10.33123803594831,
        -5.10469917604657,
        2.102747547055574,
        0.5690811113277816,
        0.07903267727860461,
        -4.87670670690869
      ],
      "residual_variance": 25.355429364938463,
      "random_intercept_variance": 18.105138533153504,
      "sigma": 5.035417496587394,
      "icc": 0.4165877117760435,
      "log_likelihood": -775.3741989085034,
      "aic": 1560.748397817007,
      "df_residual": 247
    },
    "phit": {
      "coefficients": [
        46.65518657849545,
        1.6139078945767407,
        0.2454306330725874
      ],
      "covariance": [
        [
          4.857912716932582,
          0.13899062893238442,
          -0.06974343652799755
        ],
        [
          0.13899062893238442,
          0.025679175884686854,
          -0.005167669933210969
        ],
        [
          -0.06974343652799755,
          -0.005167669933210969,
          0.0017399760316460522
        ]
      ],
      "std_errors": [
        2.2040673122508263,
        0.16024723362569118,
        0.04171301992958616
      ],
      "z_statistics": [
        21.16776847928954,
        10.07136197025741,
        5.883789605425059
      ],
      "p_values": [
        1.893112939754825e-99,
        7.39468952115571e-24,
        4.0097750762102e-09
      ],
      "conf_int": [
        [
          42.335294026981835,
          50.97507913000907
        ],
        [
          1.29982908804821,
          1.9279867011052714
        ],
        [
          0.16367461632419703,
          0.3271866498209778
        ]
      ],
      "fitted": [
        84.4575238852382,
        63.83563465574633,
        82.30551921297665,
        63.90474280292719,
        66.98877505816593,
        73.1811562477297,
        63.01909499879882,
        70.96669791619493,
        83.38513781008217,
        75.25427146758717,
        65.65312984161622,
        61.45977014042546,
        82.27436271330423,
        72.74451610508143,
        83.4330319485134,
        74.70090009629789,
        75.46288237425605,
        69.2010054675909,
        67.97589818504147,
        63.878745119290585,
        87.29028537281961,
        62.44785887126335,
        69.06552960303395,
        69.52857368694997,
        65.62411883314316,
        72.10510815590575,
        86.47180937650461,
        69.71177191352749,
        79.08423593951309,
        59.66996654335938,
        86.24632017114858,
        64.47299422839698,
        62.62375424592724,
        72.10586790141838,
        69.7717060679486,
        84.41709707780237,
        81.33640927144971,
        83.06951658509146,
        73.73143337350727,
        82.08834280842122,
        65.9985470950676,
        68.7372013103368,
        73.0180292604359,
        57.67807469042952,
        68.87387733025193,
        56.15759675356275,
        79.12567243818584,
        76.06580080777665,
        76.81769329320569,
        71.55348240221257,
        54.85338935654217,
        76.64717469397357,
        67.02382266663382,
        69.00975945244001,
        66.17317476249114,
        67.75947646473124,
        76.56632324498796,
        73.66652069398798,
        79.51725586238884,
        62.590184908994,
        54.5317506367947,
        63.90821260711515,
        79.22080789477705,
        77.42640298994571,
        72.10372612112863,
        73.18439091504627,
        68.17055367965169,
        70.42579014061769,
        64.13305857990804,
        74.74503302720281,
        62.83800978131875,
        61.504556566779165,
        68.43624298039717,
        78.16492794271606,
        76.8676460905742,
        73.6184104342214,
        71.97133423919777,
        66.19571183164427,
        65.99611373203554,
        65.38442007181378,
        63.805109112973774,
        59.55429008946387,
        77.72586066967911,
        77.06158399241481,
        75.56281237404686,
        66.89886773779999,
        78.66935023460435,
        85.53841667180673,
        66.65375947612655,
        80.58530412500276,
        80.51910305259453,
        65.52452652255766,
        80.03040964148057,
        78.17507932105173,
        73.56206915740653,
        81.19652238853172,
        71.23887699613563,
        63.3082827744694,
        68.10754403083588,
        74.40884260662875,
        83.62727363070606,
        63.28467788172492,
        66.02494093351963,
        69.86360794205278,
        69.5553910154222,
        68.64332387569765,
        81.8795005461585,
        83.62445228022602,
        78.17162684591631,
        77.18410555840916,
        78.09456235137304,
        74.11290747453744,
        84.8865745569178,
        83.48089513053222,
        79.35057889577728,
        78.43807438193926,
        69.36379906736882,
        81.14246429575653,
        80.50693961602687,
        68.18752257661671,
        80.32435534359082,
        88.8251479208054,
        89.08917707059729,
        58.05476208084059,
        80.87316975203952,
        81.65728545972435,
        88.72614494207482,
        89.4997349933522,
        88.9338862319596,
        78.24071381730116,
        88.30105250566723,
        90.4661587850592,
        77.21958172379087,
        87.93448098271935,
        80.40447205425309,
        92.8779374899,
        82.41813003511024,
        76.43414363088002,
        85.39716561086226,
        71.84780846547363,
        73.45171742325667,
        74.41346924940876,
        84.94199215001603,
        71.54006483305619,
        87.5899124924554,
        59.51133928805223,
        77.38493727818764,
        61.86856423511132,
        74.35735919999841,
        68.05914612402832,
        73.4205482699597,
        53.46467646153552,
        66.60169988047654,
        55.05499663388171,
        57.82368569060425,
        60.101297359846285,
        59.96261954439224,
        55.29708281806822,
        71.68279826918474,
        68.05286894315556,
        70.88744183233,
        72.10583423206776,
        62.60516311139982,
        53.57773573844849,
        64.05389326207653,
        66.63821262980952,
        86.88636113368378,
        65.96526265317867,
        67.4669259519908,
        75.22698104865367,
        70.10184067447794,
        58.01105656230301,
        81.37996807132592,
        78.94650357375755,
        77.82187225577938,
        84.11803912111053,
        77.42851435308603,
        76.1274352836162,
        79.28012291759389,
        75.79074767930767,
        74.17080951385037,
        66.53275617119645,
        58.92567644931046,
        80.32752738789553,
        66.89947744952462,
        68.34697969191839,
        76.16046175670105,
        82.12779624646505,
        57.472948354298886,
        81.11565643424366,
        65.07767734224915,
        82.11357811255833,
        70.70550800866741,
        68.49225192820154,
        74.55933309785557,
        65.89757684241117,
        67.79389115072097,
        68.08615946252705,
        74.45603611062977,
        60.060341113946876,
        76.52248657969396,
        65.09918806518387,
        86.31262518745923,
        68.82587127203787,
        66.00094929104397,
        73.83092721603606,
        81.98910303668258,
        82.50686383623581,
        84.6866651649553,
        71.73275937974199,
        56.60144137361855,
        72.4888212580911,
        76.58216835386355,
        57.73584886537716,
        62.687553302662536,
        61.13300152846511,
        65.60779539774862,
        72.59111823149007,
        81.19626938707101,
        67.24857539636342,
        64.76738156727104,
        81.40995009210094,
        62.58886308247025,
        76.83462927164355,
        73.267093537809,
        68.20049460286421,
        84.65653946776656,
        67.59008075759799,
        63.52894813143086,
        81.60145631586172,
        70.2008887084337,
        77.29016869418139,
        67.64563857819171,
        64.92757928608782,
        75.87356577858225,
        71.2747378287441,
        55.93041827025358,
        58.58949874901307,
        61.24601867137798,
        59.894289311518264,
        76.21665069792061,
        53.93454412496738,
        57.24289412315012,
        69.55100523486897,
        65.05982537664752,
        53.43511255731832,
        57.97352279563661,
        68.20715162952187,
        55.00378647824426,
        66.90831074504744
      ],
      "residuals": [
        -6.200523885238198,
        3.406365344253672,
        5.917480787023351,
        4.641257197072818,
        -6.851775058165927,
        -1.0341562477296975,
        -2.6640949987988236,
        -1.2966979161949297,
        -0.9431378100821775,
        -3.1252714675871687,
        -3.853129841616223,
        2.2472298595745386,
        -5.882362713304232,
        4.333483894918572,
        7.6039680514866035,
        -0.24390009629789233,
        0.5721176257439424,
        3.5609945324090972,
        1.1981018149585339,
        -4.827745119290583,
        4.792714627180388,
        1.969141128736652,
        -2.0005296030339537,
        11.274426313050029,
        2.6168811668568424,
        -6.4771081559057535,
        -0.23580937650460498,
        0.9732280864725169,
        0.35776406048690035,
        -1.589966543359381,
        2.478679828851412,
        0.3950057716030102,
        -4.986754245927237,
        3.418132098581623,
        -6.531706067948598,
        -0.2770970778023667,
        1.456590728550296,
        -1.35451658509146,
        -8.235433373507277,
        -3.3703428084212135,
        3.9494529049324,
        7.259798689663199,
        -0.14102926043590003,
        -1.8490746904295179,
        -6.256877330251932,
        -3.521596753562747,
        3.98932756181415,
        -10.08180080777666,
        7.159306706794311,
        -5.9104824022125655,
        -6.554389356542174,
        3.386825306026438,
        5.289177333366183,
        3.68624054755999,
        0.3618252375088531,
        7.8065235352687665,
        0.13667675501204712,
        -9.920520693987974,
        4.423744137611166,
        -9.788184908993998,
        -2.672750636794696,
        -6.76321260711515,
        3.8541921052229497,
        -4.469402989945721,
        4.470273878871367,
        -4.887390915046268,
        3.742446320348307,
        5.76220985938231,
        9.069941420091965,
        5.642966972797197,
        -7.088009781318753,
        -4.043556566779166,
        4.9817570196028385,
        -1.2019279427160683,
        0.542353909425799,
        -2.941410434221396,
        0.04966576080222751,
        0.8112881683557305,
        2.632886267964466,
        2.9165799281862235,
        3.757890887026228,
        0.9137099105361344,
        3.903139330320897,
        -1.9075839924148141,
        -0.14781237404685044,
        8.564132262200005,
        -0.8753502346043547,
        -0.542416671806734,
        2.582240523873452,
        -4.651304125002767,
        -5.273103052594536,
        3.165473477442333,
        -0.2854096414805696,
        1.892920678948272,
        -8.333069157406527,
        5.812477611468282,
        -7.9308769961356305,
        0.8707172255306048,
        -4.083544030835881,
        7.086157393371252,
        5.760726369293948,
        -2.5746778817249165,
        -3.546940933519629,
        -1.2886079420527778,
        4.8916089845778,
        -9.136323875697649,
        -8.158500546158493,
        -4.319452280226017,
        9.395373154083686,
        -3.336105558409159,
        -6.320562351373042,
        -10.115907474537437,
        -1.5415745569177943,
        6.318104869467788,
        -5.947578895777269,
        5.886925618060744,
        -5.448799067368817,
        -8.190464295756527,
        -3.974939616026873,
        4.613477423383287,
        4.474644656409183,
        7.773852079194597,
        -3.0421770705972904,
        6.009237919159403,
        3.5438302479604857,
        14.348714540275651,
        -3.763144942074831,
        1.2952650066477958,
        7.2611137680403885,
        -6.97071381730116,
        -0.044052505667224295,
        -1.5941587850592072,
        -0.35858172379086284,
        6.0605190172806545,
        -3.9974720542530946,
        0.098062510099993,
        4.879869964889764,
        2.9238563691199886,
        6.779834389137747,
        11.003191534526366,
        -4.676717423256662,
        1.204530750591232,
        1.595007849983972,
        -1.4920648330561903,
        -5.735912492455398,
        -0.8223392880522269,
        -1.9869372781876393,
        -1.1015642351113186,
        -3.5053591999984093,
        -4.958146124028318,
        5.193451730040309,
        -0.8526764615355162,
        -3.294699880476543,
        3.975003366118294,
        5.570314309395748,
        -3.702297359846284,
        5.629380455607759,
        4.631917181931783,
        -13.388798269184747,
        -4.2338689431555565,
        2.879558167669998,
        -3.6958342320677673,
        1.106836888600185,
        -0.021735738448491304,
        3.5901067379234775,
        1.838787370190488,
        2.201638866316216,
        8.727737346821328,
        5.910074048009193,
        2.1270189513463293,
        -13.932840674477944,
        0.602943437696986,
        -10.466968071325923,
        2.255496426242445,
        -8.308872255779377,
        4.137960878889473,
        8.546485646913965,
        4.496564716383801,
        -3.0451229175938863,
        4.10525232069233,
        -1.1738095138503724,
        -3.2387561711964565,
        -2.524676449310455,
        -1.5425273878955323,
        1.6795225504753688,
        3.6340203080816025,
        -6.745461756701047,
        -0.19579624646505067,
        -0.09594835429888349,
        9.005343565756334,
        3.622322657750857,
        2.358421887441665,
        -2.054508008667412,
        -4.056251928201533,
        -1.2603330978555647,
        -3.4195768424111677,
        6.049108849279037,
        -2.6001594625270457,
        -0.6730361106297664,
        2.8016588860531257,
        2.055513420306042,
        -0.3771880651838728,
        -8.250625187459235,
        -2.323871272037877,
        0.40905070895603046,
        1.2080727839639422,
        4.09389696331742,
        -0.1128638362358032,
        -0.2666651649552989,
        -2.392759379741989,
        1.4635586263814488,
        8.774178741908912,
        -1.1781683538635548,
        5.2141511346228455,
        -9.548553302662533,
        6.357998471534891,
        -2.0267953977486144,
        6.207881768509935,
        -10.733269387071019,
        2.703424603636577,
        1.9966184327289511,
        -2.460950092100944,
        -1.0998630824702502,
        -4.801629271643549,
        -0.3350935378090014,
        -2.4354946028642104,
        5.463460532233441,
        -2.689080757597992,
        -3.017948131430856,
        5.0285436841382705,
        -2.8708887084336965,
        1.0958313058186064,
        -14.378638578191705,
        2.302420713912184,
        4.136434221417758,
        1.0512621712558996,
        2.9135817297464186,
        -1.7414987490130684,
        1.7429813286220153,
        2.199710688481737,
        5.411349302079387,
        -0.9845441249673783,
        2.7261058768498785,
        -1.270005234868961,
        -2.7258253766475207,
        0.019887442681678635,
        3.044477204363389,
        -2.5001516295218806,
        -4.317786478244258,
        -2.6843107450474406
      ],
      "log_likelihood": -775.3741989085033,
      "aic": 1560.7483978170067,
      "df_residual": 247,
      "evaluations": 107,
      "fixed_fitted": [
        84.32339085319728,
        63.70150162370542,
        82.17138618093573,
        63.770609770886274,
        66.854642026125,
        73.04702321568878,
        62.8849619667579,
        70.83256488415401,
        83.25100477804125,
        75.12013843554625,
        65.5189968095753,
        61.32563710838455,
        82.1402296812633,
        72.61038307304051,
        83.29889891647248,
        74.56676706425696,
        75.32874934221513,
        69.06687243554998,
        66.3672006702729,
        62.270047604522006,
        85.68158785805103,
        60.83916135649477,
        67.45683208826537,
        67.91987617218139,
        64.01542131837458,
        70.49641064113717,
        84.86311186173603,
        68.1030743987589,
        77.47553842474451,
        58.0612690285908,
        84.63762265638,
        62.8642967136284,
        61.01505673115866,
        70.4971703866498,
        68.16300855318002,
        82.80839956303379,
        79.72771175668113,
        81.46081907032288,
        72.1227358587387,
        80.47964529365264,
        64.38984958029901,
        67.12850379556822,
        74.802697711963,
        59.462743141956636,
        70.65854578177904,
        57.94226520508987,
        80.91034088971296,
        77.85046925930376,
        78.6023617447328,
        73.33815085373968,
        56.63805780806929,
        78.43184314550068,
        68.80849111816093,
        70.79442790396712,
        67.95784321401825,
        69.54414491625835,
        78.35099169651507,
        79.23088541817677,
        85.08162058657763,
        68.1545496331828,
        60.0961153609835,
        69.47257733130395,
        84.78517261896585,
        82.9907677141345,
        77.66809084531742,
        78.74875563923506,
        73.73491840384048,
        75.99015486480648,
        69.69742330409683,
        80.3093977513916,
        68.40237450550755,
        67.06892129096796,
        74.00060770458596,
        83.72929266690485,
        82.43201081476299,
        79.1827751584102,
        77.53569896338657,
        71.76007655583307,
        71.56047845622433,
        65.13534988214101,
        63.556038923301,
        59.3052198997911,
        77.47679048000634,
        76.81251380274205,
        75.31374218437409,
        66.64979754812722,
        78.42028004493159,
        85.28934648213396,
        66.40468928645379,
        80.33623393533,
        80.27003286292177,
        65.2754563328849,
        79.78133945180781,
        77.92600913137896,
        73.31299896773376,
        80.94745219885895,
        70.98980680646287,
        63.059212584796626,
        67.85847384116312,
        72.15240365604272,
        81.37083468012003,
        61.02823893113889,
        63.76850198293359,
        67.60716899146675,
        67.29895206483617,
        66.38688492511162,
        79.62306159557247,
        81.36801332964,
        75.91518789533028,
        74.92766660782313,
        75.83812340078701,
        71.8564685239514,
        82.63013560633176,
        81.22445617994619,
        77.09413994519124,
        76.18163543135323,
        67.10736011678279,
        78.8860253451705,
        78.25050066544084,
        65.93108362603068,
        78.0679163930048,
        86.56870897021938,
        86.83273812001126,
        55.79832313025456,
        78.61673080145349,
        79.40084650913832,
        78.39490690614753,
        79.16849695742492,
        78.6026481960323,
        67.90947578137387,
        77.96981446973993,
        80.13492074913192,
        66.88834368786357,
        77.60324294679205,
        70.0732340183258,
        82.5466994539727,
        72.08689199918295,
        66.10290559495273,
        75.06592757493496,
        61.51657042954635,
        63.12047938732937,
        64.08223121348148,
        74.61075411408875,
        61.20882679712891,
        77.2586744565281,
        64.61603846408913,
        82.48963645422454,
        66.97326341114822,
        79.46205837603532,
        73.16384530006522,
        78.5252474459966,
        58.56937563757242,
        71.70639905651345,
        60.15969580991861,
        62.92838486664115,
        65.20599653588319,
        65.06731872042914,
        60.40178199410512,
        76.78749744522165,
        73.15756811919246,
        75.9921410083669,
        77.21053340810467,
        67.70986228743672,
        58.68243491448539,
        69.15859243811343,
        71.74291180584642,
        84.7836135866333,
        63.862515106128185,
        65.36417840494032,
        73.12423350160319,
        67.99909312742746,
        55.90830901525253,
        79.27722052427544,
        76.84375602670707,
        75.7191247087289,
        82.01529157406004,
        75.32576680603555,
        74.02468773656571,
        77.1773753705434,
        73.68800013225719,
        72.06806196679989,
        64.43000862414597,
        58.35659533798346,
        79.75844627656852,
        66.33039633819762,
        67.77789858059138,
        75.59138064537404,
        81.55871513513804,
        56.903867242971884,
        80.54657532291665,
        64.50859623092214,
        81.54449700123132,
        70.1364268973404,
        67.92317081687453,
        73.99025198652856,
        65.32849573108416,
        67.22481003939396,
        67.51707835120004,
        73.88695499930276,
        59.491260002619875,
        75.95340546836695,
        64.53010695385686,
        85.74354407613222,
        68.25679016071086,
        65.43186817971696,
        73.26184610470905,
        81.42002192535557,
        82.4278311589573,
        84.6076324876768,
        71.65372670246349,
        56.52240869634005,
        72.40978858081259,
        76.50313567658505,
        57.65681618809866,
        62.60852062538404,
        61.05396885118661,
        65.52876272047011,
        72.51208555421157,
        81.11723670979251,
        67.16954271908492,
        64.68834888999254,
        81.33091741482244,
        62.50983040519175,
        76.75559659436504,
        73.1880608605305,
        68.1214619255857,
        84.57750679048806,
        67.51104808031948,
        63.44991545415236,
        81.52242363858322,
        75.07759541533272,
        82.16687540108042,
        72.52234528509074,
        69.80428599298685,
        80.75027248548128,
        76.15144453564312,
        60.80712497715261,
        63.466205455912096,
        66.12272537827701,
        64.77099601841729,
        81.09335740481964,
        58.81125083186641,
        62.11960083004915,
        74.427711941768,
        69.93653208354655,
        58.31181926421735,
        62.85022950253564,
        73.0838583364209,
        59.88049318514329,
        71.78501745194647
      ],
      "marginal_residuals": [
        -6.0663908531972766,
        3.540498376294586,
        6.051613819064272,
        4.775390229113732,
        -6.717642026125006,
        -0.9000232156887762,
        -2.5299619667579023,
        -1.1625648841540084,
        -0.8090047780412561,
        -2.9911384355462474,
        -3.7189968095753017,
        2.381362891615453,
        -5.748229681263311,
        4.467616926959494,
        7.738101083527525,
        -0.10976706425697103,
        0.7062506577848637,
        3.6951275644500186,
        2.806799329727113,
        -3.219047604522004,
        6.401412141948967,
        3.577838643505231,
        -0.3918320882653745,
        12.883123827818608,
        4.2255786816254215,
        -4.868410641137174,
        1.3728881382639742,
        2.581925601241096,
        1.9664615752554795,
        0.018730971409198105,
        4.087377343619991,
        2.0037032863715964,
        -3.378056731158658,
        5.026829613350202,
        -4.9230085531800185,
        1.3316004369662124,
        3.065288243318875,
        0.25418092967711914,
        -6.626735858738698,
        -1.7616452936526343,
        5.558150419700979,
        8.868496204431779,
        -1.9256977119630108,
        -3.6337431419566357,
        -8.041545781779043,
        -5.306265205089865,
        2.2046591102870394,
        -11.86646925930377,
        5.3746382552672,
        -7.695150853739676,
        -8.339057808069292,
        1.6021568544993272,
        3.5045088818390724,
        1.9015720960328792,
        -1.4228432140182576,
        6.021855083741656,
        -1.6479916965150636,
        -15.484885418176766,
        -1.1406205865776258,
        -15.352549633182797,
        -8.237115360983495,
        -12.32757733130395,
        -1.7101726189658422,
        -10.033767714134513,
        -1.0940908453174245,
        -10.45175563923506,
        -1.8219184038404848,
        0.19784513519351776,
        3.505576695903173,
        0.07860224860840503,
        -12.652374505507552,
        -9.607921290967965,
        -0.5826077045859535,
        -6.76629266690486,
        -5.022010814762993,
        -8.505775158410188,
        -5.514698963386564,
        -4.753076555833061,
        -2.931478456224326,
        3.1656501178589878,
        4.006961076699,
        1.1627801002089058,
        4.1522095199936615,
        -1.6585138027420498,
        0.10125781562591385,
        8.813202451872769,
        -0.6262800449315904,
        -0.29334648213396974,
        2.831310713546216,
        -4.402233935330003,
        -5.024032862921771,
        3.4145436671150975,
        -0.03633945180780529,
        2.1419908686210363,
        -8.083998967733763,
        6.061547801141046,
        -7.681806806462866,
        1.1197874152033762,
        -3.834473841163117,
        9.342596343957283,
        8.017165319879979,
        -0.318238931138886,
        -1.2905019829335913,
        0.9678310085332527,
        7.148047935163831,
        -6.879884925111618,
        -5.902061595572462,
        -2.063013329639986,
        11.651812104669716,
        -1.0796666078231283,
        -4.064123400787011,
        -7.859468523951406,
        0.7148643936682362,
        8.574543820053819,
        -3.691139945191239,
        8.143364568646774,
        -3.192360116782787,
        -5.934025345170497,
        -1.7185006654408426,
        6.869916373969318,
        6.731083606995213,
        10.030291029780628,
        -0.7857381200112599,
        8.265676869745434,
        5.800269198546516,
        16.60515349086168,
        6.568093093852468,
        11.62650304257508,
        17.592351803967688,
        3.360524218626125,
        10.287185530260075,
        8.737079250868078,
        9.972656312136436,
        16.391757053207954,
        6.3337659816741905,
        10.429300546027292,
        15.211108000817049,
        13.255094405047274,
        17.111072425065046,
        21.33442957045365,
        5.6545206126706375,
        11.535768786518517,
        11.926245885911257,
        8.839173202871095,
        4.595325543471901,
        -5.927038464089129,
        -7.091636454224542,
        -6.206263411148221,
        -8.610058376035312,
        -10.06284530006522,
        0.0887525540034062,
        -5.957375637572419,
        -8.399399056513445,
        -1.1296958099186085,
        0.4656151333588454,
        -8.806996535883187,
        0.5246812795708564,
        -0.47278199410511945,
        -18.49349744522165,
        -9.338568119192459,
        -2.2251410083669043,
        -8.80053340810467,
        -3.9978622874367176,
        -5.126434914485394,
        -1.514592438113425,
        -3.2659118058464145,
        4.3043864133667,
        10.830484893871812,
        8.012821595059677,
        4.229766498396813,
        -11.83009312742746,
        2.70569098474747,
        -8.364220524275439,
        4.358243973292929,
        -6.206124708728893,
        6.240708425939957,
        10.649233193964449,
        6.599312263434285,
        -0.9423753705434024,
        6.207999867742814,
        0.9289380332001116,
        -1.1360086241459726,
        -1.9555953379834534,
        -0.9734462765685237,
        2.2486036618023775,
        4.203101419408611,
        -6.176380645374039,
        0.373284864861958,
        0.4731327570281181,
        9.574424677083343,
        4.191403769077866,
        2.9275029987686736,
        -1.4854268973404032,
        -3.4871708168745243,
        -0.691251986528556,
        -2.850495731084159,
        6.6181899606060455,
        -2.031078351200037,
        -0.10395499930275776,
        3.3707399973801273,
        2.6245945316330506,
        0.19189304614313585,
        -7.6815440761322265,
        -1.7547901607108685,
        0.9781318202830391,
        1.777153895290951,
        4.662978074644428,
        -0.03383115895729816,
        -0.18763248767679386,
        -2.3137267024634838,
        1.5425913036599468,
        8.853211419187417,
        -1.0991356765850497,
        5.2931838119013435,
        -9.469520625384035,
        6.437031148813389,
        -1.9477627204701093,
        6.28691444578844,
        -10.654236709792514,
        2.7824572809150823,
        2.075651110007456,
        -2.381917414822439,
        -1.0208304051917523,
        -4.722596594365044,
        -0.25606086053049637,
        -2.3564619255857053,
        5.542493209511946,
        -2.610048080319487,
        -2.938915454152358,
        5.1075763614167755,
        -7.747595415332725,
        -3.780875401080422,
        -19.255345285090733,
        -2.5742859929868445,
        -0.7402724854812703,
        -3.825444535643129,
        -1.96312497715261,
        -6.618205455912097,
        -3.1337253782770134,
        -2.6769960184172916,
        0.5346425951803582,
        -5.861250831866407,
        -2.15060083004915,
        -6.14671194176799,
        -7.602532083546549,
        -4.85681926421735,
        -1.8322295025356397,
        -7.376858336420909,
        -9.194493185143287,
        -7.561017451946469
      ],
      "random_effects": [
        0.13413303204091775,
        1.6086975147685796,
        -1.7846684515271147,
        -5.564364724188796,
        0.24907018967277064,
        2.2564389505860314,
        10.331238035927292,
        -5.104699176036904,
        2.102747547050482,
        0.5690811113270031,
        0.07903267727850147,
        -4.87670670689903
      ],
      "group_sizes": [
        18,
        24,
        15,
        22,
        20,
        27,
        19,
        21,
        16,
        25,
        23,
        20
      ],
      "n_groups": 12,
      "group_labels": [
        107,
        114,
        121,
        128,
        135,
        142,
        149,
        156,
        163,
        170,
        177,
        184
      ],
      "residual_variance": 25.355429364972327,
      "random_intercept_variance": 18.10513853263928,
      "sigma": 5.035417496590757,
      "icc": 0.416587711768816,
      "boundary": false,
      "method": "ML",
      "converged": true,
      "n_input": 250,
      "n_observations": 250,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119,
        120,
        121,
        122,
        123,
        124,
        125,
        126,
        127,
        128,
        129,
        130,
        131,
        132,
        133,
        134,
        135,
        136,
        137,
        138,
        139,
        140,
        141,
        142,
        143,
        144,
        145,
        146,
        147,
        148,
        149,
        150,
        151,
        152,
        153,
        154,
        155,
        156,
        157,
        158,
        159,
        160,
        161,
        162,
        163,
        164,
        165,
        166,
        167,
        168,
        169,
        170,
        171,
        172,
        173,
        174,
        175,
        176,
        177,
        178,
        179,
        180,
        181,
        182,
        183,
        184,
        185,
        186,
        187,
        188,
        189,
        190,
        191,
        192,
        193,
        194,
        195,
        196,
        197,
        198,
        199,
        200,
        201,
        202,
        203,
        204,
        205,
        206,
        207,
        208,
        209,
        210,
        211,
        212,
        213,
        214,
        215,
        216,
        217,
        218,
        219,
        220,
        221,
        222,
        223,
        224,
        225,
        226,
        227,
        228,
        229,
        230,
        231,
        232,
        233,
        234,
        235,
        236,
        237,
        238,
        239,
        240,
        241,
        242,
        243,
        244,
        245,
        246,
        247,
        248,
        249
      ],
      "dropped_rows": []
    },
    "python_diagnostics": {
      "backend": "statsmodels MixedLM (ML)",
      "warnings": [],
      "covariance_convention": "plug-in GLS, matching lme4"
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "Python": 2.527016818021366e-09,
        "phit": 2.5297168804172543e-09
      },
      "covariance": {
        "Python": 3.601606834990889e-08,
        "phit": 3.605482312707409e-08
      },
      "std_errors": {
        "Python": 8.170364829140908e-09,
        "phit": 8.17915690731752e-09
      },
      "z_statistics": {
        "Python": 7.73213102434056e-08,
        "phit": 7.740452545590415e-08
      },
      "p_values": {
        "Python": 5.275152202500638e-17,
        "phit": 5.290681856756831e-17
      },
      "conf_int": {
        "Python": 1.8540639246111823e-08,
        "phit": 1.8560569969849894e-08
      },
      "fixed_fitted": {
        "Python": 1.3819416722071765e-09,
        "phit": 1.3834124956701999e-09
      },
      "fitted": {
        "Python": 2.04924361923986e-08,
        "phit": 2.0514491438916593e-08
      },
      "residuals": {
        "Python": 2.04924361923986e-08,
        "phit": 2.0514491438916593e-08
      },
      "marginal_residuals": {
        "Python": 1.3819416722071765e-09,
        "phit": 1.3834124956701999e-09
      },
      "random_effects": {
        "Python": 1.951879191608441e-08,
        "phit": 1.9539809770208194e-08
      },
      "residual_variance": {
        "Python": 3.146163862766116e-08,
        "phit": 3.1495503094447486e-08
      },
      "random_intercept_variance": {
        "Python": 4.778685109840808e-07,
        "phit": 4.78382734314664e-07
      },
      "sigma": {
        "Python": 3.1240343645322355e-09,
        "phit": 3.12739700802922e-09
      },
      "icc": {
        "Python": 6.716453671007372e-09,
        "phit": 6.7236811673865304e-09
      },
      "log_likelihood": {
        "Python": 1.1368683772161603e-13,
        "phit": 0.0
      },
      "aic": {
        "Python": 2.2737367544323206e-13,
        "phit": 0.0
      },
      "df_residual": {
        "Python": 0.0,
        "phit": 0.0
      }
    },
    "tolerance": {
      "absolute": 1e-07,
      "relative": 1e-06
    },
    "extension_sha256": "2105dd47a15f21b0da6ae81a23461ef385285517e1af0519a0bb22238bc3ffc6"
  },
  {
    "name": "simple",
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "lme4": "2.0.6",
      "statsmodels": "0.15.0",
      "PHP": "8.5.10",
      "Python": "3.14.7"
    },
    "R": {
      "coefficients": [
        56.4908335948838,
        2.343119429919076
      ],
      "covariance": [
        [
          2.2160141762991237,
          -0.07784745704875635
        ],
        [
          -0.07784745704875635,
          0.011802243015723076
        ]
      ],
      "std_errors": [
        1.4886282868127703,
        0.10863812873813261
      ],
      "z_statistics": [
        37.948246782165874,
        21.568112937282468
      ],
      "p_values": [
        4.124230706e-315,
        3.5800299271149842e-103
      ],
      "conf_int": [
        [
          53.573175766363214,
          59.40849142340439
        ],
        [
          2.1301926102445106,
          2.5560462495936416
        ]
      ],
      "fixed_fitted": [
        83.6241565933467,
        62.81725605566531,
        79.96889028267294,
        65.18380667988357,
        66.75369669792936,
        69.40142165373791,
        62.91098083286207,
        68.69848582476219,
        83.17896390166209,
        76.10274322330646,
        69.47171523663549,
        59.56032004807779,
        80.835844471743,
        69.89347673402092,
        82.8743583757726,
        70.54955017439826,
        75.32951381143317,
        67.94868760718808,
        66.56624714353583,
        63.05156799865721,
        83.43670703895317,
        59.18542093929074,
        65.6289993715682,
        65.3712562342771,
        61.55197156350901,
        70.40896300860311,
        83.1321015130637,
        68.04241238438485,
        77.5554772698563,
        60.77874215163571,
        84.56140436531433,
        64.48087085090785,
        59.70090721387294,
        72.82237602141976,
        66.47252236633906,
        81.3747619406244,
        79.45340400809074,
        78.72703698481584,
        72.30688974683757,
        82.96808315296937,
        66.82399028082693,
        69.87004553972173,
        73.52531185039548,
        59.39630168798346,
        70.73699972879179,
        59.70090721387294,
        83.27268867885884,
        80.10947744846808,
        77.43832129836034,
        74.22824767937121,
        59.11512735639317,
        80.22663341996405,
        66.47252236633906,
        71.15876122617722,
        70.92444928318531,
        71.18219242047641,
        79.00821131640612,
        77.15714696677006,
        83.29611987315803,
        69.4248528480371,
        61.27079723191872,
        68.04241238438485,
        83.67101898194508,
        82.24171612969445,
        77.69606443565144,
        81.65593627221467,
        72.42404571833352,
        76.40734874919595,
        70.54955017439826,
        81.77309224371064,
        71.58052272356265,
        68.39388029887272,
        76.82911024658138,
        82.52289046128473,
        83.27268867885884,
        78.51615623612312,
        76.47764233209352,
        69.75288956822577,
        72.58806407842786,
        64.73861398819895,
        64.43400846230948,
        59.18542093929074,
        75.70441292022022,
        79.0550737050045,
        77.76635801854901,
        63.52019188464103,
        74.90775231404774,
        83.64758778764589,
        67.26918297251156,
        79.89859669977537,
        78.51615623612312,
        62.91098083286207,
        80.17977103136566,
        76.64166069218786,
        72.14287138674322,
        83.1555327073629,
        71.34621078057074,
        62.13775142098878,
        69.84661434542254,
        71.25248600337399,
        79.75800953398023,
        62.442356946878256,
        61.36452200911548,
        70.03406389981606,
        67.69094446989699,
        62.86411844426369,
        78.3287066817296,
        80.48437655725515,
        76.5479359149911,
        76.89940382947896,
        74.41569723376473,
        70.4558253972015,
        82.56975284988312,
        77.86008279574577,
        75.42323858862994,
        71.93199063805051,
        66.58967833783502,
        78.23498190453283,
        77.0165598009749,
        67.43320133260589,
        77.20400935536844,
        83.57729420474833,
        84.37395481092081,
        60.61472379154138,
        79.71114714538184,
        80.01575267127133,
        73.10355035301005,
        78.72703698481584,
        75.7747065031178,
        67.1520270010156,
        76.59479830358947,
        82.05426657530093,
        68.37044910457352,
        78.49272504182393,
        71.2056236147756,
        84.1162116736297,
        72.89266960431733,
        70.52611898009907,
        77.15714696677006,
        62.278338586783924,
        59.65404482527455,
        65.01978831978924,
        75.47010097722831,
        64.01224696492403,
        78.68017459621746,
        69.96377031691848,
        81.25760596912843,
        66.23821042334716,
        80.46094536295595,
        77.93037637864334,
        79.00821131640612,
        59.39630168798346,
        72.728651244223,
        60.005512739762416,
        61.27079723191872,
        63.590485467538606,
        67.76123805279455,
        60.35698065425028,
        74.97804589694532,
        73.43158707319873,
        73.10355035301005,
        75.39980739433075,
        67.6675132755978,
        61.27079723191872,
        70.6901373401934,
        72.07257780384566,
        84.09278047933051,
        62.23147619818554,
        62.184613809587155,
        71.08846764327964,
        66.84742147512613,
        58.85738421910207,
        77.274302938266,
        79.89859669977537,
        74.11109170787526,
        82.1011289638993,
        74.18138529077282,
        74.29854126226878,
        77.25087174396681,
        74.08766051357607,
        70.83072450598854,
        66.47252236633906,
        59.49002646518022,
        82.24171612969445,
        68.11270596728242,
        65.41811862287548,
        78.42243145892635,
        81.93711060380497,
        59.20885213358993,
        82.12456015819849,
        62.77039366706693,
        79.99232147697214,
        67.57378849840103,
        68.72191701906138,
        74.13452290217445,
        64.6448892110022,
        68.86250418485652,
        66.26164161764635,
        75.18892664563803,
        64.22312771361675,
        75.02490828554369,
        65.32439384567871,
        83.97562450783457,
        66.07419206325282,
        63.75450382763294,
        74.5094220109615,
        83.78817495344104,
        81.04672522043572,
        81.86681702090739,
        70.26837584280797,
        59.23228332788912,
        68.27672432737675,
        81.04672522043572,
        58.83395302480288,
        63.332742330247505,
        61.97373306089444,
        61.73942111790253,
        73.43158707319873,
        81.81995463230902,
        67.62065088699941,
        61.76285231220172,
        82.92122076437099,
        63.731072633333746,
        75.7512753088186,
        73.40815587889954,
        70.66670614589421,
        81.16388119193168,
        65.3478250399779,
        65.44154981717467,
        82.31200971259202,
        75.84500008601538,
        83.8818997306378,
        72.86923841001814,
        68.86250418485652,
        80.5781013344519,
        72.61149527272704,
        61.950301866595254,
        65.79301773166253,
        64.83233876539572,
        64.59802682240381,
        80.97643163753814,
        61.5754027578082,
        64.50430204520704,
        73.90021095918254,
        70.52611898009907,
        58.951108996298835,
        62.86411844426369,
        72.4943393012311,
        58.99797138489721,
        73.66589901619064
      ],
      "fitted": [
        84.51083678420989,
        63.70393624652849,
        80.85557047353613,
        66.07048687074676,
        67.64037688879255,
        70.2881018446011,
        63.797661023725254,
        69.58516601562538,
        84.06564409252528,
        76.98942341416966,
        70.35839542749868,
        60.44700023894097,
        81.72252466260619,
        70.78015692488411,
        83.76103856663579,
        71.43623036526145,
        76.21619400229636,
        68.83536779805127,
        68.34624483254666,
        64.83156568766805,
        85.216704727964,
        60.96541862830157,
        67.40899706057903,
        67.15125392328792,
        63.33196925251983,
        72.18896069761394,
        84.91209920207453,
        69.82241007339567,
        79.33547495886712,
        62.55873984064654,
        86.34140205432516,
        66.26086853991868,
        61.480904902883765,
        74.60237371043058,
        68.25252005534989,
        83.15475962963521,
        81.23340169710158,
        80.50703467382667,
        74.0868874358484,
        84.7480808419802,
        68.60398796983776,
        71.65004322873256,
        71.0034962274268,
        56.87448606501477,
        68.2151841058231,
        57.17909159090425,
        80.75087305589015,
        77.5876618254994,
        74.91650567539165,
        71.70643205640252,
        56.59331173342448,
        77.70481779699536,
        63.950706743370375,
        68.63694560320853,
        68.40263366021662,
        68.66037679750772,
        76.48639569343743,
        71.45589856171978,
        77.59487146810775,
        63.72360444298682,
        55.569548826868434,
        62.34116397933456,
        77.9697705768948,
        76.54046772464417,
        71.99481603060116,
        75.95468786716441,
        66.72279731328324,
        70.70610034414567,
        64.84830176934798,
        76.07184383866036,
        65.87927431851237,
        62.69263189382243,
        71.1278618415311,
        76.82164205623445,
        77.57144027380856,
        72.81490783107284,
        70.77639392704324,
        64.05164116317549,
        66.88681567337758,
        65.31684608190213,
        65.01224055601264,
        59.76365303299392,
        76.2826450139234,
        79.63330579870768,
        78.34459011225219,
        64.09842397834421,
        75.48598440775092,
        84.22581988134907,
        67.84741506621474,
        80.47682879347855,
        79.0943883298263,
        63.48921292656525,
        80.75800312506884,
        77.21989278589103,
        72.7211034804464,
        83.73376480106607,
        71.92444287427392,
        62.715983514691956,
        70.42484643912572,
        74.08235940924979,
        82.58788293985604,
        65.27223035275406,
        64.19439541499129,
        72.86393730569188,
        70.5208178757728,
        65.6939918501395,
        81.1585800876054,
        83.31424996313096,
        79.37780932086692,
        79.72927723535477,
        77.24557063964055,
        73.28569880307731,
        85.39962625575893,
        80.68995620162158,
        78.25311199450576,
        74.76186404392632,
        69.41955174371084,
        81.06485531040865,
        79.84643320685072,
        70.2630747384817,
        80.03388276124426,
        86.40716761062414,
        87.20382821679662,
        63.44459719741719,
        82.54102055125766,
        82.84562607714714,
        83.03428472717603,
        88.65777135898182,
        85.70544087728378,
        77.08276137518158,
        86.52553267775545,
        91.9850009494669,
        78.3011834787395,
        88.42345941598991,
        81.13635798894158,
        94.04694604779569,
        82.82340397848331,
        80.45685335426505,
        87.08788134093604,
        72.20907296094991,
        69.58477919944053,
        74.95052269395522,
        85.4008353513943,
        73.94298133909001,
        88.61090897038343,
        64.49331759768341,
        75.78715324989336,
        60.767757704112086,
        74.99049264372088,
        72.45992365940828,
        73.53775859717105,
        53.9258489687484,
        67.25819852498793,
        54.535060020527354,
        55.80034451268365,
        58.12003274830353,
        62.290785333559484,
        54.88652793501521,
        69.50759317771023,
        67.96113435396366,
        67.63309763377498,
        69.92935467509568,
        62.19706055636273,
        55.80034451268365,
        65.21968462095833,
        66.60212508461059,
        86.51171603953682,
        64.65041175839185,
        64.60354936979347,
        73.50740320348595,
        69.26635703533242,
        61.27631977930838,
        79.69323849847231,
        82.31753225998168,
        76.53002726808157,
        84.5200645241056,
        76.60032085097913,
        76.71747682247509,
        79.66980730417312,
        76.50659607378238,
        73.24966006619485,
        68.89145792654537,
        59.7243829228479,
        82.47607258736213,
        68.3470624249501,
        65.65247508054316,
        78.65678791659403,
        82.17146706147264,
        59.44320859125761,
        82.35891661586616,
        63.004750124734606,
        80.22667793463981,
        67.8081449560687,
        68.95627347672905,
        74.36887935984211,
        64.87924566866985,
        69.0968606425242,
        66.49599807531402,
        75.4232831033057,
        64.45748417128442,
        75.25926474321136,
        65.55875030334639,
        84.20998096550224,
        66.3085485209205,
        63.98886028530062,
        74.74377846862917,
        84.02253141110872,
        81.22445480362087,
        82.04454660409256,
        70.44610542599312,
        59.41001291107427,
        68.45445391056191,
        81.22445480362087,
        59.01168260798803,
        63.51047191343265,
        62.15146264407959,
        61.917150701087685,
        73.60931665638388,
        81.99768421549417,
        67.79838047018457,
        61.94058189538687,
        83.09895034755614,
        63.90880221651889,
        75.92900489200376,
        73.58588546208469,
        70.84443572907936,
        81.34161077511682,
        65.52555462316306,
        65.61927940035983,
        82.48973929577717,
        70.7019774785867,
        78.73887712320912,
        67.72621580258946,
        63.71948157742786,
        75.43507872702322,
        67.46847266529836,
        56.80727925916658,
        60.649995124233854,
        59.68931615796704,
        59.45500421497513,
        75.83340903010946,
        56.43238015037952,
        59.361279437778364,
        68.75718835175387,
        65.3830963726704,
        53.80808638887016,
        57.72109583683501,
        67.35131669380242,
        53.854948777468536,
        68.52287640876196
      ],
      "residuals": [
        -6.253836784209881,
        3.538063753471512,
        7.367429526463866,
        2.475513129253244,
        -7.503376888792545,
        1.8588981553989044,
        -3.4426610237252575,
        0.08483398437462597,
        -1.6236440925252822,
        -4.860423414169659,
        -8.55839542749868,
        3.259999761059028,
        -5.330524662606194,
        6.2978430751158925,
        7.275961433364216,
        3.020769634738542,
        -0.1811940022963654,
        3.9266322019487347,
        0.827755167453347,
        -5.7805656876680445,
        6.866295272035998,
        3.451581371698431,
        -0.3439970605790279,
        13.651746076712072,
        4.909030747480166,
        -6.560960697613936,
        1.323900797925475,
        0.8625899266043291,
        0.10652504113286909,
        -4.47873984064654,
        2.383597945674836,
        -1.3928685399186804,
        -3.8439049028837644,
        0.9216262895694172,
        -5.0125200553498885,
        0.9852403703647923,
        1.5595983028984222,
        1.207965326173337,
        -8.590887435848401,
        -6.030080841980194,
        1.344012030162233,
        4.346956771267443,
        1.8735037725732013,
        -1.0454860650147708,
        -5.598184105823101,
        -4.543091590904247,
        2.3641269441098416,
        -11.603661825499401,
        9.060494324608356,
        -6.063432056402519,
        -8.294311733424479,
        2.329182203004649,
        8.362293256629627,
        4.059054396791467,
        -1.867633660216626,
        6.905623202492279,
        0.2166043065625729,
        -7.7098985617197755,
        6.346128531892248,
        -10.921604442986819,
        -3.7105488268684326,
        -5.196163979334557,
        5.1052294231052,
        -3.58346772464418,
        4.579183969398841,
        -7.657687867164412,
        5.190202686716759,
        5.481899655854335,
        8.35469823065202,
        4.316156161339649,
        -10.129274318512373,
        -5.231631893822431,
        2.2901381584689062,
        0.14135794376554145,
        -0.16144027380856585,
        -2.1379078310728374,
        1.2446060729567563,
        2.955358836824516,
        1.7421843266224215,
        2.9841539180978742,
        2.55075944398736,
        0.7043469670060816,
        5.346354986076605,
        -4.479305798707685,
        -2.9295901122521855,
        11.364576021655779,
        2.3080155922490775,
        0.7701801186509272,
        1.3885849337852676,
        -4.542828793478549,
        -3.8483883298263066,
        5.200787073434746,
        -1.0130031250688347,
        2.848107214108964,
        -7.492103480446403,
        3.2752351989339274,
        -8.616442874273922,
        1.4630164853080458,
        -6.400846439125715,
        7.412640590750215,
        6.800117060143961,
        -4.562230352754064,
        -1.7163954149912897,
        -4.288937305691874,
        3.9261821242271964,
        -6.186991850139499,
        -7.437580087605397,
        -4.009249963130955,
        8.189190679133077,
        -5.881277235354773,
        -5.471570639640547,
        -9.28869880307731,
        -2.054626255758933,
        9.109043798378423,
        -4.8501119945057525,
        9.56313595607368,
        -5.5045517437108415,
        -8.112855310408648,
        -3.3144332068507225,
        2.5379252615182963,
        4.765117238755749,
        10.191832389375861,
        -1.156828216796626,
        0.6194028025828047,
        1.875979448742342,
        13.160373922852855,
        1.9287152728239647,
        2.137228641018183,
        10.489559122716216,
        -5.81276137518158,
        1.731467322244555,
        -3.113000949466894,
        -1.440183478739499,
        5.571540584010094,
        -4.729357988941587,
        -1.0709460477956867,
        4.474596021516689,
        -1.0988533542650458,
        5.0891186590639705,
        10.641927039050088,
        -0.809779199440527,
        0.6674773060447734,
        1.1361646486056998,
        -3.894981339090009,
        -6.756908970383435,
        -5.804317597683415,
        -0.3891532498933685,
        -0.0007577041120825356,
        -4.13849264372088,
        -9.358923659408276,
        5.0762414028289555,
        -1.3138489687483954,
        -3.9511985249879302,
        4.4949399794726475,
        7.593655487316347,
        -1.7210327483035286,
        3.301214666440515,
        5.042472064984793,
        -11.213593177710237,
        -4.142134353963655,
        6.133902366225016,
        -1.5193546750956841,
        1.5149394436372745,
        -2.2443445126836536,
        2.4243153790416727,
        1.8748749153894124,
        2.576283960463172,
        10.042588241608144,
        8.773450630206526,
        3.8465967965140493,
        -13.097357035332422,
        -2.6623197793083833,
        -8.780238498472315,
        -1.115532259981677,
        -7.017027268081563,
        3.7359354758943937,
        9.374679149020864,
        3.906523177524903,
        -3.4348073041731197,
        3.389403926217625,
        -0.25266006619484926,
        -5.597457926545374,
        -3.323382922847898,
        -3.691072587362129,
        0.23193757504989776,
        6.328524919456839,
        -9.24178791659402,
        -0.23946706147263797,
        -2.066208591257606,
        7.762083384133831,
        5.695249875265397,
        4.245322065360185,
        0.8428550439312943,
        -4.520273476729045,
        -1.0698793598421048,
        -2.4012456686698513,
        4.746139357475798,
        -1.0099980753140159,
        -1.6402831033057055,
        -1.5954841712844186,
        3.318735256788642,
        -0.8367503033463919,
        -6.147980965502242,
        0.19345147907949922,
        2.421139714699379,
        0.29522153137082796,
        2.0604685888912826,
        1.1695451963791328,
        2.375453395907442,
        -1.1061054259931211,
        -1.3450129110742708,
        12.808546089438096,
        -5.820454803620876,
        3.9383173920119745,
        -10.37147191343265,
        5.339537355920413,
        1.663849298912318,
        5.1896833436161245,
        -11.534684215494181,
        2.1536195298154297,
        4.8234181046131255,
        -4.149950347556143,
        -2.419802216518896,
        -3.8960048920037593,
        -0.6538854620846877,
        -5.079435729079364,
        8.778389224883185,
        -0.6245546231630641,
        -5.108279400359827,
        4.140260704222825,
        -3.3719774785867003,
        -0.3528771232091259,
        -14.459215802589462,
        3.5105184225721473,
        4.5749212729767805,
        4.857527334701629,
        2.036720740833424,
        -3.801995124233855,
        3.2996838420329553,
        2.6389957850248678,
        5.794590969890535,
        -3.4823801503795195,
        0.6077205622216368,
        -0.4761883517538621,
        -3.049096372670391,
        -0.3530863888701603,
        3.2969041631649887,
        -1.6443166938024234,
        -3.168948777468536,
        -4.298876408761956
      ],
      "marginal_residuals": [
        -5.367156593346692,
        4.424743944334693,
        8.254109717327054,
        3.3621933201164325,
        -6.616696697929356,
        2.745578346262093,
        -2.555980832862076,
        0.9715141752378145,
        -0.7369639016620937,
        -3.9737432233064567,
        -7.671715236635492,
        4.146679951922209,
        -4.443844471743006,
        7.184523265979081,
        8.162641624227405,
        3.9074498256017307,
        0.7054861885668231,
        4.813312392811923,
        2.607752856464174,
        -4.0005679986572105,
        8.646292961046825,
        5.231579060709258,
        1.436000628431799,
        15.4317437657229,
        6.689028436490993,
        -4.780963008603109,
        3.103898486936302,
        2.642587615615156,
        1.886522730143696,
        -2.698742151635713,
        4.163595634685663,
        0.38712914909214646,
        -2.0639072138729375,
        2.701623978580244,
        -3.2325223663390616,
        2.765238059375605,
        3.3395959919092633,
        2.987963015184164,
        -6.810889746837574,
        -4.250083152969367,
        3.12400971917306,
        6.12695446027827,
        -0.648311850395487,
        -3.567301687983459,
        -8.11999972879179,
        -7.064907213872935,
        -0.15768867885884674,
        -14.12547744846809,
        6.538678701639668,
        -8.585247679371207,
        -10.816127356393167,
        -0.19263341996403938,
        5.840477633660939,
        1.5372387738227786,
        -4.389449283185314,
        4.383807579523591,
        -2.3052113164061154,
        -13.411146966770055,
        0.6448801268419686,
        -16.622852848037105,
        -9.411797231918719,
        -10.897412384384843,
        -0.596018981945079,
        -9.28471612969446,
        -1.1220644356514384,
        -13.358936272214677,
        -0.51104571833352,
        -0.2193487491959445,
        2.65344982560174,
        -1.3850922437106306,
        -15.830522723562652,
        -10.932880298872718,
        -3.411110246581373,
        -5.559890461284738,
        -5.862688678858845,
        -7.839156236123117,
        -4.456642332093523,
        -2.7458895682257634,
        -3.9590640784278577,
        3.5623860118010526,
        3.128991537690524,
        1.28257906070926,
        5.9245870797797835,
        -3.9010737050045066,
        -2.351358018549007,
        11.942808115358964,
        2.886247685952256,
        1.3484122123541056,
        1.966817027488446,
        -3.9645966997753703,
        -3.2701562361231282,
        5.779019167137925,
        -0.4347710313656563,
        3.4263393078121425,
        -6.913871386743224,
        3.853467292637106,
        -8.038210780570743,
        2.0412485790112243,
        -5.8226143454225365,
        10.242513996626016,
        9.629990466019777,
        -1.7323569468782551,
        1.113477990884519,
        -1.4590638998160586,
        6.756055530103012,
        -3.3571184442636905,
        -4.607706681729596,
        -1.1793765572551393,
        11.019064085008893,
        -3.051403829478957,
        -2.641697233764731,
        -6.458825397201494,
        0.7752471501168827,
        11.938917204254238,
        -2.0202385886299368,
        12.393009361949495,
        -2.674678337835026,
        -5.282981904532832,
        -0.4845598009749068,
        5.367798667394112,
        7.594990644631565,
        13.021705795251677,
        1.6730451890791898,
        3.4492762084586133,
        4.705852854618158,
        15.990247328728671,
        11.859449646989944,
        12.067963015184162,
        20.420293496882195,
        4.117972998984399,
        11.662201696410534,
        6.817733424699071,
        8.49055089542648,
        15.502274958176073,
        5.201376385224393,
        8.859788326370293,
        14.405330395682668,
        8.831881019900933,
        15.01985303322995,
        20.572661413216075,
        9.120955174725452,
        10.598211680210753,
        11.066899022771693,
        6.03575303507597,
        3.173825403782544,
        -11.274770316918485,
        -5.859605969128438,
        -5.471210423347152,
        -9.60894536295595,
        -14.829376378643346,
        -0.39421131640611407,
        -6.784301687983458,
        -9.421651244223,
        -0.975512739762415,
        2.1232027680812777,
        -7.191485467538605,
        -2.1692380527945545,
        -0.42798065425027687,
        -16.68404589694532,
        -9.612587073198725,
        0.663449646989946,
        -6.989807394330754,
        -3.955513275597795,
        -7.714797231918723,
        -3.046137340193397,
        -3.595577803845657,
        4.99521952066948,
        12.461523801814458,
        11.19238619041284,
        6.265532356720357,
        -10.678421475126129,
        -0.24338421910207586,
        -6.361302938266007,
        1.3034033002246304,
        -4.5980917078752555,
        6.154871036100701,
        11.793614709227171,
        6.325458737731211,
        -1.0158717439668123,
        5.808339486423932,
        2.166275494011458,
        -3.1785223663390667,
        -3.0890264651802184,
        -3.456716129694456,
        0.4662940327175704,
        6.562881377124512,
        -9.007431458926348,
        -0.005110603804965308,
        -1.8318521335899263,
        7.996439841801504,
        5.929606332933076,
        4.479678523027857,
        1.077211501598967,
        -4.2859170190613725,
        -0.8355229021744464,
        -2.166889211002193,
        4.980495815143485,
        -0.7756416176463432,
        -1.4059266456380328,
        -1.361127713616746,
        3.5530917144563148,
        -0.6023938456787192,
        -5.9136245078345695,
        0.4278079367471719,
        2.6554961723670587,
        0.5295779890385006,
        2.2948250465589553,
        1.3472747795642874,
        2.553182979092611,
        -0.9283758428079665,
        -1.1672833278891233,
        12.98627567262325,
        -5.642725220435722,
        4.116046975197122,
        -10.193742330247503,
        5.517266939105561,
        1.8415788820974726,
        5.367412926801279,
        -11.356954632309026,
        2.3313491130005843,
        5.001147687798273,
        -3.972220764370988,
        -2.2420726333337484,
        -3.7182753088186047,
        -0.47615587889953304,
        -4.9017061458942095,
        8.956118808068325,
        -0.44682503997790946,
        -4.930549817174672,
        4.31799028740798,
        -8.515000086015377,
        -5.495899730637802,
        -19.60223841001814,
        -1.632504184856515,
        -0.5681013344518959,
        -0.2854952727270472,
        -3.1063018665952526,
        -8.945017731662531,
        -1.8433387653957212,
        -2.5040268224038087,
        0.6515683624618589,
        -8.625402757808196,
        -4.53530204520704,
        -5.6192109591825385,
        -8.192118980099067,
        -5.496108996298837,
        -1.8461184442636878,
        -6.7873393012311,
        -8.311971384897213,
        -9.441899016190632
      ],
      "random_effects": [
        0.8866801908631821,
        1.7799976890108247,
        -2.5218156229686857,
        -5.7012484050502845,
        0.5782320937031791,
        2.829873405875811,
        9.930734374165985,
        -5.470452719235066,
        2.41893556020631,
        0.2343564576676782,
        0.17772958318514928,
        -5.1430226074286765
      ],
      "residual_variance": 28.97253825238996,
      "random_intercept_variance": 19.002586692500483,
      "sigma": 5.382614443965865,
      "icc": 0.3960924898961486,
      "log_likelihood": -791.5680446239315,
      "aic": 1591.136089247863,
      "df_residual": 248
    },
    "Python": {
      "coefficients": [
        56.49083359295403,
        2.3431194302075236
      ],
      "covariance": [
        [
          2.2160140554323133,
          -0.07784745731265776
        ],
        [
          -0.07784745731265776,
          0.011802243055631646
        ]
      ],
      "std_errors": [
        1.4886282462160636,
        0.10863812892180924
      ],
      "z_statistics": [
        37.948247815764475,
        21.568112903471953
      ],
      "p_values": [
        0.0,
        3.580032543365646e-103
      ],
      "conf_int": [
        [
          53.573175844001526,
          59.40849134190654
        ],
        [
          2.1301926101729585,
          2.5560462502420886
        ]
      ],
      "fixed_fitted": [
        83.62415659475715,
        62.817256054514345,
        79.96889028363341,
        65.18380667902395,
        66.75369669726298,
        69.40142165339749,
        62.91098083172265,
        68.69848582433524,
        83.17896390301773,
        76.10274322379101,
        69.47171523630371,
        59.56032004652589,
        80.83584447281021,
        69.89347673374107,
        82.87435837709074,
        70.54955017419917,
        75.32951381182252,
        67.94868760666883,
        66.56624714284638,
        63.0515679975351,
        83.43670704034055,
        59.18542093769268,
        65.62899937076338,
        65.37125623344055,
        61.55197156220228,
        70.40896300838672,
        83.13210151441358,
        68.04241238387712,
        77.55547727051967,
        60.7787421502338,
        84.56140436684016,
        64.48087084996169,
        59.70090721233834,
        72.82237602150047,
        66.47252236563808,
        81.37476194175792,
        79.45340400898776,
        78.72703698562343,
        72.30688974685482,
        82.96808315429905,
        66.82399028016921,
        69.87004553943899,
        73.52531185056273,
        59.39630168641136,
        70.73699972861577,
        59.70090721233834,
        83.27268868022603,
        80.10947744944588,
        77.43832129900929,
        74.22824767962499,
        59.11512735478646,
        80.22663342095625,
        66.47252236563808,
        71.15876122605313,
        70.92444928303237,
        71.18219242035521,
        79.00821131724834,
        77.15714696738439,
        83.2961198745281,
        69.42485284769955,
        61.27079723057738,
        68.04241238387712,
        83.67101898336131,
        82.24171613093472,
        77.69606443633212,
        81.65593627338284,
        72.42404571836519,
        76.40734874971798,
        70.54955017419917,
        81.7730922448932,
        71.58052272349049,
        68.39388029840825,
        76.82911024715534,
        82.52289046255962,
        83.27268868022603,
        78.51615623690475,
        76.47764233262421,
        69.75288956792862,
        72.58806407847972,
        64.73861398728451,
        64.43400846135754,
        59.18542093769268,
        75.70441292065573,
        79.0550737058525,
        77.76635801923834,
        63.5201918835766,
        74.90775231438516,
        83.64758778905923,
        67.26918297190863,
        79.8985967007272,
        78.51615623690475,
        62.91098083172265,
        80.1797710323521,
        76.64166069273874,
        72.1428713867403,
        83.15553270871565,
        71.34621078046973,
        62.13775141975417,
        69.84661434513691,
        71.25248600326142,
        79.75800953491475,
        62.44235694568114,
        61.36452200778568,
        70.03406389955352,
        67.690944469346,
        62.8641184431185,
        78.32870668248816,
        80.48437655827908,
        76.54793591553043,
        76.89940383006157,
        74.41569723404159,
        70.45582539699087,
        82.56975285116377,
        77.86008279644665,
        75.42323858903083,
        71.93199063802162,
        66.58967833714846,
        78.23498190527985,
        77.01655980157194,
        67.43320133202317,
        77.20400935598855,
        83.577294206153,
        84.37395481242356,
        60.61472379011927,
        79.7111471463106,
        80.01575267223757,
        73.10355035312537,
        78.72703698562343,
        75.77470650356196,
        67.15202700039826,
        76.59479830413459,
        82.05426657651812,
        68.37044910410617,
        78.49272504260267,
        71.20562361465728,
        84.11621167510073,
        72.8926696044067,
        70.52611897989709,
        77.15714696738439,
        62.278338585566615,
        59.65404482373419,
        65.01978831890942,
        75.47010097763497,
        64.01224696392018,
        78.68017459701929,
        69.9637703166473,
        81.25760597024755,
        66.23821042261733,
        80.460945363977,
        77.93037637935288,
        79.00821131724834,
        59.39630168641136,
        72.72865124429217,
        60.00551273826532,
        61.27079723057738,
        63.59048546648283,
        67.76123805225222,
        60.356980652796445,
        74.9780458972914,
        73.43158707335442,
        73.10355035312537,
        75.39980739472875,
        67.66751327504392,
        61.27079723057738,
        70.69013734001163,
        72.07257780383406,
        84.09278048079867,
        62.23147619696247,
        62.184613808358314,
        71.08846764314691,
        66.84742147447129,
        58.85738421746363,
        77.27430293889476,
        79.8985967007272,
        74.11109170811461,
        82.10112896512226,
        74.18138529102083,
        74.29854126253122,
        77.25087174459269,
        74.08766051381254,
        70.83072450582408,
        66.47252236563808,
        59.490026463619664,
        82.24171613093472,
        68.11270596678335,
        65.4181186220447,
        78.42243145969645,
        81.93711060500775,
        59.20885213199476,
        82.12456015942433,
        62.7703936659102,
        79.99232147793549,
        67.57378849783562,
        68.7219170186373,
        74.13452290241668,
        64.64488921007622,
        68.86250418444976,
        66.2616416169194,
        75.18892664601007,
        64.22312771263886,
        75.02490828589555,
        65.3243938448364,
        83.97562450928828,
        66.0741920625028,
        63.75450382659736,
        74.50942201124988,
        83.78817495487168,
        81.04672522152887,
        81.86681702210151,
        70.26837584257427,
        59.23228332629684,
        68.27672432689788,
        81.04672522152887,
        58.833953023161556,
        63.33274232916,
        61.973733059639635,
        61.739421116618885,
        73.43158707335442,
        81.81995463349736,
        67.62065088643976,
        61.76285231092096,
        82.9212207656949,
        63.73107263229528,
        75.75127530925988,
        73.40815587905234,
        70.66670614570955,
        81.16388119303926,
        65.34782503913847,
        65.44154981634676,
        82.31200971384094,
        75.84500008646818,
        83.88189973207999,
        72.86923841010463,
        68.86250418444976,
        80.57810133548737,
        72.6114952727818,
        61.950301865337565,
        65.7930177308779,
        64.83233876449282,
        64.59802682147206,
        80.97643163862266,
        61.57540275650436,
        64.50430204426377,
        73.90021095939593,
        70.52611897989709,
        58.951108994671934,
        62.8641184431185,
        72.49433930127142,
        58.99797138327608,
        73.66589901637518
      ],
      "fitted": [
        84.51083678001427,
        63.70393623977147,
        80.85557046889053,
        66.07048686428107,
        67.6403768825201,
        70.28810183865461,
        63.797661016979774,
        69.58516600959236,
        84.06564408827485,
        76.98942340904813,
        70.35839542156083,
        60.447000231783015,
        81.72252465806733,
        70.78015691899819,
        83.76103856234786,
        71.43623035945629,
        76.21619399707964,
        68.83536779192595,
        68.34624482334462,
        64.83156567803334,
        85.21670472083879,
        60.96541861819092,
        67.40899705126162,
        67.15125391393879,
        63.33196924270052,
        72.18896068888496,
        84.91209919491182,
        69.82241006437536,
        79.33547495101791,
        62.55873983073204,
        86.3414020473384,
        66.26086853045993,
        61.48090489283658,
        74.60237370199872,
        68.25252004613633,
        83.15475962225617,
        81.233401689486,
        80.50703466612167,
        74.08688742735306,
        84.74808083479729,
        68.60398796066745,
        71.65004321993723,
        71.00349624656016,
        56.87448608240879,
        68.2151841246132,
        57.17909160833577,
        80.75087307622346,
        77.58766184544331,
        74.91650569500672,
        71.70643207562242,
        56.59331175078388,
        77.70481781695368,
        63.95070676163551,
        68.63694562205056,
        68.4026336790298,
        68.66037681635264,
        76.48639571324577,
        71.45589859197483,
        77.59487149911854,
        63.723604472289985,
        55.56954885516781,
        62.34116400846755,
        77.96977060795174,
        76.54046775552516,
        71.99481606092256,
        75.95468789797327,
        66.72279734295563,
        70.70610037430842,
        64.8483017987896,
        76.07184386948364,
        65.87927434808093,
        62.69263192299868,
        71.12786187174578,
        76.82164208715005,
        77.57144030481646,
        72.81490786149519,
        70.77639395721465,
        64.05164119251906,
        66.88681570307016,
        65.31684607763599,
        65.01224055170901,
        59.76365302804416,
        76.2826450110072,
        79.63330579620397,
        78.34459010958982,
        64.09842397392808,
        75.48598440473664,
        84.22581987941071,
        67.84741506226011,
        80.47682879107867,
        79.09438832725623,
        63.48921292207412,
        80.75800312270357,
        77.21989278309022,
        72.72110347709177,
        83.73376479906713,
        71.92444287082121,
        62.715983510105644,
        70.42484643548839,
        74.0823593966358,
        82.58788292828912,
        65.27223033905551,
        64.19439540116005,
        72.86393729292789,
        70.52081786272036,
        65.69399183649287,
        81.15858007586253,
        83.31424995165345,
        79.3778093089048,
        79.72927722343594,
        77.24557062741596,
        73.28569879036525,
        85.39962624453814,
        80.68995618982102,
        78.2531119824052,
        74.76186403139599,
        69.41955173052283,
        81.06485529865422,
        79.84643319494631,
        70.26307472539754,
        80.03388274936292,
        86.40716759952737,
        87.20382820579793,
        63.44459718349365,
        82.54102053968496,
        82.84562606561194,
        83.03428466724088,
        88.65777129973893,
        85.70544081767747,
        77.08276131451376,
        86.52553261825008,
        91.98500089063361,
        78.30118341822168,
        88.42345935671818,
        81.13635792877278,
        94.04694598921623,
        82.82340391852222,
        80.4568532940126,
        87.0878812814999,
        72.20907289968213,
        69.5847791378497,
        74.95052263302492,
        85.40083529175047,
        73.94298127803569,
        88.6109089111348,
        64.49331762778048,
        75.78715328138074,
        60.767757733750514,
        74.99049267511019,
        72.45992369048606,
        73.53775862838152,
        53.92584899754455,
        67.25819855542535,
        54.5350600493985,
        55.800344541710565,
        58.12003277761602,
        62.29078536338541,
        54.88652796392963,
        69.50759320842458,
        67.96113438448761,
        67.63309766425856,
        69.92935470586194,
        62.1970605861771,
        55.800344541710565,
        65.21968465114482,
        66.60212511496725,
        86.51171602388312,
        64.65041174004693,
        64.60354935144278,
        73.50740318623137,
        69.26635701755575,
        61.27631976054809,
        79.69323848197922,
        82.31753224381166,
        76.53002725119907,
        84.52006450820672,
        76.60032083410529,
        76.71747680561568,
        79.66980728767714,
        76.506596056897,
        73.24966004890854,
        68.89145790872254,
        59.72438292029581,
        82.47607258761086,
        68.34706242345949,
        65.65247507872084,
        78.6567879163726,
        82.17146706168388,
        59.443208588670906,
        82.35891661610047,
        63.004750122586344,
        80.22667793461163,
        67.80814495451176,
        68.95627347531344,
        74.36887935909282,
        64.87924566675235,
        69.0968606411259,
        66.49599807359554,
        75.42328310268621,
        64.457484169315,
        75.25926474257169,
        65.55875030151253,
        84.20998096596442,
        66.30854851917894,
        63.9888602832735,
        74.74377846792602,
        84.02253141154782,
        81.22445480395024,
        82.04454660452288,
        70.44610542499564,
        59.4100129087182,
        68.45445390931924,
        81.22445480395024,
        59.01168260558292,
        63.51047191158136,
        62.151462642061,
        61.91715069904025,
        73.60931665577579,
        81.99768421591872,
        67.79838046886113,
        61.940581893342326,
        83.09895034811626,
        63.908802214716644,
        75.92900489168125,
        73.58588546147371,
        70.84443572813092,
        81.34161077546062,
        65.52555462155983,
        65.61927939876813,
        82.4897392962623,
        70.70197750896764,
        78.73887715457946,
        67.72621583260411,
        63.71948160694924,
        75.43507875798684,
        67.46847269528126,
        56.80727928783704,
        60.64999515337738,
        59.68931618699229,
        59.45500424397154,
        75.83340906112213,
        56.432380179003836,
        59.36127946676324,
        68.75718838189542,
        65.38309640239657,
        53.80808641717141,
        57.721095865617976,
        67.3513167237709,
        53.85494880577556,
        68.52287643887465
      ],
      "residuals": [
        -6.253836780014268,
        3.538063760228532,
        7.367429531109465,
        2.4755131357189413,
        -7.503376882520101,
        1.8588981613453939,
        -3.442661016979777,
        0.08483399040764539,
        -1.6236440882748582,
        -4.860423409048124,
        -8.558395421560832,
        3.2599997682169857,
        -5.330524658067333,
        6.297843081001815,
        7.275961437652143,
        3.020769640543705,
        -0.1811939970796459,
        3.9266322080740537,
        0.827755176655387,
        -5.780565678033341,
        6.866295279161207,
        3.451581381809085,
        -0.34399705126162416,
        13.651746086061209,
        4.909030757299483,
        -6.560960688884961,
        1.3239008050881864,
        0.8625899356246407,
        0.10652504898207837,
        -4.478739830732039,
        2.3835979526615887,
        -1.3928685304599355,
        -3.8439048928365764,
        0.9216262980012857,
        -5.0125200461363235,
        0.9852403777438354,
        1.559598310514005,
        1.2079653338783345,
        -8.590887427353067,
        -6.030080834797289,
        1.34401203933254,
        4.346956780062769,
        1.8735037534398344,
        -1.045486082408786,
        -5.598184124613205,
        -4.543091608335764,
        2.3641269237765385,
        -11.603661845443312,
        9.060494304993284,
        -6.063432075622416,
        -8.294311750783883,
        2.3291821830463277,
        8.362293238364494,
        4.059054377949437,
        -1.867633679029808,
        6.905623183647364,
        0.21660428675423304,
        -7.709898591974827,
        6.346128500881463,
        -10.921604472289985,
        -3.710548855167808,
        -5.196164008467548,
        5.105229392048258,
        -3.583467755525163,
        4.5791839390774385,
        -7.657687897973275,
        5.190202657044367,
        5.481899625691582,
        8.354698201210397,
        4.316156130516362,
        -10.129274348080926,
        -5.23163192299868,
        2.2901381282542275,
        0.1413579128499407,
        -0.1614403048164661,
        -2.1379078614951794,
        1.2446060427853496,
        2.9553588074809483,
        1.7421842969298496,
        2.9841539223640154,
        2.5507594482909894,
        0.7043469719558431,
        5.3463549889928,
        -4.479305796203974,
        -2.9295901095898103,
        11.364576026071916,
        2.308015595263356,
        0.7701801205892878,
        1.3885849377398927,
        -4.542828791078676,
        -3.848388327256231,
        5.200787077925881,
        -1.0130031227035659,
        2.8481072169097814,
        -7.492103477091774,
        3.275235200932869,
        -8.61644287082121,
        1.4630164898943576,
        -6.40084643548839,
        7.41264060336421,
        6.800117071710886,
        -4.56223033905551,
        -1.7163954011600495,
        -4.2889372929278835,
        3.926182137279639,
        -6.186991836492872,
        -7.4375800758625275,
        -4.0092499516534446,
        8.189190691095192,
        -5.881277223435944,
        -5.471570627415957,
        -9.288698790365245,
        -2.0546262445381416,
        9.109043810178989,
        -4.8501119824051955,
        9.563135968604016,
        -5.504551730522827,
        -8.112855298654225,
        -3.314433194946318,
        2.5379252746024576,
        4.76511725063709,
        10.191832400472634,
        -1.156828205797936,
        0.6194028165063443,
        1.8759794603150368,
        13.160373934388062,
        1.9287153327591113,
        2.137228700261076,
        10.489559182322523,
        -5.812761314513764,
        1.7314673817499227,
        -3.1130008906336144,
        -1.4401834182216788,
        5.571540643281821,
        -4.729357928772785,
        -1.0709459892162272,
        4.4745960814777845,
        -1.0988532940125992,
        5.089118718500103,
        10.641927100317872,
        -0.8097791378496879,
        0.6674773669750778,
        1.136164708249538,
        -3.8949812780356865,
        -6.756908911134801,
        -5.804317627780485,
        -0.389153281380743,
        -0.0007577337505111359,
        -4.138492675110186,
        -9.358923690486066,
        5.0762413716184795,
        -1.3138489975445466,
        -3.95119855542535,
        4.494939950601498,
        7.593655458289433,
        -1.721032777616017,
        3.3012146366145885,
        5.042472036070372,
        -11.213593208424584,
        -4.142134384487605,
        6.133902335741439,
        -1.519354705861943,
        1.5149394138229013,
        -2.244344541710568,
        2.4243153488551883,
        1.874874885032753,
        2.576283976116869,
        10.042588259953064,
        8.773450648557215,
        3.8465968137686275,
        -13.097357017555751,
        -2.662319760548094,
        -8.780238481979225,
        -1.115532243811657,
        -7.0170272511990675,
        3.7359354917932848,
        9.374679165894705,
        3.90652319438432,
        -3.4348072876771454,
        3.389403943103005,
        -0.2526600489085382,
        -5.5974579087225464,
        -3.3233829202958063,
        -3.6910725876108614,
        0.23193757654050273,
        6.328524921279154,
        -9.241787916372587,
        -0.23946706168388232,
        -2.0662085886709036,
        7.7620833838995225,
        5.695249877413659,
        4.245322065388365,
        0.8428550454882355,
        -4.520273475313431,
        -1.069879359092809,
        -2.4012456667523523,
        4.746139358874103,
        -1.0099980735955398,
        -1.6402831026862117,
        -1.595484169314993,
        3.3187352574283153,
        -0.8367503015125379,
        -6.147980965964422,
        0.19345148082105368,
        2.4211397167264934,
        0.29522153207398105,
        2.0604685884521814,
        1.1695451960497678,
        2.3754533954771233,
        -1.1061054249956328,
        -1.3450129087182034,
        12.808546090680764,
        -5.820454803950241,
        3.9383173944170835,
        -10.37147191158136,
        5.339537357939001,
        1.663849300959754,
        5.189683344224221,
        -11.53468421591873,
        2.1536195311388724,
        4.82341810665767,
        -4.149950348116263,
        -2.419802214716647,
        -3.896004891681244,
        -0.6538854614737062,
        -5.0794357281309175,
        8.778389224539382,
        -0.6245546215598381,
        -5.108279398768126,
        4.140260703737695,
        -3.371977508967646,
        -0.3528771545794598,
        -14.459215832604109,
        3.5105183930507664,
        4.574921242013161,
        4.8575273047187295,
        2.0367207121629605,
        -3.8019951533773835,
        3.2996838130077037,
        2.6389957560284643,
        5.7945909388778745,
        -3.482380179003833,
        0.6077205332367583,
        -0.4761883818954118,
        -3.0490964023965716,
        -0.3530864171714114,
        3.296904134382025,
        -1.6443167237709133,
        -3.168948805775557,
        -4.298876438874643
      ],
      "marginal_residuals": [
        -5.367156594757148,
        4.424743945485659,
        8.254109716366585,
        3.3621933209760613,
        -6.616696697262981,
        2.745578346602514,
        -2.55598083172265,
        0.9715141756647654,
        -0.7369639030177382,
        -3.973743223791004,
        -7.6717152363037115,
        4.146679953474113,
        -4.443844472810213,
        7.184523266258935,
        8.162641622909263,
        3.907449825800825,
        0.7054861881774741,
        4.813312393331174,
        2.6077528571536277,
        -4.0005679975351,
        8.646292959659448,
        5.231579062307318,
        1.4360006292366165,
        15.43174376655945,
        6.689028437797717,
        -4.7809630083867205,
        3.103898485586427,
        2.6425876161228814,
        1.886522729480319,
        -2.698742150233805,
        4.163595633159829,
        0.38712915003830517,
        -2.063907212338343,
        2.7016239784995264,
        -3.232522365638083,
        2.765238058242076,
        3.3395959910122457,
        2.987963014376575,
        -6.810889746854826,
        -4.250083154299048,
        3.124009719830781,
        6.126954460561009,
        -0.6483118505627345,
        -3.567301686411362,
        -8.119999728615774,
        -7.0649072123383405,
        -0.15768868022603044,
        -14.125477449445881,
        6.538678700990715,
        -8.585247679624985,
        -10.81612735478646,
        -0.19263342095624125,
        5.840477634361918,
        1.5372387739468678,
        -4.389449283032377,
        4.383807579644795,
        -2.305211317248336,
        -13.41114696738439,
        0.6448801254719001,
        -16.622852847699555,
        -9.411797230577378,
        -10.897412383877118,
        -0.5960189833613043,
        -9.284716130934726,
        -1.1220644363321242,
        -13.358936273382838,
        -0.511045718365196,
        -0.21934874971798024,
        2.653449825800834,
        -1.385092244893201,
        -15.830522723490489,
        -10.93288029840825,
        -3.411110247155335,
        -5.559890462559622,
        -5.862688680226029,
        -7.839156236904742,
        -4.456642332624213,
        -2.7458895679286144,
        -3.959064078479713,
        3.5623860127154927,
        3.1289915386424667,
        1.2825790623073203,
        5.924587079344278,
        -3.9010737058524967,
        -2.351358019238333,
        11.942808116423393,
        2.8862476856148334,
        1.348412210940765,
        1.96681702809137,
        -3.964596700727199,
        -3.2701562369047537,
        5.779019168277351,
        -0.4347710323520886,
        3.4263393072612587,
        -6.913871386740297,
        3.853467291284346,
        -8.038210780469733,
        2.041248580245835,
        -5.822614345136913,
        10.24251399673858,
        9.629990465085257,
        -1.7323569456811398,
        1.113477992214321,
        -1.459063899553513,
        6.7560555306540095,
        -3.3571184431185017,
        -4.607706682488157,
        -1.179376558279074,
        11.019064084469562,
        -3.051403830061574,
        -2.6416972340415867,
        -6.458825396990875,
        0.7752471488362289,
        11.938917203553359,
        -2.020238589030825,
        12.393009361978386,
        -2.674678337148457,
        -5.282981905279854,
        -0.48455980157194745,
        5.367798667976828,
        7.59499064401146,
        13.021705793847005,
        1.6730451875764345,
        3.449276209880722,
        4.705852853689407,
        15.990247327762432,
        11.859449646874623,
        12.067963014376573,
        20.420293496438035,
        4.117972999601733,
        11.66220169586542,
        6.817733423481883,
        8.490550895893833,
        15.502274957397333,
        5.201376385342712,
        8.85978832489927,
        14.405330395593296,
        8.831881020102912,
        15.019853032615615,
        20.572661414433384,
        9.120955176265817,
        10.598211681090575,
        11.066899022365035,
        6.035753036079825,
        3.173825402980711,
        -11.274770316647299,
        -5.859605970247557,
        -5.471210422617325,
        -9.608945363977,
        -14.82937637935288,
        -0.3942113172483346,
        -6.784301686411361,
        -9.421651244292164,
        -0.9755127382653157,
        2.123202769422619,
        -7.191485466482831,
        -2.1692380522522257,
        -0.4279806527964425,
        -16.684045897291398,
        -9.612587073354419,
        0.6634496468746249,
        -6.989807394728757,
        -3.955513275043913,
        -7.714797230577382,
        -3.046137340011626,
        -3.595577803834061,
        4.995219519201328,
        12.46152380303753,
        11.192386191641681,
        6.265532356853086,
        -10.678421474471293,
        -0.24338421746363537,
        -6.361302938894767,
        1.3034032992728015,
        -4.598091708114609,
        6.154871034877743,
        11.793614708979163,
        6.325458737468779,
        -1.0158717445926868,
        5.808339486187464,
        2.1662754941759204,
        -3.178522365638088,
        -3.0890264636196605,
        -3.4567161309347227,
        0.4662940332166414,
        6.562881377955293,
        -9.007431459696448,
        -0.005110605007743629,
        -1.8318521319947578,
        7.996439840575661,
        5.929606334089804,
        4.4796785220645035,
        1.0772115021643742,
        -4.285917018637292,
        -0.8355229024166704,
        -2.1668892100762136,
        4.980495815550242,
        -0.7756416169194011,
        -1.405926646010073,
        -1.3611277126388543,
        3.553091714104454,
        -0.6023938448363992,
        -5.913624509288283,
        0.42780793749719237,
        2.655496173402639,
        0.5295779887501197,
        2.29482504512832,
        1.3472747784711316,
        2.553182977898487,
        -0.928375842574269,
        -1.1672833262968396,
        12.986275673102128,
        -5.6427252215288775,
        4.116046976838447,
        -10.193742329159996,
        5.517266940360365,
        1.8415788833811177,
        5.367412926645585,
        -11.356954633497367,
        2.331349113560236,
        5.001147689079033,
        -3.9722207656948996,
        -2.242072632295283,
        -3.71827530925988,
        -0.47615587905234236,
        -4.901706145709554,
        8.956118806960745,
        -0.44682503913847427,
        -4.930549816346762,
        4.317990286159059,
        -8.515000086468177,
        -5.495899732079991,
        -19.602238410104626,
        -1.6325041844497576,
        -0.5681013354873699,
        -0.28549527278180165,
        -3.1063018653375636,
        -8.945017730877908,
        -1.8433387644928203,
        -2.50402682147206,
        0.6515683613773433,
        -8.625402756504357,
        -4.535302044263766,
        -5.619210959395929,
        -8.192118979897089,
        -5.4961089946719355,
        -1.846118443118499,
        -6.78733930127143,
        -8.31197138327608,
        -9.441899016375174
      ],
      "random_effects": [
        0.886680185257125,
        1.7799976804982363,
        -2.5218156040025757,
        -5.701248375409567,
        0.5782320903514737,
        2.8298733933743767,
        9.930734314115504,
        -5.4704526888668115,
        2.418935543084461,
        0.2343564566761431,
        0.17772958242136389,
        -5.143022577500524
      ],
      "residual_variance": 28.972538357576944,
      "random_intercept_variance": 19.002585216197318,
      "sigma": 5.382614453736859,
      "icc": 0.3960924704441019,
      "log_likelihood": -791.5680446239318,
      "aic": 1591.1360892478635,
      "df_residual": 248
    },
    "phit": {
      "coefficients": [
        56.490833592935964,
        2.3431194302102156
      ],
      "covariance": [
        [
          2.2160140543043276,
          -0.07784745731512054
        ],
        [
          -0.07784745731512054,
          0.01180224305600408
        ]
      ],
      "std_errors": [
        1.4886282458371962,
        0.10863812892352334
      ],
      "z_statistics": [
        37.948247825410455,
        21.568112903156432
      ],
      "p_values": [
        4.12406732e-315,
        3.5800325675276325e-103
      ],
      "conf_int": [
        [
          53.57317584472602,
          59.408491341145904
        ],
        [
          2.1301926101722906,
          2.5560462502481407
        ]
      ],
      "fitted": [
        84.51083677997512,
        63.703936239708405,
        80.85557046884719,
        66.07048686422073,
        67.64037688246158,
        70.28810183859912,
        63.79766101691681,
        69.58516600953605,
        84.06564408823519,
        76.98942340900034,
        70.35839542150542,
        60.4470002317162,
        81.72252465802497,
        70.78015691894326,
        83.76103856230786,
        71.43623035940213,
        76.21619399703097,
        68.83536779186879,
        68.34624482325873,
        64.83156567794342,
        85.21670472077228,
        60.965418618096564,
        67.40899705117465,
        67.15125391385153,
        63.33196924260888,
        72.18896068880349,
        84.91209919484496,
        69.82241006429118,
        79.33547495094464,
        62.55873983063951,
        86.34140204727319,
        66.26086853037164,
        61.480904892742814,
        74.60237370192002,
        68.25252004605032,
        83.1547596221873,
        81.23340168941492,
        80.50703466604976,
        74.08688742727377,
        84.74808083473025,
        68.60398796058186,
        71.65004321985514,
        71.00349624673872,
        56.87448608257111,
        68.21518412478856,
        57.17909160849844,
        80.75087307641321,
        77.58766184562943,
        74.91650569518977,
        71.70643207580179,
        56.59331175094588,
        77.70481781713993,
        63.950706761805954,
        68.63694562222639,
        68.40263367920538,
        68.6603768165285,
        76.48639571343061,
        71.45589859225717,
        77.59487149940794,
        63.723604472563466,
        55.56954885543191,
        62.34116400873944,
        77.96977060824157,
        76.54046775581334,
        71.99481606120553,
        75.95468789826079,
        66.72279734323254,
        70.70610037458991,
        64.84830179906437,
        76.0718438697713,
        65.87927434835686,
        62.692631923270966,
        71.12786187202774,
        76.82164208743856,
        77.57144030510584,
        72.8149078617791,
        70.77639395749621,
        64.0516411927929,
        66.88681570334725,
        65.31684607759617,
        65.01224055166884,
        59.76365302799796,
        76.28264501097998,
        79.63330579618058,
        78.34459010956496,
        64.09842397388685,
        75.4859844047085,
        84.2258198793926,
        67.84741506222319,
        80.47682879105626,
        79.09438832723224,
        63.4892129220322,
        80.75800312268149,
        77.21989278306405,
        72.72110347706045,
        83.73376479904846,
        71.92444287078898,
        62.715983510062834,
        70.42484643545444,
        74.08235939651809,
        82.58788292818116,
        65.27223033892767,
        64.19439540103097,
        72.86393729280877,
        70.52081786259856,
        65.69399183636551,
        81.15858007575295,
        83.31424995154634,
        79.37780930879319,
        79.72927722332471,
        77.24557062730187,
        73.28569879024661,
        85.39962624443342,
        80.6899561897109,
        78.25311198229227,
        74.76186403127906,
        69.41955173039975,
        81.06485529854453,
        79.84643319483521,
        70.26307472527543,
        80.03388274925203,
        86.40716759942381,
        87.20382820569529,
        63.444597183363705,
        82.54102053957698,
        82.84562606550429,
        83.03428466668154,
        88.65777129918607,
        85.70544081712119,
        77.0827613139476,
        86.52553261769476,
        91.98500089008456,
        78.3011834176569,
        88.42345935616504,
        81.13635792821127,
        94.04694598866955,
        82.82340391796262,
        80.45685329345031,
        87.08788128094521,
        72.20907289911034,
        69.58477913727491,
        74.9505226324563,
        85.40083529119386,
        73.9429812774659,
        88.61090891058186,
        64.49331762806135,
        75.78715328167459,
        60.76775773402712,
        74.99049267540312,
        72.4599236907761,
        73.53775862867278,
        53.92584899781329,
        67.25819855570941,
        54.53506004966794,
        55.80034454198146,
        58.12003277788957,
        62.29078536366375,
        54.88652796419947,
        69.50759320871121,
        67.96113438477248,
        67.63309766454304,
        69.92935470614906,
        62.19706058645534,
        55.80034454198146,
        65.21968465142652,
        66.60212511525054,
        86.51171602373704,
        64.65041173987572,
        64.60354935127151,
        73.50740318607033,
        69.26635701738985,
        61.27631976037301,
        79.6932384818253,
        82.31753224366075,
        76.53002725104152,
        84.52006450805835,
        76.60032083394782,
        76.71747680545833,
        79.6698072875232,
        76.50659605673941,
        73.24966004874722,
        68.8914579085562,
        59.724382920271985,
        82.47607258761317,
        68.34706242344558,
        65.65247507870383,
        78.65678791637052,
        82.17146706168585,
        59.443208588646755,
        82.35891661610266,
        63.004750122566286,
        80.22667793461137,
        67.80814495449722,
        68.95627347530024,
        74.36887935908584,
        64.87924566673446,
        69.09686064111284,
        66.4959980735795,
        75.42328310268043,
        64.45748416929662,
        75.25926474256572,
        65.55875030149542,
        84.20998096596874,
        66.30854851916268,
        63.988860283254574,
        74.74377846791947,
        84.02253141155192,
        81.22445480395331,
        82.04454660452689,
        70.44610542498631,
        59.4100129086962,
        68.45445390930763,
        81.22445480395331,
        59.011682605560466,
        63.51047191156408,
        62.151462642042155,
        61.917150699021136,
        73.60931665577012,
        81.99768421592267,
        67.79838046884878,
        61.940581893323234,
        83.09895034812148,
        63.90880221469982,
        75.92900489167823,
        73.58588546146801,
        70.84443572812205,
        81.34161077546382,
        65.52555462154487,
        65.61927939875328,
        82.48973929626683,
        70.70197750925118,
        78.73887715487223,
        67.72621583288421,
        63.71948160722473,
        75.43507875827582,
        67.46847269556109,
        56.8072792881046,
        60.64999515364935,
        59.68931618726317,
        59.45500424424214,
        75.83340906141156,
        56.432380179270965,
        59.36127946703373,
        68.75718838217671,
        65.383096402674,
        53.808086417435526,
        57.72109586588658,
        67.35131672405058,
        53.85494880603973,
        68.52287643915568
      ],
      "residuals": [
        -6.253836779975117,
        3.5380637602915996,
        7.367429531152808,
        2.4755131357792806,
        -7.5033768824615805,
        1.8588981614008873,
        -3.4426610169168157,
        0.0848339904639488,
        -1.6236440882351957,
        -4.860423409000333,
        -8.558395421505423,
        3.259999768283798,
        -5.33052465802497,
        6.29784308105674,
        7.275961437692146,
        3.0207696405978623,
        -0.18119399703097372,
        3.9266322081312097,
        0.8277551767412774,
        -5.7805656779434145,
        6.866295279227714,
        3.4515813819034378,
        -0.34399705117465373,
        13.651746086148464,
        4.909030757391122,
        -6.56096068880349,
        1.3239008051550485,
        0.8625899357088258,
        0.10652504905534954,
        -4.478739830639512,
        2.3835979527268023,
        -1.3928685303716435,
        -3.843904892742813,
        0.9216262980799854,
        -5.012520046050319,
        0.9852403778127012,
        1.5595983105850877,
        1.2079653339502414,
        -8.59088742727377,
        -6.030080834730242,
        1.344012039418132,
        4.346956780144865,
        1.873503753261275,
        -1.0454860825711094,
        -5.598184124788567,
        -4.543091608498436,
        2.364126923586781,
        -11.603661845629432,
        9.060494304810234,
        -6.063432075801785,
        -8.29431175094588,
        2.3291821828600803,
        8.362293238194049,
        4.059054377773606,
        -1.8676336792053831,
        6.905623183471505,
        0.21660428656939246,
        -7.709898592257169,
        6.346128500592059,
        -10.921604472563466,
        -3.7105488554319095,
        -5.196164008739437,
        5.105229391758428,
        -3.583467755813345,
        4.579183938794472,
        -7.657687898260789,
        5.190202656767454,
        5.481899625410094,
        8.35469820093563,
        4.3161561302287055,
        -10.129274348356859,
        -5.231631923270967,
        2.29013812797227,
        0.14135791256143193,
        -0.16144030510584173,
        -2.137907861779098,
        1.24460604250379,
        2.955358807207105,
        1.742184296652752,
        2.9841539224038343,
        2.5507594483311635,
        0.7043469720020425,
        5.346354989020028,
        -4.479305796180583,
        -2.9295901095649555,
        11.364576026113141,
        2.3080155952914936,
        0.7701801206073924,
        1.3885849377768125,
        -4.542828791056266,
        -3.848388327232243,
        5.200787077967796,
        -1.0130031226814822,
        2.8481072169359436,
        -7.4921034770604535,
        3.275235200951542,
        -8.61644287078898,
        1.4630164899371678,
        -6.40084643545444,
        7.412640603481918,
        6.800117071818846,
        -4.5622303389276695,
        -1.7163954010309723,
        -4.288937292808768,
        3.9261821374014403,
        -6.1869918363655145,
        -7.4375800757529476,
        -4.009249951546337,
        8.189190691206804,
        -5.881277223324716,
        -5.4715706273018725,
        -9.288698790246613,
        -2.054626244433422,
        9.109043810289108,
        -4.850111982292262,
        9.563135968720943,
        -5.504551730399747,
        -8.112855298544531,
        -3.3144331948352175,
        2.5379252747245715,
        4.765117250747977,
        10.191832400576189,
        -1.156828205695291,
        0.6194028166362884,
        1.875979460423025,
        13.16037393449571,
        1.9287153333184506,
        2.1372287008139352,
        10.489559182878807,
        -5.812761313947604,
        1.7314673823052402,
        -3.113000890084564,
        -1.4401834176568968,
        5.571540643834965,
        -4.729357928211272,
        -1.0709459886695498,
        4.47459608203738,
        -1.0988532934503041,
        5.089118719054795,
        10.64192710088966,
        -0.8097791372749015,
        0.6674773675436967,
        1.1361647088061488,
        -3.8949812774659023,
        -6.756908910581856,
        -5.804317628061348,
        -0.38915328167459506,
        -0.0007577340271183175,
        -4.138492675403114,
        -9.358923690776095,
        5.076241371327228,
        -1.3138489978132881,
        -3.9511985557094107,
        4.494939950332061,
        7.593655458018539,
        -1.7210327778895689,
        3.3012146363362476,
        5.042472035800529,
        -11.213593208711217,
        -4.142134384772476,
        6.133902335456952,
        -1.519354706149059,
        1.5149394135446599,
        -2.2443445419814623,
        2.4243153485734865,
        1.8748748847494596,
        2.576283976262957,
        10.042588260124276,
        8.773450648728485,
        3.846596813929665,
        -13.097357017389854,
        -2.662319760373016,
        -8.780238481825307,
        -1.115532243660752,
        -7.017027251041512,
        3.735935491941646,
        9.374679166052175,
        3.9065231945416627,
        -3.434807287523199,
        3.3894039432605894,
        -0.2526600487472166,
        -5.597457908556208,
        -3.323382920271982,
        -3.691072587613178,
        0.23193757655441516,
        6.3285249212961645,
        -9.241787916370512,
        -0.23946706168584342,
        -2.0662085886467523,
        7.762083383897334,
        5.695249877433717,
        4.245322065388621,
        0.8428550455027732,
        -4.520273475300229,
        -1.0698793590858315,
        -2.401245666734461,
        4.746139358887163,
        -1.0099980735794958,
        -1.6402831026804279,
        -1.5954841692966184,
        3.318735257434284,
        -0.8367503014954281,
        -6.147980965968742,
        0.1934514808373109,
        2.4211397167454223,
        0.29522153208053226,
        2.0604685884480745,
        1.1695451960466983,
        2.375453395473116,
        -1.1061054249863105,
        -1.345012908696205,
        12.808546090692374,
        -5.820454803953311,
        3.9383173944395367,
        -10.371471911564079,
        5.339537357957845,
        1.6638493009788675,
        5.189683344229891,
        -11.534684215922681,
        2.1536195311512216,
        4.823418106676762,
        -4.149950348121479,
        -2.4198022146998213,
        -3.8960048916782313,
        -0.6538854614680076,
        -5.07943572812205,
        8.778389224536184,
        -0.6245546215448741,
        -5.108279398753275,
        4.140260703733162,
        -3.371977509251181,
        -0.3528771548722318,
        -14.459215832884205,
        3.5105183927752748,
        4.574921241724184,
        4.857527304438904,
        2.0367207118953985,
        -3.801995153649351,
        3.2996838127368306,
        2.638995755757861,
        5.794590938588442,
        -3.4823801792709617,
        0.6077205329662689,
        -0.47618838217670145,
        -3.049096402673996,
        -0.35308641743552727,
        3.2969041341134186,
        -1.644316724050583,
        -3.1689488060397295,
        -4.298876439155677
      ],
      "log_likelihood": -791.5680446239317,
      "aic": 1591.1360892478633,
      "df_residual": 248,
      "evaluations": 107,
      "fixed_fitted": [
        83.62415659477026,
        62.817256054503545,
        79.96889028364232,
        65.18380667901586,
        66.75369669725671,
        69.40142165339425,
        62.91098083171195,
        68.69848582433119,
        83.17896390303032,
        76.10274322379547,
        69.47171523630055,
        59.56032004651134,
        80.8358444728201,
        69.8934767337384,
        82.874358377103,
        70.54955017419726,
        75.3295138118261,
        67.94868760666392,
        66.56624714283988,
        63.051567997524565,
        83.43670704035344,
        59.18542093767771,
        65.6289993707558,
        65.37125623343269,
        61.55197156219003,
        70.40896300838465,
        83.13210151442611,
        68.04241238387233,
        77.5554772705258,
        60.77874215022066,
        84.56140436685435,
        64.4808708499528,
        59.70090721232396,
        72.82237602150117,
        66.47252236563148,
        81.37476194176845,
        79.45340400899607,
        78.72703698563092,
        72.30688974685492,
        82.9680831543114,
        66.82399028016302,
        69.87004553943629,
        73.52531185056424,
        59.39630168639663,
        70.73699972861408,
        59.70090721232396,
        83.27268868023873,
        80.10947744945494,
        77.43832129901529,
        74.2282476796273,
        59.1151273547714,
        80.22663342096544,
        66.47252236563148,
        71.15876122605191,
        70.9244492830309,
        71.18219242035401,
        79.00821131725613,
        77.15714696739006,
        83.29611987454084,
        69.42485284769636,
        61.2707972305648,
        68.04241238387233,
        83.67101898337447,
        82.24171613094623,
        77.69606443633842,
        81.65593627339368,
        72.42404571836543,
        76.4073487497228,
        70.54955017419726,
        81.77309224490419,
        71.58052272348975,
        68.39388029840386,
        76.82911024716063,
        82.52289046257145,
        83.27268868023873,
        78.516156236912,
        76.4776423326291,
        69.75288956792579,
        72.58806407848014,
        64.73861398727593,
        64.4340084613486,
        59.18542093767771,
        75.70441292065973,
        79.05507370586034,
        77.76635801924472,
        63.52019188356661,
        74.90775231438826,
        83.64758778907236,
        67.26918297190295,
        79.89859670073602,
        78.516156236912,
        62.91098083171195,
        80.17977103236124,
        76.64166069274381,
        72.14287138674021,
        83.15553270872822,
        71.34621078046874,
        62.137751419742585,
        69.8466143451342,
        71.25248600326032,
        79.7580095349234,
        62.442356945669914,
        61.36452200777321,
        70.03406389955101,
        67.69094446934079,
        62.86411844310775,
        78.32870668249518,
        80.48437655828857,
        76.54793591553542,
        76.89940383006694,
        74.41569723404412,
        70.45582539698884,
        82.56975285117566,
        77.86008279645313,
        75.42323858903451,
        71.93199063802129,
        66.58967833714199,
        78.23498190528676,
        77.01655980157744,
        67.43320133201767,
        77.20400935599427,
        83.57729420616606,
        84.37395481243753,
        60.61472379010594,
        79.7111471463192,
        80.01575267224652,
        73.1035503531264,
        78.72703698563092,
        75.77470650356604,
        67.15202700039245,
        76.59479830413962,
        82.05426657652941,
        68.37044910410175,
        78.49272504260989,
        71.20562361465612,
        84.1162116751144,
        72.89266960440747,
        70.52611897989516,
        77.15714696739006,
        62.2783385855552,
        59.65404482371976,
        65.01978831890115,
        75.47010097763871,
        64.01224696391075,
        78.6801745970267,
        69.9637703166447,
        81.25760597025794,
        66.23821042261046,
        80.46094536398647,
        77.93037637935944,
        79.00821131725613,
        59.39630168639663,
        72.72865124429276,
        60.005512738251284,
        61.2707972305648,
        63.59048546647291,
        67.7612380522471,
        60.356980652782816,
        74.97804589729456,
        73.43158707335583,
        73.1035503531264,
        75.3998073947324,
        67.66751327503869,
        61.2707972305648,
        70.69013734000987,
        72.0725778038339,
        84.09278048081231,
        62.23147619695099,
        62.18461380834679,
        71.0884676431456,
        66.84742147446512,
        58.857384217448285,
        77.27430293890058,
        79.89859670073602,
        74.11109170811679,
        82.10112896513363,
        74.18138529102309,
        74.2985412625336,
        77.25087174459847,
        74.08766051381468,
        70.83072450582249,
        66.47252236563148,
        59.49002646360504,
        82.24171613094623,
        68.11270596677863,
        65.41811862203689,
        78.42243145970357,
        81.9371106050189,
        59.20885213197981,
        82.12456015943572,
        62.77039366589934,
        79.99232147794443,
        67.57378849783028,
        68.72191701863329,
        74.1345229024189,
        64.64488921006752,
        68.8625041844459,
        66.26164161691256,
        75.18892664601348,
        64.22312771262968,
        75.02490828589877,
        65.32439384482848,
        83.9756245093018,
        66.07419206249574,
        63.75450382658763,
        74.50942201125252,
        83.78817495488498,
        81.04672522153902,
        81.8668170221126,
        70.26837584257203,
        59.232283326281916,
        68.27672432689334,
        81.04672522153902,
        58.83395302314618,
        63.332742329149795,
        61.97373305962787,
        61.73942111660685,
        73.43158707335583,
        81.81995463350839,
        67.62065088643449,
        61.76285231090895,
        82.92122076570719,
        63.73107263228553,
        75.75127530926395,
        73.40815587905372,
        70.66670614570776,
        81.16388119304953,
        65.34782503913058,
        65.44154981633899,
        82.31200971385255,
        75.84500008647234,
        83.88189973209339,
        72.86923841010537,
        68.8625041844459,
        80.57810133549698,
        72.61149527278225,
        61.95030186532577,
        65.79301773087052,
        64.83233876448433,
        64.5980268214633,
        80.97643163863272,
        61.57540275649213,
        64.5043020442549,
        73.90021095939787,
        70.52611897989516,
        58.95110899465669,
        62.86411844310775,
        72.49433930127174,
        58.9979713832609,
        73.66589901637684
      ],
      "marginal_residuals": [
        -5.36715659477025,
        4.424743945496459,
        8.254109716357675,
        3.3621933209841472,
        -6.616696697256714,
        2.745578346605754,
        -2.555980831711956,
        0.9715141756688155,
        -0.736963903030329,
        -3.9737432237954664,
        -7.671715236300557,
        4.146679953488658,
        -4.443844472820103,
        7.184523266261607,
        8.162641622897013,
        3.907449825802729,
        0.705486188173893,
        4.813312393336076,
        2.607752857160122,
        -4.000567997524563,
        8.646292959646559,
        5.2315790623222895,
        1.436000629244191,
        15.431743766567308,
        6.6890284378099665,
        -4.780963008384646,
        3.103898485573893,
        2.6425876161276705,
        1.8865227294741942,
        -2.69874215022066,
        4.163595633145647,
        0.38712915004720116,
        -2.0639072123239615,
        2.70162397849883,
        -3.2325223656314748,
        2.765238058231546,
        3.3395959910039323,
        2.987963014369086,
        -6.810889746854926,
        -4.2500831543113975,
        3.1240097198369767,
        6.126954460563709,
        -0.6483118505642409,
        -3.5673016863966325,
        -8.119999728614083,
        -7.064907212323959,
        -0.15768868023873495,
        -14.125477449454948,
        6.538678700984718,
        -8.585247679627301,
        -10.816127354771403,
        -0.19263342096543568,
        5.840477634368526,
        1.53723877394809,
        -4.389449283030899,
        4.383807579645989,
        -2.3052113172561235,
        -13.41114696739006,
        0.6448801254591672,
        -16.622852847696358,
        -9.411797230564801,
        -10.897412383872329,
        -0.5960189833744636,
        -9.284716130946236,
        -1.1220644363384196,
        -13.358936273393681,
        -0.5110457183654376,
        -0.21934874972279772,
        2.6534498258027384,
        -1.385092244904186,
        -15.83052272348975,
        -10.932880298403859,
        -3.4111102471606216,
        -5.55989046257146,
        -5.862688680238733,
        -7.83915623691199,
        -4.456642332629102,
        -2.7458895679257864,
        -3.9590640784801394,
        3.562386012724076,
        3.1289915386514053,
        1.2825790623222915,
        5.92458707934027,
        -3.901073705860341,
        -2.3513580192447137,
        11.942808116433383,
        2.8862476856117354,
        1.3484122109276342,
        1.9668170280970543,
        -3.964596700736024,
        -3.270156236912001,
        5.779019168288045,
        -0.4347710323612404,
        3.4263393072561854,
        -6.913871386740212,
        3.853467291271784,
        -8.038210780468738,
        2.0412485802574167,
        -5.822614345134198,
        10.242513996739689,
        9.629990465076602,
        -1.7323569456699133,
        1.113477992226791,
        -1.459063899551012,
        6.756055530659211,
        -3.357118443107751,
        -4.607706682495177,
        -1.179376558288567,
        11.019064084464574,
        -3.0514038300669455,
        -2.6416972340441163,
        -6.458825396988843,
        0.7752471488243344,
        11.938917203546879,
        -2.0202385890345056,
        12.393009361978713,
        -2.674678337141991,
        -5.282981905286761,
        -0.48455980157744705,
        5.367798667982328,
        7.594990644005733,
        13.021705793833945,
        1.6730451875624652,
        3.4492762098940517,
        4.7058528536807955,
        15.99024732775348,
        11.8594496468736,
        12.067963014369084,
        20.420293496433956,
        4.117972999607545,
        11.66220169586039,
        6.817733423470585,
        8.490550895898252,
        15.502274957390114,
        5.2013763853438775,
        8.8597883248856,
        14.405330395592529,
        8.831881020104845,
        15.019853032609944,
        20.572661414444802,
        9.120955176280248,
        10.598211681098846,
        11.066899022361298,
        6.035753036089247,
        3.173825402973293,
        -11.274770316644698,
        -5.859605970257945,
        -5.471210422610461,
        -9.608945363986464,
        -14.829376379359445,
        -0.39421131725612213,
        -6.784301686396631,
        -9.421651244292761,
        -0.9755127382512825,
        2.1232027694351956,
        -7.191485466472912,
        -2.1692380522470955,
        -0.4279806527828143,
        -16.684045897294567,
        -9.612587073355826,
        0.6634496468736018,
        -6.989807394732409,
        -3.955513275038683,
        -7.714797230564805,
        -3.0461373400098637,
        -3.5955778038338906,
        4.995219519187685,
        12.461523803049005,
        11.192386191653206,
        6.2655323568543935,
        -10.678421474465125,
        -0.24338421744828764,
        -6.361302938900579,
        1.3034032992639766,
        -4.598091708116783,
        6.154871034866375,
        11.793614708976904,
        6.325458737466391,
        -1.0158717445984706,
        5.808339486185318,
        2.166275494177512,
        -3.17852236563148,
        -3.0890264636050375,
        -3.4567161309462335,
        0.4662940332213594,
        6.562881377963109,
        -9.007431459703568,
        -0.00511060501889915,
        -1.831852131979808,
        7.996439840564278,
        5.9296063341006615,
        4.479678522055565,
        1.0772115021697175,
        -4.285917018633285,
        -0.8355229024188873,
        -2.1668892100675166,
        4.980495815554107,
        -0.7756416169125515,
        -1.4059266460134836,
        -1.3611277126296741,
        3.553091714101228,
        -0.6023938448284838,
        -5.913624509301798,
        0.42780793750425516,
        2.6554961734123665,
        0.5295779887474765,
        2.2948250451150187,
        1.347274778460985,
        2.5531829778874027,
        -0.9283758425720237,
        -1.1672833262819182,
        12.986275673106661,
        -5.642725221539024,
        4.1160469768538235,
        -10.193742329149792,
        5.5172669403721315,
        1.8415788833931543,
        5.367412926644178,
        -11.356954633508394,
        2.3313491135655084,
        5.001147689091049,
        -3.972220765707192,
        -2.2420726322855344,
        -3.7182753092639445,
        -0.4761558790537208,
        -4.901706145707763,
        8.956118806950471,
        -0.44682503913058724,
        -4.9305498163389885,
        4.317990286147449,
        -8.515000086472341,
        -5.495899732093392,
        -19.602238410105365,
        -1.6325041844458923,
        -0.5681013354969764,
        -0.2854952727822564,
        -3.1063018653257686,
        -8.945017730870518,
        -1.8433387644843364,
        -2.504026821463306,
        0.651568361367282,
        -8.625402756492129,
        -4.535302044254898,
        -5.619210959397861,
        -8.192118979895156,
        -5.496108994656694,
        -1.8461184431077484,
        -6.787339301271743,
        -8.311971383260897,
        -9.441899016376837
      ],
      "random_effects": [
        0.8866801852048607,
        1.7799976804188482,
        -2.5218156038255217,
        -5.7012483751328915,
        0.5782320903202466,
        2.8298733932577633,
        9.930734313555144,
        -5.470452688583345,
        2.4189355429247255,
        0.23435645666694488,
        0.17772958241428888,
        -5.143022577221165
      ],
      "group_sizes": [
        18,
        24,
        15,
        22,
        20,
        27,
        19,
        21,
        16,
        25,
        23,
        20
      ],
      "n_groups": 12,
      "group_labels": [
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12
      ],
      "residual_variance": 28.97253835855859,
      "random_intercept_variance": 19.002585202419784,
      "sigma": 5.382614453828046,
      "icc": 0.39609247026256655,
      "boundary": false,
      "method": "ML",
      "converged": true,
      "n_input": 250,
      "n_observations": 250,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119,
        120,
        121,
        122,
        123,
        124,
        125,
        126,
        127,
        128,
        129,
        130,
        131,
        132,
        133,
        134,
        135,
        136,
        137,
        138,
        139,
        140,
        141,
        142,
        143,
        144,
        145,
        146,
        147,
        148,
        149,
        150,
        151,
        152,
        153,
        154,
        155,
        156,
        157,
        158,
        159,
        160,
        161,
        162,
        163,
        164,
        165,
        166,
        167,
        168,
        169,
        170,
        171,
        172,
        173,
        174,
        175,
        176,
        177,
        178,
        179,
        180,
        181,
        182,
        183,
        184,
        185,
        186,
        187,
        188,
        189,
        190,
        191,
        192,
        193,
        194,
        195,
        196,
        197,
        198,
        199,
        200,
        201,
        202,
        203,
        204,
        205,
        206,
        207,
        208,
        209,
        210,
        211,
        212,
        213,
        214,
        215,
        216,
        217,
        218,
        219,
        220,
        221,
        222,
        223,
        224,
        225,
        226,
        227,
        228,
        229,
        230,
        231,
        232,
        233,
        234,
        235,
        236,
        237,
        238,
        239,
        240,
        241,
        242,
        243,
        244,
        245,
        246,
        247,
        248,
        249
      ],
      "dropped_rows": []
    },
    "python_diagnostics": {
      "backend": "statsmodels MixedLM (ML)",
      "warnings": [],
      "covariance_convention": "plug-in GLS, matching lme4"
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "Python": 1.9297701214782137e-09,
        "phit": 1.947839223248593e-09
      },
      "covariance": {
        "Python": 1.2086681033807167e-07,
        "phit": 1.219947960429124e-07
      },
      "std_errors": {
        "Python": 4.059670666300974e-08,
        "phit": 4.097557404492136e-08
      },
      "z_statistics": {
        "Python": 1.0335986004861297e-06,
        "phit": 1.0432445805008683e-06
      },
      "p_values": {
        "Python": 2.6162506617388735e-109,
        "phit": 2.6404126482489567e-109
      },
      "conf_int": {
        "Python": 8.149785202249404e-08,
        "phit": 8.225848802112523e-08
      },
      "fixed_fitted": {
        "Python": 1.641325297896401e-09,
        "phit": 1.6567014426982496e-09
      },
      "fitted": {
        "Python": 6.159083909551555e-08,
        "phit": 6.216562553618132e-08
      },
      "residuals": {
        "Python": 6.159083909551555e-08,
        "phit": 6.216562553618132e-08
      },
      "marginal_residuals": {
        "Python": 1.641325297896401e-09,
        "phit": 1.6567014426982496e-09
      },
      "random_effects": {
        "Python": 6.005048014401382e-08,
        "phit": 6.061084079078682e-08
      },
      "residual_variance": {
        "Python": 1.0518698445594055e-07,
        "phit": 1.0616863121981623e-07
      },
      "random_intercept_variance": {
        "Python": 1.4763031650488756e-06,
        "phit": 1.490080698829388e-06
      },
      "sigma": {
        "Python": 9.77099379184665e-09,
        "phit": 9.862180405662002e-09
      },
      "icc": {
        "Python": 1.9452046695622727e-08,
        "phit": 1.9633582037936748e-08
      },
      "log_likelihood": {
        "Python": 2.2737367544323206e-13,
        "phit": 1.1368683772161603e-13
      },
      "aic": {
        "Python": 4.547473508864641e-13,
        "phit": 2.2737367544323206e-13
      },
      "df_residual": {
        "Python": 0.0,
        "phit": 0.0
      }
    },
    "tolerance": {
      "absolute": 1e-07,
      "relative": 1e-06
    },
    "extension_sha256": "2105dd47a15f21b0da6ae81a23461ef385285517e1af0519a0bb22238bc3ffc6"
  },
  {
    "name": "no_intercept",
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "lme4": "2.0.6",
      "statsmodels": "0.15.0",
      "PHP": "8.5.10",
      "Python": "3.14.7"
    },
    "R": {
      "coefficients": [
        1.5803559139275558,
        0.2616890654087006
      ],
      "covariance": [
        [
          0.02566111653843883,
          -0.005134011478634646
        ],
        [
          -0.005134011478634646,
          0.00172090675974261
        ]
      ],
      "std_errors": [
        0.16019087532827464,
        0.04148381322567406
      ],
      "z_statistics": [
        9.865455261974049,
        6.308221088189236
      ],
      "p_values": [
        5.876724552773544e-23,
        2.8226082465205523e-10
      ],
      "conf_int": [
        [
          1.2663875676321918,
          1.8943242602229198
        ],
        [
          0.18038228554499314,
          0.3429958452724081
        ]
      ],
      "fixed_fitted": [
        38.536936911335914,
        17.796285649234225,
        36.46149839306789,
        17.72810266630172,
        20.922323902368177,
        27.366191449381187,
        16.92003614097409,
        25.04717676407158,
        37.42019940361453,
        29.174910645579857,
        19.335260677632427,
        15.458278833554221,
        36.37630607377481,
        26.87112874461448,
        37.48952665348309,
        28.917782371469528,
        29.44369417151804,
        23.209465528684476,
        20.41382939375727,
        16.255959206124512,
        39.99634417459844,
        14.96205105649572,
        21.631828720625762,
        22.14099803081044,
        18.206851641637368,
        24.586215047667014,
        39.14190902357428,
        22.176202581179123,
        31.59925495327097,
        11.904622735163077,
        38.81579903860519,
        16.803890699620485,
        15.118696339811432,
        24.442346666195494,
        22.33421827299812,
        37.056431703122676,
        33.88684614537579,
        35.77830630727742,
        26.206499122979643,
        34.477894371487956,
        18.29003855000091,
        21.02750969882344,
        28.990952188787226,
        13.481810883215259,
        24.739425718610608,
        11.8423492408945,
        34.91886079916637,
        31.845916570546933,
        32.807747359385395,
        27.387247783620413,
        10.486861392362682,
        32.45878005967706,
        23.022460515023003,
        24.859025671910086,
        21.848579267562496,
        23.524513653540467,
        32.445614196547616,
        33.49476301883324,
        39.365060235674946,
        22.14821370034645,
        14.044768919061985,
        23.63642756615967,
        39.02649989407969,
        37.198908870735174,
        31.79613504361602,
        32.711002909261204,
        27.918456686826318,
        30.084300500339847,
        23.72587131376091,
        34.36800576937205,
        22.28322825149995,
        21.052472828143017,
        27.937673147199977,
        37.96950130561379,
        36.54133300470031,
        33.36199629662234,
        31.728014476750747,
        25.972921958974116,
        25.590139511192152,
        19.209937578088734,
        17.544266324297602,
        13.326494397691341,
        31.71155692139344,
        30.802411296210487,
        29.281609770682667,
        20.897750640115845,
        32.76530542834298,
        39.565477153606864,
        20.4116620688917,
        34.508991319474724,
        34.52127885638288,
        19.468887638054834,
        33.900482379649496,
        32.134348034637505,
        27.485443146324915,
        34.96545375486617,
        25.056110192684642,
        17.152183197755054,
        21.807240898526615,
        26.301341283171045,
        35.620556556173185,
        14.968408299384201,
        17.954812417126984,
        21.528051320257333,
        21.339881234304066,
        20.656751564580826,
        33.84268645525631,
        35.57400430540289,
        29.99593950938941,
        28.921930678780953,
        30.041592628582663,
        26.033560009806635,
        36.794721832358235,
        35.578257545275015,
        31.32041363135744,
        30.55675283729028,
        21.20161569585221,
        33.06244417947937,
        32.45786102852626,
        19.896850116539838,
        32.25194438857142,
        40.93380432005011,
        41.16756601491139,
        9.501601608207931,
        32.686817702512144,
        33.504616384379084,
        32.84640913904591,
        33.334130436360155,
        32.90778259595547,
        22.02315563573553,
        32.18386452663565,
        34.165114880930304,
        20.86133759517991,
        31.679233390829634,
        24.08724735938393,
        36.6130519094377,
        26.133164674379962,
        19.89464118096278,
        29.05389957884759,
        15.498921595660589,
        17.366400981242663,
        18.07019983548384,
        28.669707829196806,
        15.06684789166573,
        31.30060196770505,
        18.342988748589185,
        36.72357551397986,
        21.079705497542907,
        33.54319494261662,
        26.979461501589377,
        32.63141343298779,
        12.529262685127588,
        25.737298679109546,
        14.188412064748253,
        17.06466073387839,
        19.35409179984877,
        18.956200494075063,
        14.425465451837386,
        31.0201460077112,
        27.242460370998096,
        30.284473188694733,
        31.445922167538864,
        21.77941664897593,
        12.53743990230787,
        23.142917989188028,
        25.815560263373147,
        38.9995539707503,
        18.003081521192346,
        19.607031061718175,
        27.34738203830257,
        22.136970026723564,
        9.724221844661072,
        33.5371443453724,
        30.785155918708917,
        29.9329713139733,
        36.16724066173637,
        29.509341673655467,
        28.11505003110086,
        31.299600620913253,
        27.768700527828592,
        26.23669603360739,
        18.353927588131782,
        12.296768277772857,
        33.75246387930259,
        20.28188039326439,
        21.986805912648812,
        29.5383101901422,
        35.69025105618926,
        10.764660662554917,
        34.59982537515301,
        18.659655134653427,
        35.791676600836375,
        24.372346426317137,
        21.943646663539145,
        28.088165618056717,
        19.42149686021077,
        21.190595446450608,
        21.65814054731089,
        27.914816738242706,
        13.222859917467174,
        30.127990725097042,
        18.529484497740864,
        40.03009781238681,
        22.458091365743485,
        19.5850936839117,
        27.28903252134215,
        35.43140321143792,
        36.67031776396534,
        38.945356384229235,
        25.82862481706982,
        10.356527935732096,
        26.754166487324834,
        30.35314372499931,
        11.589962665810354,
        16.59999846438695,
        15.023935589479043,
        19.809206443656645,
        26.554218128973215,
        35.22655033434209,
        21.206113165301367,
        18.911715164519553,
        35.388367888680726,
        16.470891590333412,
        30.939778608867286,
        27.276377734286473,
        22.038487917948558,
        38.95537438105706,
        21.706491967017243,
        17.370713014054086,
        35.62908112392723,
        29.145000481022613,
        36.2221130498312,
        26.598868995592696,
        23.940947523896053,
        34.9097229401238,
        30.48382724954961,
        14.762144308855591,
        17.367012460967217,
        20.25710270058255,
        18.829875141957597,
        35.25165638380592,
        12.656528779533579,
        16.00845815599279,
        28.568651346261188,
        23.982224382646685,
        12.281332874563093,
        16.88581213204145,
        27.220053527829343,
        13.95111354230011,
        25.76493930358647
      ],
      "fitted": [
        84.50316653297186,
        63.76251527087017,
        82.42772801470383,
        63.69433228793767,
        66.88855352400412,
        73.33242107101714,
        62.88626576261004,
        71.01340638570753,
        83.38642902525048,
        75.1411402672158,
        65.30149029926838,
        61.424508455190164,
        82.34253569541076,
        72.83735836625043,
        83.45575627511903,
        74.88401199310547,
        75.40992379315398,
        69.17569515032042,
        67.99230635561426,
        63.834436167981494,
        87.57482113645543,
        62.5405280183527,
        69.21030568248275,
        69.71947499266743,
        65.78532860349435,
        72.164692009524,
        86.72038598543125,
        69.7546795430361,
        79.17773191512796,
        59.483099697020066,
        86.39427600046218,
        64.38236766147747,
        62.697173301668414,
        72.02082362805248,
        69.91269523485511,
        84.63490866497966,
        81.46532310723278,
        83.35678326913441,
        73.78497608483663,
        82.05637133334494,
        65.8685155118579,
        68.60598666068043,
        72.96687578064667,
        57.4577344750747,
        68.71534931047006,
        55.81827283275395,
        78.89478439102581,
        75.82184016240637,
        76.78367095124484,
        71.36317137547987,
        54.462784984222125,
        76.43470365153652,
        66.99838410688244,
        68.83494926376954,
        65.82450285942194,
        67.50043724539992,
        76.42153778840708,
        73.44891380880576,
        79.31921102564746,
        62.10236449031896,
        53.9989197090345,
        63.590578356132184,
        78.98065068405221,
        77.1530596607077,
        71.75028583358853,
        72.66515369923371,
        67.87260747679883,
        70.03845129031237,
        63.68002210373343,
        74.32215655934456,
        62.237379041472465,
        61.00662361811553,
        67.89182393717249,
        77.9236520955863,
        76.49548379467282,
        73.31614708659485,
        71.68216526672326,
        65.92707274894663,
        65.54429030116466,
        65.32911364015484,
        63.663442386363705,
        59.445670459757444,
        77.83073298345954,
        76.92158735827658,
        75.40078583274877,
        67.01692670218195,
        78.88448149040909,
        85.68465321567297,
        66.5308381309578,
        80.62816738154083,
        80.64045491844898,
        65.58806370012094,
        80.01965844171559,
        78.25352409670361,
        73.60461920839101,
        81.08462981693228,
        71.17528625475074,
        63.27135925982115,
        67.92641696059272,
        74.50673841700936,
        83.82595369001149,
        63.17380543322251,
        66.1602095509653,
        69.73344845409565,
        69.54527836814238,
        68.86214869841913,
        82.04808358909463,
        83.7794014392412,
        78.20133664322772,
        77.12732781261926,
        78.24698976242098,
        74.23895714364494,
        85.00011896619654,
        83.78365467911333,
        79.52581076519576,
        78.7621499711286,
        69.40701282969053,
        81.26784131331769,
        80.66325816236457,
        68.10224725037816,
        80.45734152240973,
        89.1392014538884,
        89.3729631487497,
        57.70699874204624,
        80.89221483635046,
        81.7100135182174,
        89.82909369992734,
        90.31681499724158,
        89.89046715683688,
        79.00584019661694,
        89.16654908751707,
        91.14779944181171,
        77.84402215606133,
        88.66191795171105,
        81.06993192026535,
        93.59573647031911,
        83.11584923526138,
        76.8773257418442,
        86.036584139729,
        72.481606156542,
        74.34908554212407,
        75.05288439636526,
        85.65239239007823,
        72.04953245254714,
        88.28328652858647,
        58.82183067938784,
        77.20241744477852,
        61.558547428341555,
        74.02203687341527,
        67.45830343238802,
        73.11025536378645,
        53.00810461592624,
        66.2161406099082,
        54.66725399554691,
        57.54350266467704,
        59.832933730647426,
        59.435042424873714,
        54.904307382636034,
        71.49898793850986,
        67.72130230179675,
        70.76331511949338,
        71.9247640983375,
        62.258258579774576,
        53.01628183310652,
        63.62175991998668,
        66.2944021941718,
        87.13088654530374,
        66.13441409574578,
        67.73836363627161,
        75.47871461285601,
        70.268302601277,
        57.85555441921451,
        81.66847691992584,
        78.91648849326236,
        78.06430388852674,
        84.29857323628981,
        77.64067424820891,
        76.2463826056543,
        79.4309331954667,
        75.90003310238203,
        74.36802860816084,
        66.48526016268522,
        58.80941449094124,
        80.26511009247096,
        66.79452660643278,
        68.4994521258172,
        76.0509564033106,
        82.20289726935765,
        57.277306875723305,
        81.1124715883214,
        65.17230134782181,
        82.30432281400476,
        70.88499263948552,
        68.45629287670754,
        74.6008118312251,
        65.93414307337916,
        67.703241659619,
        68.17078676047927,
        74.42746295141109,
        59.735506130635564,
        76.64063693826543,
        65.04213071090925,
        86.54274402555521,
        68.97073757891187,
        66.09773989708009,
        73.80167873451055,
        81.9440494246063,
        82.63557204736072,
        84.91061066762462,
        71.7938791004652,
        56.32178221912748,
        72.7194207707202,
        76.3183980083947,
        57.555216949205736,
        62.56525274778233,
        60.98918987287443,
        65.77446072705203,
        72.5194724123686,
        81.19180461773747,
        67.17136744869674,
        64.87696944791493,
        81.35362217207611,
        62.43614587372879,
        76.90503289226267,
        73.24163201768185,
        68.00374220134394,
        84.92062866445245,
        67.67174625041262,
        63.33596729744947,
        81.5943354073226,
        69.84513655398922,
        76.92224912279781,
        67.2990050685593,
        64.64108359686266,
        75.60985901309041,
        71.18396332251622,
        55.4622803818222,
        58.067148533933825,
        60.95723877354916,
        59.5300112149242,
        75.95179245677252,
        53.35666485250019,
        56.7085942289594,
        69.2687874192278,
        64.68236045561329,
        52.9814689475297,
        57.58594820500806,
        67.92018960079595,
        54.651249615266714,
        66.46507537655307
      ],
      "residuals": [
        -6.246166532971856,
        3.4794847291298368,
        5.795271985296168,
        4.851667712062337,
        -6.751553524004123,
        -1.1854210710171316,
        -2.5312657626100403,
        -1.3434063857075245,
        -0.9444290252504857,
        -3.0121402672157984,
        -3.501490299268383,
        2.2824915448098366,
        -5.950535695410764,
        4.240641633749576,
        7.581243724880977,
        -0.42701199310548077,
        0.6250762068460176,
        3.5863048496795784,
        1.1816936443857458,
        -4.783436167981492,
        4.508178863544572,
        1.876471981647299,
        -2.145305682482757,
        11.083525007332568,
        2.4556713965056503,
        -6.536692009524003,
        -0.48438598543124556,
        0.9303204569638979,
        0.2642680848720289,
        -1.4030996970200675,
        2.3307239995378097,
        0.48563233852252097,
        -5.060173301668414,
        3.503176371947518,
        -6.672695234855105,
        -0.49490866497966124,
        1.3276768927672293,
        -1.6417832691344074,
        -8.288976084836634,
        -3.338371333344938,
        4.0794844881421,
        7.391013339319571,
        -0.089875780646679,
        -1.628734475074701,
        -6.098349310470063,
        -3.182272832753945,
        4.220215608974186,
        -9.83784016240638,
        7.19332904875516,
        -5.720171375479865,
        -6.163784984222126,
        3.599296348463483,
        5.314615893117562,
        3.861050736230453,
        0.710497140578056,
        8.06556275460008,
        0.28146221159292395,
        -9.702913808805754,
        4.62178897435254,
        -9.300364490318962,
        -2.1399197090345012,
        -6.445578356132181,
        4.094349315947795,
        -4.196059660707704,
        4.823714166411463,
        -4.368153699233716,
        4.040392523201163,
        6.149548709687636,
        9.522977896266575,
        6.065843440655442,
        -6.487379041472465,
        -3.5456236181155347,
        5.526176062827517,
        -0.9606520955863118,
        0.9145162053271747,
        -2.6391470865948463,
        0.33883473327674096,
        1.0799272510533768,
        3.08470969883534,
        2.9718863598451577,
        3.899557613636297,
        1.0223295402425592,
        3.798267016540464,
        -1.767587358276586,
        0.014214167251239473,
        8.446073297818046,
        -1.0904814904090898,
        -0.6886532156729714,
        2.7051618690422004,
        -4.6941673815408365,
        -5.394454918448986,
        3.101936299879057,
        -0.2746584417155873,
        1.8144759032963833,
        -8.375619208391015,
        5.9243701830677225,
        -7.867286254750745,
        0.9076407401788487,
        -3.902416960592717,
        6.988261582990646,
        5.562046309988517,
        -2.463805433222511,
        -3.682209550965304,
        -1.1584484540956481,
        4.901721631857626,
        -9.355148698419136,
        -8.327083589094627,
        -4.474401439241191,
        9.365663356772274,
        -3.2793278126192575,
        -6.47298976242098,
        -10.241957143644939,
        -1.6551189661965395,
        6.015345320886681,
        -6.1228107651957515,
        5.562850028871409,
        -5.49201282969053,
        -8.31584131331769,
        -4.131258162364574,
        4.698752749621846,
        4.341658477590272,
        7.4597985461116,
        -3.3259631487497074,
        6.357001257953755,
        3.5247851636495398,
        14.295986481782606,
        -4.866093699927347,
        0.4781850027584227,
        6.304532843163116,
        -7.735840196616948,
        -0.909549087517064,
        -2.2757994418117136,
        -0.9830221560613239,
        5.333082048288958,
        -4.6629319202653505,
        -0.6197364703191113,
        4.182150764738623,
        2.4806742581558012,
        6.1404158602710055,
        10.369393843457999,
        -5.574085542124067,
        0.5651156036347373,
        0.8846076099217726,
        -2.0015324525471385,
        -6.4292865285864735,
        -0.13283067938783688,
        -1.8044174447785224,
        -0.791547428341552,
        -3.1700368734152704,
        -4.357303432388022,
        5.503744636213554,
        -0.3961046159262409,
        -2.9091406099081922,
        4.3627460044530935,
        5.850497335322956,
        -3.433933730647425,
        6.156957575126285,
        5.024692617363968,
        -13.20498793850986,
        -3.9023023017967517,
        3.0036848805066114,
        -3.5147640983375084,
        1.4537414202254269,
        0.5397181668934792,
        4.022240080013326,
        2.182597805828209,
        1.9571134546962554,
        8.558585904254215,
        5.638636363728381,
        1.8752853871439896,
        -14.099302601277003,
        0.7584455807854837,
        -10.75547691992584,
        2.2855115067376346,
        -8.551303888526732,
        3.9574267637101883,
        8.334325751791084,
        4.377617394345691,
        -3.1959331954666936,
        3.9959668976179756,
        -1.3710286081608416,
        -3.191260162685225,
        -2.40841449094124,
        -1.4801100924709658,
        1.784473393567211,
        3.4815478741827945,
        -6.635956403310587,
        -0.270897269357647,
        0.09969312427669763,
        9.008528411678597,
        3.527698652178188,
        2.167677185995231,
        -2.233992639485521,
        -4.020292876707529,
        -1.3018118312250948,
        -3.4561430733791596,
        6.139758340381007,
        -2.6847867604792697,
        -0.6444629514110858,
        3.126493869364438,
        1.9373630617345725,
        -0.32013071090925393,
        -8.480744025555211,
        -2.4687375789118704,
        0.31226010291990747,
        1.2373212654894559,
        4.138950575393693,
        -0.24157204736071947,
        -0.49061066762462247,
        -2.453879100465201,
        1.74321778087252,
        8.5435792292798,
        -0.9143980083946985,
        5.394783050794267,
        -9.426252747782328,
        6.501810127125573,
        -2.1934607270520274,
        6.2795275876314065,
        -10.728804617737481,
        2.780632551303256,
        1.887030552085065,
        -2.4046221720761167,
        -0.9471458737287932,
        -4.872032892262666,
        -0.30963201768184945,
        -2.238742201343939,
        5.1993713355475535,
        -2.7707462504126283,
        -2.8249672974494686,
        5.035664592677392,
        -2.5151365539892225,
        1.4637508772021874,
        -14.032005068559293,
        2.588916403137347,
        4.400140986909591,
        1.1420366774837731,
        3.3817196181778044,
        -1.2191485339338257,
        2.03176122645084,
        2.5639887850758,
        5.676207543227477,
        -0.40666485250018525,
        3.2604057710406025,
        -0.9877874192278,
        -2.348360455613289,
        0.4735310524702996,
        3.432051794991942,
        -2.213189600795957,
        -3.965249615266714,
        -2.24107537655307
      ],
      "marginal_residuals": [
        39.72006308866409,
        49.44571435076578,
        51.76150160693211,
        50.81789733369828,
        39.21467609763182,
        44.780808550618815,
        43.434963859025906,
        44.62282323592842,
        45.02180059638546,
        42.95408935442015,
        42.46473932236757,
        48.248721166445776,
        40.01569392622518,
        50.20687125538552,
        53.54747334651692,
        45.539217628530466,
        46.59130582848196,
        49.552534471315525,
        48.76017060624274,
        42.795040793875486,
        52.08665582540156,
        49.45494894350428,
        45.433171279374235,
        58.66200196918956,
        50.03414835836263,
        41.04178495233299,
        47.094090976425726,
        48.508797418820876,
        47.84274504672902,
        46.175377264836925,
        49.9092009613948,
        48.06410930037951,
        42.518303660188565,
        51.08165333380451,
        40.90578172700188,
        47.083568296877324,
        48.906153854624215,
        45.936693692722585,
        39.28950087702035,
        44.24010562851205,
        51.65796144999908,
        54.96949030117656,
        43.88604781121277,
        42.34718911678474,
        37.877574281389386,
        40.7936507591055,
        48.19613920083363,
        34.13808342945306,
        51.16925264061461,
        38.25575221637959,
        37.812138607637316,
        47.575219940322945,
        49.290539484977,
        47.83697432808991,
        44.6864207324375,
        52.041486346459536,
        44.25738580345239,
        30.251236981166763,
        44.57593976432506,
        30.65378629965355,
        37.814231080938015,
        33.50857243384033,
        44.04850010592031,
        35.75809112926482,
        44.77786495638398,
        35.58599709073879,
        43.99454331317368,
        46.10369949966015,
        49.4771286862391,
        46.01999423062796,
        33.46677174850005,
        36.40852717185698,
        45.48032685280003,
        38.993498694386204,
        40.868666995299684,
        37.31500370337767,
        40.29298552324926,
        41.03407804102589,
        43.038860488807856,
        49.09106242191127,
        50.0187336757024,
        47.14150560230866,
        49.91744307860657,
        44.35158870378951,
        46.13339022931734,
        54.56524935988415,
        45.02869457165702,
        45.43052284639313,
        48.8243379311083,
        41.42500868052527,
        40.72472114361712,
        49.22111236194516,
        45.84451762035051,
        47.93365196536249,
        37.74355685367509,
        52.04354624513383,
        38.25188980731536,
        47.02681680224495,
        42.216759101473386,
        55.19365871682896,
        53.76744344382682,
        45.7415917006158,
        44.52318758287302,
        47.04694867974267,
        53.10711876569594,
        38.850248435419175,
        39.87831354474369,
        43.73099569459712,
        57.571060490610584,
        44.926069321219046,
        41.73240737141734,
        37.963439990193365,
        46.550278167641764,
        54.22074245472499,
        42.082586368642566,
        53.76824716270973,
        42.71338430414779,
        39.88955582052063,
        44.07413897147374,
        52.904149883460164,
        52.54705561142859,
        55.665195679949896,
        44.87943398508861,
        54.56239839179206,
        51.73018229748786,
        62.50138361562092,
        52.116590860954084,
        57.46086956363985,
        63.287217404044526,
        49.24684436426446,
        56.07313547336435,
        54.706885119069696,
        55.99966240482009,
        62.31576660917037,
        52.319752640616066,
        56.3629480905623,
        61.16483532562004,
        59.463358819037225,
        63.123100421152415,
        67.35207840433941,
        51.40859901875734,
        57.547800164516154,
        57.867292170803196,
        54.98115210833427,
        50.55339803229495,
        40.346011251410815,
        38.674424486020136,
        39.68729450245709,
        37.30880505738338,
        36.12153849841062,
        45.98258656701221,
        40.08273731487242,
        37.56970132089046,
        44.84158793525175,
        46.32933926612161,
        37.04490820015123,
        46.635799505924936,
        45.50353454816262,
        27.273853992288796,
        36.57653962900191,
        43.48252681130526,
        36.96407783246113,
        41.93258335102408,
        41.01856009769213,
        44.50108201081198,
        42.66143973662686,
        50.088446029249695,
        56.689918478807655,
        53.76996893828182,
        50.00661796169743,
        34.03202997327644,
        48.889778155338924,
        37.3758556546276,
        50.41684408129108,
        39.58002868602671,
        52.08875933826363,
        56.465658326344524,
        52.50894996889913,
        44.935399379086746,
        52.12729947217141,
        46.76030396639261,
        44.940072411868215,
        44.10423172222715,
        45.03253612069741,
        48.297119606735606,
        49.99419408735118,
        39.87668980985781,
        46.24174894381074,
        46.612339337445086,
        55.521174624846985,
        50.040344865346576,
        48.68032339916362,
        44.27865357368286,
        42.492353336460866,
        45.210834381943286,
        43.05650313978923,
        52.652404553549395,
        43.82785945268911,
        45.868183261757295,
        49.639140082532826,
        48.45000927490296,
        46.19251550225913,
        38.031902187613184,
        44.04390863425651,
        46.824906316088295,
        47.74996747865785,
        50.65159678856208,
        45.72368223603466,
        45.474643615770766,
        43.51137518293018,
        47.7084720642679,
        54.50883351267517,
        45.05085627500068,
        51.36003733418965,
        36.53900153561305,
        52.467064410520955,
        43.771793556343354,
        52.24478187102679,
        35.2364496656579,
        48.74588683469863,
        47.85228483548045,
        43.56063211131927,
        45.01810840966658,
        41.093221391132715,
        45.65562226571353,
        43.72651208205144,
        51.16462561894294,
        43.19450803298275,
        43.14028698594592,
        51.00091887607277,
        38.184999518977385,
        42.163886950168795,
        26.668131004407307,
        43.28905247610395,
        45.100277059876205,
        41.84217275045039,
        44.08185569114441,
        39.48098753903278,
        42.73189729941745,
        43.26412485804241,
        46.37634361619408,
        40.29347122046642,
        43.96054184400721,
        39.712348653738815,
        38.35177561735332,
        41.17366712543691,
        44.13218786795855,
        38.48694647217065,
        36.734886457699886,
        38.45906069641353
      ],
      "random_effects": [
        45.96622962163595,
        47.578476961856985,
        43.97592359185945,
        39.954150789972516,
        46.1191760620661,
        48.20539713383831,
        56.98268456088142,
        40.47884193079865,
        48.13133257455344,
        46.51264621316839,
        45.96525428339538,
        40.70013607296661
      ],
      "residual_variance": 25.376508074901643,
      "random_intercept_variance": 2125.625970366458,
      "sigma": 5.037510106679851,
      "icc": 0.9882024738096583,
      "log_likelihood": -803.6695094011228,
      "aic": 1615.3390188022456,
      "df_residual": 248
    },
    "Python": {
      "coefficients": [
        1.5803559110477978,
        0.2616890668548089
      ],
      "covariance": [
        [
          0.025661116629626442,
          -0.005134011494281957
        ],
        [
          -0.005134011494281957,
          0.0017209067642669613
        ]
      ],
      "std_errors": [
        0.16019087561289638,
        0.04148381328020558
      ],
      "z_statistics": [
        9.865455226468399,
        6.308221114756499
      ],
      "p_values": [
        5.87672663200586e-23,
        2.8226077621197687e-10
      ],
      "conf_int": [
        [
          1.2663875641945852,
          1.8943242579010104
        ],
        [
          0.1803822868842216,
          0.34299584682539624
        ]
      ],
      "fixed_fitted": [
        38.53693698981587,
        17.796285716222677,
        36.46149847819497,
        17.728102721184367,
        20.92232396712163,
        27.366191536621237,
        16.920036202655822,
        25.0471768419805,
        37.42019947812979,
        29.174910709602123,
        19.335260720144724,
        15.458278903764638,
        36.376306154134355,
        26.87112882668008,
        37.489526729891125,
        28.917782461593447,
        29.44369424085787,
        23.209465600154225,
        20.413829456629784,
        16.255959263439745,
        39.99634426207219,
        14.962051125822018,
        21.631828794874167,
        22.140998109149958,
        18.20685171716559,
        24.586215114551223,
        39.14190910783604,
        22.17620264647449,
        31.599255023490304,
        11.904622779697089,
        38.815799113981,
        16.803890752879756,
        15.118696407448525,
        24.442346720323396,
        22.334218346947324,
        37.056431784569654,
        33.88684621883004,
        35.77830639478398,
        26.20649918941119,
        34.47789443078903,
        18.290038599859823,
        21.02750974871301,
        28.99095226456711,
        13.481810943316507,
        24.739425784715664,
        11.842349290426316,
        34.91886085939457,
        31.845916629471283,
        32.80774743686357,
        27.38724784705427,
        10.486861437307219,
        32.458780121407486,
        23.022460592775474,
        24.859025736585735,
        21.84857931676354,
        23.5245137107254,
        32.445614264243986,
        33.49476310150145,
        39.36506032035696,
        22.14821375863554,
        14.044768972983857,
        23.63642763952432,
        39.02649997503275,
        37.198908948672724,
        31.796135114226544,
        32.71100296530156,
        27.918456762137588,
        30.084300567877776,
        23.725871375194036,
        34.36800583398845,
        22.28322829985128,
        21.052472885486655,
        27.937673200785202,
        37.96950138641613,
        36.541333073894386,
        33.361996371821384,
        31.72801455302354,
        25.97292203677295,
        25.590139572824114,
        19.209937643366533,
        17.544266381880487,
        13.326494457979463,
        31.71155700140755,
        30.802411354594163,
        29.2816098270494,
        20.897750720759294,
        32.765305518128535,
        39.56547723765446,
        20.411662128268375,
        34.50899139416053,
        34.52127893798819,
        19.468887713821662,
        33.9004824495791,
        32.13434811234282,
        27.485443220636874,
        34.96545381593249,
        25.05611025752036,
        17.1521832645519,
        21.807240952841152,
        26.30134135535249,
        35.620556637698336,
        14.968408352603706,
        17.954812492191458,
        21.528051372100023,
        21.33988129671981,
        20.656751647144116,
        33.84268653404072,
        35.574004383070786,
        29.995939575742277,
        28.921930737456854,
        30.041592705755548,
        26.033560084456695,
        36.79472190643642,
        35.57825763597286,
        31.32041371060361,
        30.55675292961963,
        21.20161576296195,
        33.06244425441663,
        32.45786110616127,
        19.896850172258723,
        32.251944464139484,
        40.93380441200755,
        41.16756610421221,
        9.501601640275616,
        32.686817768057544,
        33.504616452934016,
        32.84640923822158,
        33.33413051036006,
        32.9077826822316,
        22.02315570459805,
        32.18386460484686,
        34.165114943031966,
        20.861337651583455,
        31.679233456845772,
        24.08724741956243,
        36.61305197484745,
        26.13316473750303,
        19.894641221340443,
        29.05389963697534,
        15.498921652624645,
        17.366401061532954,
        18.07019989306984,
        28.669707893562773,
        15.066847937648582,
        31.30060203069982,
        18.34298878317943,
        36.72357559416811,
        21.079705565720896,
        33.54319500917829,
        26.97946154442141,
        32.631413501710895,
        12.529262739965002,
        25.73729874085794,
        14.188412125734866,
        17.06466080448835,
        19.35409187161349,
        18.956200542970066,
        14.425465512392035,
        31.02014608750453,
        27.242460437580228,
        30.284473273713004,
        31.44592224759473,
        21.779416713936698,
        12.537439947900157,
        23.14291804670295,
        25.81556032880563,
        38.99955404946412,
        18.003081592226785,
        19.607031141848385,
        27.3473821170774,
        22.136970097724703,
        9.724221886668639,
        33.53714442769416,
        30.7851559728166,
        29.932971392055606,
        36.16724073466963,
        29.50934174904839,
        28.115050098208204,
        31.299600690986356,
        27.76870059406715,
        26.236696107521926,
        18.35392764008568,
        12.29676833086098,
        33.752463938194886,
        20.28188044774324,
        21.986805989904003,
        29.53831024467587,
        35.690251127299554,
        10.764660708570075,
        34.59982543930852,
        18.659655206645166,
        35.79167668214585,
        24.372346506071093,
        21.943646724181654,
        28.088165685828397,
        19.42149692712217,
        21.19059550223494,
        21.658140618569213,
        27.914816799830653,
        13.222859952214886,
        30.12799079972801,
        18.529484556355218,
        40.03009789737612,
        22.458091442351414,
        19.585093756140047,
        27.289032582839717,
        35.43140327194362,
        36.67031784490444,
        38.94535647367581,
        25.828624891516426,
        10.35652797937576,
        26.75416657675699,
        30.35314377102935,
        11.589962718244239,
        16.599998522209816,
        15.023935645327978,
        19.809206527110536,
        26.554218191752085,
        35.2265504034706,
        21.206113227326284,
        18.911715242897735,
        35.388367953245385,
        16.470891645468633,
        30.939778684384244,
        27.276377801172167,
        22.038487969476463,
        38.95537447404287,
        21.706492043071787,
        17.370713065684363,
        35.629081192841426,
        29.145000546157014,
        36.22211311424189,
        26.598869061405402,
        23.940947594878985,
        34.90972301365633,
        30.483827338108227,
        14.762144363373979,
        17.36701251083511,
        20.257102771182527,
        18.829875205831925,
        35.2516564572538,
        12.656528824274284,
        16.00845820474033,
        28.568651417849352,
        23.98222444561256,
        12.281332930236882,
        16.88581219376632,
        27.220053598932815,
        13.951113606968942,
        25.764939360842455
      ],
      "fitted": [
        84.50316653691277,
        63.76251526331958,
        82.42772802529187,
        63.69433226828127,
        66.88855351421853,
        73.33242108371815,
        62.886265749752724,
        71.0134063890774,
        83.38642902522669,
        75.14114025669903,
        65.30149026724163,
        61.42450845086154,
        82.34253570123126,
        72.83735837377698,
        83.45575627698803,
        74.88401200869035,
        75.40992378795477,
        69.17569514725113,
        67.99230634874638,
        63.83443615555635,
        87.57482115418878,
        62.54052801793861,
        69.21030568699076,
        69.71947500126656,
        65.78532860928219,
        72.16469200666782,
        86.72038599995264,
        69.75467953859109,
        79.1777319156069,
        59.48309967181369,
        86.3942760060976,
        64.38236764499635,
        62.69717329956512,
        72.02082361244,
        69.91269523906392,
        84.63490867668625,
        81.46532311094663,
        83.35678328690058,
        73.78497608152779,
        82.05637132290562,
        65.86851549197642,
        68.6059866408296,
        72.96687579132208,
        57.45773447007147,
        68.71534931147063,
        55.81827281718128,
        78.89478438614954,
        75.82184015622624,
        76.78367096361853,
        71.36317137380924,
        54.46278496406219,
        76.43470364816245,
        66.99838411953044,
        68.8349492633407,
        65.8245028435185,
        67.50043723748037,
        76.42153779099895,
        73.44891382122897,
        79.31921104008448,
        62.10236447836306,
        53.99891969271138,
        63.59057835925184,
        78.98065069476027,
        77.15305966840025,
        71.75028583395407,
        72.66515368502908,
        67.87260748186512,
        70.0384512876053,
        63.680022094921554,
        74.32215655371597,
        62.2373790195788,
        61.00662360521417,
        67.89182392051272,
        77.92365210614365,
        76.4954837936219,
        73.31614709154891,
        71.68216527275106,
        65.92707275650048,
        65.54429029255164,
        65.32911363360368,
        63.66344237211764,
        59.44567044821662,
        77.83073299164471,
        76.92158734483132,
        75.40078581728656,
        67.01692671099644,
        78.8844815083657,
        85.68465322789162,
        66.53083811850553,
        80.62816738439768,
        80.64045492822535,
        65.58806370405881,
        80.01965843981625,
        78.25352410257997,
        73.60461921087403,
        81.08462980616964,
        71.17528624775751,
        63.271359254789054,
        67.92641694307831,
        74.50673841538884,
        83.82595369773469,
        63.17380541264005,
        66.1602095522278,
        69.73344843213637,
        69.54527835675616,
        68.86214870718047,
        82.04808359407707,
        83.77940144310713,
        78.20133663577863,
        77.1273277974932,
        78.2469897657919,
        74.23895714449304,
        85.00011896647277,
        83.78365469600921,
        79.52581077063996,
        78.76214998965598,
        69.4070128229983,
        81.26784131445298,
        80.66325816619761,
        68.10224723229507,
        80.45734152417583,
        89.1392014720439,
        89.37296316424856,
        57.70699870031196,
        80.8922148280939,
        81.71001351297036,
        89.82909373063984,
        90.31681500277833,
        89.89046717464987,
        79.00584019701631,
        89.16654909726512,
        91.14779943545022,
        77.84402214400171,
        88.66191794926404,
        81.06993191198069,
        93.59573646726571,
        83.1158492299213,
        76.87732571375871,
        86.0365841293936,
        72.48160614504292,
        74.34908555395123,
        75.05288438548811,
        85.65239238598105,
        72.04953243006685,
        88.28328652311808,
        58.821830648557615,
        77.2024174595463,
        61.558547431099086,
        74.02203687455648,
        67.4583034097996,
        73.11025536708908,
        53.00810460534319,
        66.21614060623612,
        54.66725399111305,
        57.54350266986654,
        59.83293373699168,
        59.43504240834825,
        54.90430737777022,
        71.49898795288271,
        67.7213023029584,
        70.76331513909119,
        71.92476411297292,
        62.258258579314884,
        53.01628181327834,
        63.62175991208113,
        66.29440219418382,
        87.13088655154743,
        66.1344140943101,
        67.7383636439317,
        75.47871461916071,
        70.26830259980802,
        57.855554388751955,
        81.66847692977748,
        78.91648847489992,
        78.06430389413893,
        84.29857323675296,
        77.64067425113171,
        76.24638260029153,
        79.43093319306968,
        75.90003309615047,
        74.36802860960525,
        66.485260142169,
        58.809414477445365,
        80.26511008477928,
        66.79452659432764,
        68.49945213648839,
        76.05095639126026,
        82.20289727388393,
        57.277306855154464,
        81.1124715858929,
        65.17230135322956,
        82.30432282873024,
        70.88499265265548,
        68.45629287076605,
        74.60081183241279,
        65.93414307370657,
        67.70324164881933,
        68.1707867651536,
        74.42746294641503,
        59.73550609879928,
        76.6406369463124,
        65.0421307029396,
        86.54274404396051,
        68.9707375889358,
        66.09773990272444,
        73.80167872942411,
        81.94404941852801,
        82.63557205905201,
        84.91061068782338,
        71.793879105664,
        56.32178219352334,
        72.71942079090456,
        76.31839798517693,
        57.555216932391815,
        62.565252736357394,
        60.98918985947556,
        65.77446074125811,
        72.51947240589966,
        81.19180461761817,
        67.17136744147386,
        64.8769694570453,
        81.35362216739296,
        62.43614585961621,
        76.90503289853183,
        73.24163201531974,
        68.00374218362404,
        84.92062868819045,
        67.67174625721937,
        63.33596727983194,
        81.594335406989,
        69.84513655323221,
        76.9222491213171,
        67.2990050684806,
        64.6410836019542,
        75.60985902073153,
        71.18396334518343,
        55.46228037044918,
        58.06714851791031,
        60.95723877825773,
        59.53001121290713,
        75.951792464329,
        53.356664831349484,
        56.70859421181553,
        69.26878742492455,
        64.68236045268776,
        52.98146893731209,
        57.58594820084152,
        67.92018960600802,
        54.65124961404415,
        66.46507536791765
      ],
      "residuals": [
        -6.246166536912767,
        3.4794847366804262,
        5.795271974708129,
        4.8516677317187344,
        -6.751553514218529,
        -1.1854210837181398,
        -2.531265749752727,
        -1.3434063890774013,
        -0.9444290252266967,
        -3.012140256699027,
        -3.5014902672416355,
        2.282491549138463,
        -5.95053570123126,
        4.240641626223024,
        7.58124372301198,
        -0.4270120086903546,
        0.6250762120452293,
        3.5863048527488672,
        1.1816936512536245,
        -4.783436155556345,
        4.508178845811216,
        1.876471982061389,
        -2.145305686990767,
        11.083524998733438,
        2.4556713907178107,
        -6.5366920066678205,
        -0.48438599995263587,
        0.9303204614089111,
        0.2642680843930947,
        -1.4030996718136919,
        2.330723993902396,
        0.485632355003645,
        -5.060173299565122,
        3.5031763875600035,
        -6.67269523906392,
        -0.4949086766862507,
        1.3276768890533788,
        -1.6417832869005764,
        -8.288976081527792,
        -3.3383713229056156,
        4.079484508023569,
        7.391013359170401,
        -0.08987579132208623,
        -1.6287344700714712,
        -6.098349311470635,
        -3.1822728171812784,
        4.220215613850456,
        -9.83784015622625,
        7.193329036381471,
        -5.720171373809237,
        -6.163784964062188,
        3.599296351837552,
        5.31461588046956,
        3.861050736659294,
        0.7104971564814946,
        8.065562762519633,
        0.2814622090010488,
        -9.702913821228968,
        4.62178895991552,
        -9.300364478363058,
        -2.1399196927113806,
        -6.44557835925184,
        4.0943493052397315,
        -4.1960596684002525,
        4.8237141660459315,
        -4.368153685029085,
        4.04039251813488,
        6.149548712394704,
        9.522977905078449,
        6.065843446284035,
        -6.487379019578803,
        -3.5456236052141747,
        5.526176079487286,
        -0.9606521061436553,
        0.9145162063780958,
        -2.6391470915489066,
        0.33883472724893693,
        1.079927243499526,
        3.0847097074483685,
        2.971886366396319,
        3.899557627882359,
        1.0223295517833861,
        3.798267008355296,
        -1.7675873448313268,
        0.014214182713445211,
        8.44607328900355,
        -1.0904815083656985,
        -0.6886532278916206,
        2.705161881494476,
        -4.694167384397687,
        -5.3944549282253575,
        3.1019362959411865,
        -0.2746584398162497,
        1.8144758974200244,
        -8.375619210874035,
        5.924370193830356,
        -7.867286247757512,
        0.9076407452109478,
        -3.9024169430783076,
        6.988261584611166,
        5.5620463022653155,
        -2.463805412640049,
        -3.6822095522277962,
        -1.1584484321363675,
        4.901721643243846,
        -9.355148707180469,
        -8.327083594077067,
        -4.474401443107126,
        9.365663364221362,
        -3.2793277974931954,
        -6.472989765791894,
        -10.241957144493043,
        -1.6551189664727701,
        6.015345303990799,
        -6.122810770639958,
        5.562850010344022,
        -5.492012822998298,
        -8.315841314452982,
        -4.131258166197611,
        4.698752767704931,
        4.341658475824175,
        7.45979852795611,
        -3.325963164248563,
        6.357001299688029,
        3.524785171906103,
        14.295986487029637,
        -4.866093730639847,
        0.47818499722167473,
        6.3045328253501225,
        -7.735840197016316,
        -0.9095490972651135,
        -2.2757994354502245,
        -0.9830221440017084,
        5.3330820507359675,
        -4.662931911980692,
        -0.6197364672657102,
        4.182150770078707,
        2.480674286241296,
        6.140415870606404,
        10.369393854957082,
        -5.574085553951221,
        0.5651156145118819,
        0.8846076140189609,
        -2.0015324300668453,
        -6.42928652311808,
        -0.13283064855761495,
        -1.8044174595463005,
        -0.7915474310990831,
        -3.170036874556473,
        -4.357303409799599,
        5.503744632910923,
        -0.39610460534319003,
        -2.9091406062361216,
        4.362746008886951,
        5.850497330133457,
        -3.4339337369916763,
        6.1569575916517465,
        5.024692622229779,
        -13.204987952882718,
        -3.902302302958404,
        3.0036848609088054,
        -3.5147641129729266,
        1.4537414206851196,
        0.5397181867216574,
        4.022240087918874,
        2.1825978058161866,
        1.95711344845256,
        8.558585905689895,
        5.6386363560682895,
        1.875285380839287,
        -14.099302599808027,
        0.7584456112480424,
        -10.755476929777487,
        2.285511525100077,
        -8.551303894138925,
        3.9574267632470423,
        8.334325748868281,
        4.37761739970847,
        -3.1959331930696777,
        3.995966903849535,
        -1.371028609605247,
        -3.191260142169,
        -2.408414477445362,
        -1.4801100847792839,
        1.7844734056723581,
        3.481547863511608,
        -6.635956391260251,
        -0.27089727388393214,
        0.09969314484553848,
        9.00852841410709,
        3.527698646770446,
        2.1676771712697587,
        -2.2339926526554876,
        -4.020292870766042,
        -1.3018118324127812,
        -3.4561430737065635,
        6.139758351180674,
        -2.6847867651535893,
        -0.6444629464150324,
        3.1264939012007247,
        1.937363053687605,
        -0.32013070293960766,
        -8.480744043960513,
        -2.4687375889358094,
        0.3122600972755549,
        1.2373212705758903,
        4.138950581471988,
        -0.24157205905200385,
        -0.49061068782337713,
        -2.453879105664001,
        1.7432178064766575,
        8.54357920909544,
        -0.914397985176933,
        5.394783067608188,
        -9.426252736357391,
        6.501810140524441,
        -2.1934607412581073,
        6.279527594100344,
        -10.72880461761818,
        2.7806325585261362,
        1.8870305429546903,
        -2.404622167392958,
        -0.9471458596162137,
        -4.8720328985318275,
        -0.3096320153197354,
        -2.2387421836240406,
        5.199371311809557,
        -2.770746257219372,
        -2.824967279831938,
        5.035664593010992,
        -2.5151365532322103,
        1.4637508786829017,
        -14.032005068480593,
        2.5889163980458108,
        4.400140979268471,
        1.1420366548165646,
        3.3817196295508225,
        -1.2191485179103125,
        2.031761221742265,
        2.5639887870928746,
        5.676207535670997,
        -0.40666483134948095,
        3.260405788184471,
        -0.987787424924548,
        -2.348360452687757,
        0.47353106268791123,
        3.4320517991584794,
        -2.2131896060080294,
        -3.965249614044147,
        -2.241075367917645
      ],
      "marginal_residuals": [
        39.720063010184134,
        49.44571428377733,
        51.76150152180503,
        50.817897278815636,
        39.21467603287837,
        44.78080846337877,
        43.434963797344174,
        44.6228231580195,
        45.021800521870205,
        42.95408929039788,
        42.46473927985527,
        48.248721096235364,
        40.01569384586564,
        50.206871173319925,
        53.54747327010888,
        45.53921753840655,
        46.59130575914213,
        49.552534399845776,
        48.76017054337022,
        42.79504073656025,
        52.086655737927806,
        49.45494887417799,
        45.43317120512583,
        58.662001890850036,
        50.03414828283441,
        41.04178488544878,
        47.09409089216396,
        48.50879735352551,
        47.84274497650969,
        46.175377220302906,
        49.90920088601899,
        48.06410924712024,
        42.518303592551476,
        51.0816532796766,
        40.90578165305268,
        47.08356821543035,
        48.90615378116997,
        45.93669360521602,
        39.289500810588805,
        44.240105569210975,
        51.65796140014017,
        54.96949025128699,
        43.88604773543288,
        42.34718905668349,
        37.87757421528433,
        40.79365070957368,
        48.196139140605425,
        34.13808337052871,
        51.16925256313643,
        38.25575215294573,
        37.81213856269278,
        47.57521987859252,
        49.29053940722453,
        47.83697426341426,
        44.686420683236456,
        52.0414862892746,
        44.25738573575602,
        30.251236898498554,
        44.57593967964304,
        30.65378624136446,
        37.81423102701615,
        33.50857236047568,
        44.048500024967254,
        35.75809105132727,
        44.777864885773454,
        35.58599703469844,
        43.99454323786241,
        46.10369943212223,
        49.47712862480597,
        46.01999416601156,
        33.46677170014872,
        36.40852711451335,
        45.48032679921481,
        38.99349861358387,
        40.86866692610561,
        37.31500362817862,
        40.29298544697646,
        41.034077963227055,
        43.03886042717589,
        49.09106235663347,
        50.01873361811951,
        47.14150554202054,
        49.917442998592456,
        44.35158864540583,
        46.133390172950605,
        54.5652492792407,
        45.02869448187146,
        45.43052276234553,
        48.82433787173163,
        41.425008605839466,
        40.7247210620118,
        49.22111228617834,
        45.8445175504209,
        47.93365188765718,
        37.743556779363125,
        52.04354618406751,
        38.25188974247964,
        47.0268167354481,
        42.216759047158845,
        55.19365864464751,
        53.76744336230167,
        45.74159164739629,
        44.523187507808544,
        47.04694862789998,
        53.10711870328019,
        38.850248352855886,
        39.87831346595928,
        43.73099561692922,
        57.571060424257716,
        44.926069262543145,
        41.73240729424445,
        37.963439915543304,
        46.55027809356358,
        54.220742364027146,
        42.082586289396396,
        53.76824707038037,
        42.71338423703805,
        39.889555745583365,
        44.07413889383873,
        52.90414982774128,
        52.54705553586052,
        55.66519558799246,
        44.879433895787784,
        54.56239835972438,
        51.73018223194246,
        62.501383547065984,
        52.11659076177841,
        57.46086948963994,
        63.287217317768395,
        49.24684429540194,
        56.073135395153145,
        54.706885056968034,
        55.99966234841655,
        62.31576654315423,
        52.319752580437566,
        56.36294802515255,
        61.16483526249697,
        59.46335877865956,
        63.12310036302466,
        67.35207834737535,
        51.40859893846705,
        57.547800106930154,
        57.86729210643723,
        54.98115206235142,
        50.55339796930018,
        40.34601121682057,
        38.674424405831886,
        39.68729443427911,
        37.30880499082171,
        36.12153845557859,
        45.98258649828911,
        40.082737260035,
        37.569701259142064,
        44.84158787426514,
        46.32933919551165,
        37.04490812838651,
        46.63579945702993,
        45.503534487607965,
        27.27385391249547,
        36.576539562419775,
        43.48252672628699,
        36.96407775240527,
        41.932583286063306,
        41.01856005209984,
        44.50108195329706,
        42.66143967119437,
        50.08844595053587,
        56.68991840777321,
        53.769968858151614,
        50.0066178829226,
        34.0320299022753,
        48.88977811333136,
        37.37585557230584,
        50.4168440271834,
        39.5800286079444,
        52.08875926533037,
        56.465658250951606,
        52.508949901791794,
        44.93539930901365,
        52.12729940593285,
        46.76030389247808,
        44.94007235991432,
        44.104231669139025,
        45.03253606180511,
        48.29711955225675,
        49.994194010095995,
        39.876689755324136,
        46.24174887270045,
        46.612339291429926,
        55.52117456069148,
        50.04034479335483,
        48.680323317854146,
        44.2786534939289,
        42.49235327581835,
        45.210834314171606,
        43.05650307287783,
        52.65240449776506,
        43.82785938143079,
        45.86818320016935,
        49.63914004778512,
        48.45000920027199,
        46.19251544364478,
        38.031902102623874,
        44.04390855764858,
        46.82490624385995,
        47.749967417160285,
        50.651596728056376,
        45.72368215509557,
        45.47464352632419,
        43.51137510848358,
        47.708472020624235,
        54.50883342324302,
        45.050856228970645,
        51.360037281755766,
        36.53900147779019,
        52.46706435467202,
        43.77179347288947,
        52.24478180824792,
        35.2364495965294,
        48.745886772673714,
        47.85228475710226,
        43.56063204675461,
        45.018108354531364,
        41.09322131561576,
        45.655622198827835,
        43.72651203052354,
        51.164625525957135,
        43.194507956928206,
        43.14028693431564,
        51.00091880715857,
        38.184999453842984,
        42.1638868857581,
        26.6681309385946,
        43.28905240512102,
        45.10027698634367,
        41.842172661891766,
        44.081855636626024,
        39.48098748916489,
        42.73189722881747,
        43.264124794168076,
        46.3763435427462,
        40.29347117572572,
        43.96054179525967,
        39.71234858215065,
        38.351775554387444,
        41.17366706976311,
        44.13218780623368,
        38.48694640106718,
        36.73488639303106,
        38.45906063915755
      ],
      "random_effects": [
        45.9662295470969,
        47.5784768921166,
        43.97592352675497,
        39.95415071972752,
        46.11917599023715,
        48.20539706003635,
        56.982684492418265,
        40.478841865378186,
        48.13133250208332,
        46.51264614658439,
        45.96525421414758,
        40.7001360070752
      ],
      "residual_variance": 25.376508173626036,
      "random_intercept_variance": 2125.625806252831,
      "sigma": 5.037510116478779,
      "icc": 0.9882024728641947,
      "log_likelihood": -803.6695094011228,
      "aic": 1615.3390188022456,
      "df_residual": 248
    },
    "phit": {
      "coefficients": [
        1.580355911115453,
        0.2616890668208345
      ],
      "covariance": [
        [
          0.025661116627484125,
          -0.005134011493914352
        ],
        [
          -0.005134011493914353,
          0.0017209067641606709
        ]
      ],
      "std_errors": [
        0.16019087560620962,
        0.041483813278924475
      ],
      "z_statistics": [
        9.865455227302549,
        6.30822111413233
      ],
      "p_values": [
        5.876726583465406e-23,
        2.8226077735693453e-10
      ],
      "conf_int": [
        [
          1.2663875642753464,
          1.8943242579555597
        ],
        [
          0.1803822868527581,
          0.3429958467889109
        ]
      ],
      "fitted": [
        84.50316653682017,
        63.76251526349697,
        82.42772802504311,
        63.69433226874307,
        66.88855351444843,
        73.33242108341975,
        62.88626575005479,
        71.01340638899823,
        83.38642902522724,
        75.1411402569461,
        65.30149026799405,
        61.42450845096324,
        82.3425357010945,
        72.83735837360015,
        83.45575627694411,
        74.88401200832419,
        75.40992378807692,
        69.17569514732324,
        67.99230634890773,
        63.83443615584825,
        87.57482115377215,
        62.54052801794835,
        69.21030568688485,
        69.71947500106452,
        65.7853286091462,
        72.16469200673492,
        86.72038599961147,
        69.75467953869551,
        79.17773191559564,
        59.48309967240588,
        86.3942760059652,
        64.38236764538355,
        62.69717329961453,
        72.0208236128068,
        69.91269523896504,
        84.63490867641121,
        81.46532311085937,
        83.35678328648316,
        73.78497608160552,
        82.05637132315087,
        65.8685154924435,
        68.60598664129597,
        72.96687579107129,
        57.45773447018904,
        68.71534931144714,
        55.81827281754716,
        78.8947843862641,
        75.82184015637145,
        76.78367096332784,
        71.3631713738485,
        54.462784964535835,
        76.43470364824174,
        66.99838411923331,
        68.8349492633508,
        65.82450284389215,
        67.50043723766643,
        76.42153779093806,
        73.4489138209371,
        79.3192110397453,
        62.10236447864395,
        53.99891969309488,
        63.59057835917855,
        78.98065069450868,
        77.15305966821951,
        71.75028583394547,
        72.6651536853628,
        67.87260748174609,
        70.03845128766889,
        63.68002209512858,
        74.3221565538482,
        62.237379020093165,
        61.00662360551728,
        67.89182392090413,
        77.92365210589561,
        76.4954837936466,
        73.31614709143251,
        71.68216527260944,
        65.92707275632301,
        65.54429029275398,
        65.32911363375761,
        63.66344237245235,
        59.44567044848777,
        77.83073299145241,
        76.9215873451472,
        75.40078581764983,
        67.01692671078938,
        78.88448150794383,
        85.68465322760457,
        66.53083811879809,
        80.62816738433057,
        80.64045492799568,
        65.58806370396631,
        80.01965843986088,
        78.25352410244193,
        73.60461921081571,
        81.0846298064225,
        71.17528624792182,
        63.271359254907296,
        67.9264169434898,
        74.50673841542691,
        83.82595369755323,
        63.17380541312362,
        66.16020955219815,
        69.73344843265227,
        69.54527835702366,
        68.86214870697464,
        82.04808359396,
        83.7794014430163,
        78.20133663595362,
        77.12732779784857,
        78.2469897657127,
        74.23895714447312,
        85.00011896646626,
        83.78365469561226,
        79.52581077051205,
        78.7621499892207,
        69.40701282315553,
        81.2678413144263,
        80.66325816610757,
        68.10224723271992,
        80.45734152413434,
        89.13920147161735,
        89.37296316388444,
        57.70699870129246,
        80.89221482828788,
        81.71001351309363,
        89.8290937299183,
        90.31681500264824,
        89.89046717423136,
        79.00584019700693,
        89.1665490970361,
        91.14779943559968,
        77.84402214428505,
        88.66191794932152,
        81.06993191217532,
        93.59573646733745,
        83.11584923004675,
        76.87732571441853,
        86.03658412963642,
        72.48160614531307,
        74.34908555367336,
        75.05288438574365,
        85.6523923860773,
        72.049532430595,
        88.28328652324655,
        58.821830649281935,
        77.20241745919935,
        61.558547431034306,
        74.02203687452968,
        67.45830341033029,
        73.11025536701149,
        53.00810460559184,
        66.2161406063224,
        54.66725399121723,
        57.543502669744626,
        59.832933736842634,
        59.43504240873651,
        54.90430737788455,
        71.49898795254505,
        67.72130230293112,
        70.76331513863077,
        71.92476411262908,
        62.25825857932569,
        53.01628181374419,
        63.621759912266874,
        66.29440219418353,
        87.13088655140075,
        66.13441409434384,
        67.73836364375174,
        75.4787146190126,
        70.26830259984254,
        57.85555438946765,
        81.66847692954603,
        78.91648847533132,
        78.06430389400708,
        84.29857323674207,
        77.64067425106305,
        76.24638260041752,
        79.430933193126,
        75.90003309629688,
        74.36802860957131,
        66.48526014265101,
        58.80941447776243,
        80.26511008495996,
        66.79452659461202,
        68.49945213623768,
        76.05095639154335,
        82.2028972737776,
        57.2773068556377,
        81.11247158594995,
        65.1723013531025,
        82.30432282838427,
        70.88499265234606,
        68.45629287090563,
        74.60081183238488,
        65.93414307369886,
        67.70324164907305,
        68.17078676504377,
        74.42746294653242,
        59.73550609954722,
        76.64063694612334,
        65.04213070312684,
        86.54274404352809,
        68.9707375887003,
        66.09773990259183,
        73.8016787295436,
        81.9440494186708,
        82.63557205877734,
        84.91061068734885,
        71.79387910554186,
        56.32178219412488,
        72.71942079043038,
        76.3183979857224,
        57.55521693278684,
        62.565252736625816,
        60.98918985979035,
        65.77446074092437,
        72.51947240605165,
        81.19180461762097,
        67.17136744164355,
        64.8769694568308,
        81.35362216750298,
        62.43614585994777,
        76.90503289838453,
        73.24163201537525,
        68.00374218404035,
        84.92062868763276,
        67.67174625705945,
        63.335967280245846,
        81.59433540699683,
        69.84513655325,
        76.92224912135188,
        67.29900506848246,
        64.64108360183457,
        75.60985902055202,
        71.18396334465089,
        55.462280370716385,
        58.06714851828677,
        60.957238778147115,
        59.53001121295452,
        75.95179246415148,
        53.3566648318464,
        56.70859421221831,
        69.26878742479072,
        64.6823604527565,
        52.981468937552144,
        57.58594820093942,
        67.92018960588557,
        54.65124961407288,
        66.46507536812054
      ],
      "residuals": [
        -6.246166536820169,
        3.479484736503032,
        5.79527197495689,
        4.8516677312569385,
        -6.751553514448432,
        -1.1854210834197403,
        -2.531265750054793,
        -1.3434063889982326,
        -0.9444290252272509,
        -3.012140256946097,
        -3.5014902679940576,
        2.282491549036763,
        -5.950535701094509,
        4.240641626399849,
        7.581243723055891,
        -0.4270120083241977,
        0.6250762119230728,
        3.5863048526767614,
        1.1816936510922744,
        -4.78343615584825,
        4.50817884622785,
        1.8764719820516547,
        -2.1453056868848535,
        11.083524998935474,
        2.4556713908537944,
        -6.536692006734924,
        -0.48438599961146167,
        0.9303204613044898,
        0.2642680844043497,
        -1.4030996724058795,
        2.3307239940347984,
        0.48563235461644183,
        -5.060173299614533,
        3.503176387193207,
        -6.672695238965041,
        -0.49490867641121383,
        1.3276768891406334,
        -1.641783286483161,
        -8.288976081605526,
        -3.3383713231508665,
        4.0794845075564865,
        7.391013358704029,
        -0.08987579107129307,
        -1.6287344701890376,
        -6.098349311447144,
        -3.182272817547158,
        4.220215613735888,
        -9.837840156371456,
        7.193329036672168,
        -5.720171373848501,
        -6.163784964535836,
        3.5992963517582695,
        5.314615880766695,
        3.8610507366492044,
        0.7104971561078486,
        8.06556276233357,
        0.2814622090619423,
        -9.702913820937091,
        4.621788960254705,
        -9.30036447864395,
        -2.1399196930948747,
        -6.445578359178548,
        4.0943493054913205,
        -4.196059668219519,
        4.823714166054529,
        -4.368153685362799,
        4.04039251825391,
        6.149548712331111,
        9.522977904871425,
        6.065843446151803,
        -6.487379020093165,
        -3.545623605517278,
        5.526176079095876,
        -0.960652105895619,
        0.9145162063533974,
        -2.6391470914325055,
        0.3388347273905623,
        1.079927243676991,
        3.08470970724602,
        2.971886366242387,
        3.899557627547651,
        1.022329551512236,
        3.7982670085475974,
        -1.7675873451472057,
        0.014214182350173132,
        8.446073289210617,
        -1.090481507943835,
        -0.6886532276045756,
        2.705161881201917,
        -4.694167384330569,
        -5.394454927995682,
        3.101936296033685,
        -0.2746584398608718,
        1.8144758975580686,
        -8.375619210815714,
        5.924370193577502,
        -7.867286247921818,
        0.9076407450927064,
        -3.902416943489797,
        6.988261584573095,
        5.562046302446774,
        -2.463805413123616,
        -3.6822095521981524,
        -1.1584484326522642,
        4.901721642976341,
        -9.355148706974639,
        -8.327083593959998,
        -4.474401443016291,
        9.36566336404637,
        -3.279327797848566,
        -6.472989765712697,
        -10.241957144473119,
        -1.6551189664662616,
        6.0153453043877505,
        -6.1228107705120465,
        5.5628500107793,
        -5.492012823155527,
        -8.315841314426308,
        -4.131258166107571,
        4.698752767280084,
        4.341658475865671,
        7.459798528382649,
        -3.3259631638844382,
        6.35700129870753,
        3.524785171712125,
        14.295986486906372,
        -4.866093729918305,
        0.4781849973517609,
        6.304532825768632,
        -7.735840197006937,
        -0.9095490970360913,
        -2.27579943559968,
        -0.9830221442850444,
        5.333082050678485,
        -4.662931912175324,
        -0.6197364673374466,
        4.182150769953253,
        2.480674285581472,
        6.140415870363583,
        10.369393854686933,
        -5.574085553673356,
        0.5651156142563423,
        0.8846076139227108,
        -2.0015324305949918,
        -6.429286523246546,
        -0.1328306492819351,
        -1.8044174591993567,
        -0.7915474310343029,
        -3.1700368745296714,
        -4.357303410330289,
        5.503744632988514,
        -0.39610460559183736,
        -2.9091406063223957,
        4.362746008782771,
        5.850497330255372,
        -3.433933736842633,
        6.156957591263492,
        5.024692622115452,
        -13.204987952545054,
        -3.902302302931119,
        3.003684861369223,
        -3.5147641126290807,
        1.4537414206743122,
        0.5397181862558043,
        4.022240087733131,
        2.182597805816471,
        1.9571134485992445,
        8.558585905656159,
        5.638636356248256,
        1.8752853809873926,
        -14.099302599842545,
        0.7584456105323483,
        -10.755476929546035,
        2.285511524668678,
        -8.551303894007077,
        3.957426763257928,
        8.334325748936948,
        4.377617399582476,
        -3.1959331931259953,
        3.9959669037031205,
        -1.3710286095713116,
        -3.191260142651018,
        -2.4084144777624275,
        -1.4801100849599607,
        1.7844734053879705,
        3.481547863762316,
        -6.6359563915433455,
        -0.2708972737775923,
        0.09969314436230547,
        9.008528414050048,
        3.5276986468975053,
        2.167677171615722,
        -2.2339926523460605,
        -4.020292870905621,
        -1.301811832384871,
        -3.456143073698861,
        6.139758350926954,
        -2.684786765043768,
        -0.6444629465324141,
        3.126493900452779,
        1.9373630538766662,
        -0.3201307031268499,
        -8.480744043528091,
        -2.468737588700307,
        0.3122600974081706,
        1.2373212704564054,
        4.138950581329198,
        -0.24157205877733645,
        -0.4906106873488483,
        -2.4538791055418585,
        1.743217805875119,
        8.543579209569629,
        -0.9143979857224025,
        5.394783067213162,
        -9.426252736625813,
        6.501810140209649,
        -2.1934607409243654,
        6.279527593948359,
        -10.72880461762098,
        2.7806325583564444,
        1.887030543169189,
        -2.4046221675029784,
        -0.9471458599477742,
        -4.872032898384532,
        -0.309632015375243,
        -2.2387421840403476,
        5.199371312367248,
        -2.770746257059457,
        -2.8249672802458434,
        5.035664593003162,
        -2.5151365532500023,
        1.4637508786481135,
        -14.032005068482455,
        2.5889163981654377,
        4.400140979447983,
        1.1420366553491021,
        3.381719629283616,
        -1.2191485182867723,
        2.031761221852882,
        2.5639887870454814,
        5.676207535848519,
        -0.406664831846399,
        3.2604057877816928,
        -0.9877874247907101,
        -2.348360452756495,
        0.47353106244785437,
        3.4320517990605808,
        -2.2131896058855745,
        -3.9652496140728815,
        -2.2410753681205335
      ],
      "log_likelihood": -803.6695094011227,
      "aic": 1615.3390188022454,
      "df_residual": 248,
      "evaluations": 107,
      "fixed_fitted": [
        38.53693698797208,
        17.796285714648867,
        36.46149847619501,
        17.728102719894967,
        20.92232396560033,
        27.366191534571644,
        16.92003620120669,
        25.047176840150126,
        37.42019947637914,
        29.174910708097993,
        19.33526071914595,
        15.458278902115135,
        36.3763061522464,
        26.871128824752056,
        37.48952672809601,
        28.917782459476093,
        29.443694239228815,
        23.20946559847513,
        20.413829455152673,
        16.255959262093196,
        39.996344260017096,
        14.962051124193286,
        21.63182879312979,
        22.14099810730947,
        18.206851715391153,
        24.586215112979858,
        39.14190910585641,
        22.176202644940453,
        31.599255021840584,
        11.904622778650818,
        38.81579911221013,
        16.803890751628494,
        15.118696405859477,
        24.442346719051727,
        22.33421834520998,
        37.05643178265616,
        33.88684621710431,
        35.77830639272811,
        26.20649918785046,
        34.47789442939582,
        18.290038598688447,
        21.027509747540915,
        28.99095226278675,
        13.481810941904504,
        24.739425783162602,
        11.842349289262629,
        34.918860857979574,
        31.84591662808692,
        32.80774743504331,
        27.387247845563962,
        10.486861436251305,
        32.4587801199572,
        23.02246059094878,
        24.85902573506626,
        21.84857931560762,
        23.524513709381907,
        32.445614262653535,
        33.49476309955926,
        39.365060318367455,
        22.148213757266106,
        14.04476897171703,
        23.63642763780071,
        39.02649997313084,
        37.19890894684167,
        31.796135112567633,
        32.71100296398495,
        27.91845676036824,
        30.08430056629105,
        23.72587137375074,
        34.36800583247036,
        22.283228298715322,
        21.052472884139434,
        27.93767319952628,
        37.96950138451777,
        36.54133307226875,
        33.36199637005467,
        31.728014551231603,
        25.972922034945164,
        25.59013957137614,
        19.209937641832912,
        17.54426638052765,
        13.32649445656307,
        31.711556999527712,
        30.802411353222507,
        29.28160982572513,
        20.897750718864682,
        32.76530551601913,
        39.565477235679865,
        20.41166212687339,
        34.508991392405875,
        34.52127893607097,
        19.468887712041617,
        33.900482447936184,
        32.13434811051722,
        27.485443218891007,
        34.965453814497806,
        25.056110255997122,
        17.152183262982593,
        21.8072409515651,
        26.301341353656674,
        35.620556635783,
        14.968408351353382,
        17.954812490427912,
        21.52805137088204,
        21.339881295253427,
        20.656751645204398,
        33.842686532189774,
        35.57400438124607,
        29.99593957418339,
        28.92193073607833,
        30.041592703942463,
        26.033560082702884,
        36.79472190469603,
        35.57825763384202,
        31.320413708741818,
        30.556752927450464,
        21.20161576138529,
        33.062444252656064,
        32.457861104337326,
        19.896850170949676,
        32.2519444623641,
        40.93380440984711,
        41.16756610211419,
        9.501601639522226,
        32.686817766517635,
        33.50461645132339,
        32.84640923589157,
        33.33413050862152,
        32.90778268020464,
        22.023155702980212,
        32.18386460300938,
        34.16511494157296,
        20.86133765025832,
        31.6792334552948,
        24.087247418148607,
        36.613051973310725,
        26.13316473602003,
        19.89464122039182,
        29.053899635609696,
        15.498921651286345,
        17.366401059646638,
        18.07019989171693,
        28.669707892050575,
        15.066847936568273,
        31.300602029219828,
        18.342988782366767,
        36.72357559228418,
        21.079705564119138,
        33.5431950076145,
        26.97946154341512,
        32.63141350009633,
        12.529262738676668,
        25.737298739407237,
        14.188412124302063,
        17.06466080282946,
        19.35409186992747,
        18.95620054182134,
        14.425465510969381,
        31.020146085629882,
        27.24246043601596,
        30.2844732717156,
        31.445922245713916,
        21.779416712410523,
        12.537439946829023,
        23.142918045351706,
        25.815560327268372,
        38.999554047614836,
        18.003081590557922,
        19.607031139965827,
        27.34738211522668,
        22.13697009605662,
        9.724221885681727,
        33.53714442576011,
        30.7851559715454,
        29.932971390221162,
        36.16724073295615,
        29.509341747277123,
        28.1150500966316,
        31.29960068934007,
        27.768700592510953,
        26.23669610578539,
        18.353927638865088,
        12.296768329613741,
        33.752463936811274,
        20.281880446463326,
        21.98680598808899,
        29.538310243394662,
        35.690251125628905,
        10.764660707489007,
        34.59982543780126,
        18.65965520495381,
        35.79167668023558,
        24.372346504197374,
        21.94364672275693,
        28.088165684236184,
        19.421496925550173,
        21.19059550092436,
        21.65814061689509,
        27.91481679838372,
        13.222859951398531,
        30.127990797974647,
        18.529484554978147,
        40.0300978953794,
        22.458091440551605,
        19.585093754443136,
        27.2890325813949,
        35.431403270522104,
        36.67031784300288,
        38.94535647157437,
        25.82862488976739,
        10.356527978350409,
        26.754166574655898,
        30.353143769947927,
        11.589962717012371,
        16.599998520851344,
        15.023935644015877,
        19.809206525149893,
        26.55421819027717,
        35.2265504018465,
        21.20611322586909,
        18.911715241056335,
        35.38836795172851,
        16.4708916441733,
        30.93977868261006,
        27.276377799600766,
        22.038487968265876,
        38.95537447185828,
        21.70649204128498,
        17.370713064471374,
        35.62908119122237,
        29.145000544626754,
        36.222113112728636,
        26.59886905985921,
        23.940947593211327,
        34.90972301192877,
        30.48382733602765,
        14.762144362093139,
        17.36701250966352,
        20.25710276952387,
        18.829875204331277,
        35.251656455528234,
        12.656528823223155,
        16.00845820359506,
        28.56865141616747,
        23.98222444413325,
        12.281332928928897,
        16.885812192316173,
        27.220053597262325,
        13.951113605449631,
        25.76493935949729
      ],
      "marginal_residuals": [
        39.72006301202793,
        49.44571428535114,
        51.76150152380499,
        50.81789728010504,
        39.21467603439967,
        44.780808465428365,
        43.434963798793305,
        44.62282315984987,
        45.021800523620854,
        42.95408929190201,
        42.46473928085405,
        48.24872109788487,
        40.015693847753596,
        50.20687117524795,
        53.547473271903996,
        45.5392175405239,
        46.59130576077118,
        49.552534401524866,
        48.760170544847334,
        42.7950407379068,
        52.0866557399829,
        49.454948875806714,
        45.433171206870206,
        58.662001892690526,
        50.03414828460885,
        41.04178488702014,
        47.09409089414359,
        48.50879735505955,
        47.84274497815941,
        46.17537722134918,
        49.909200887789865,
        48.0641092483715,
        42.51830359414052,
        51.081653280948274,
        40.90578165479002,
        47.08356821734384,
        48.90615378289569,
        45.93669360727189,
        39.289500812149534,
        44.240105570604186,
        51.657961401311546,
        54.96949025245908,
        43.88604773721325,
        42.347189058095495,
        37.877574216837395,
        40.793650710737374,
        48.19613914202042,
        34.138083371913076,
        51.16925256495669,
        38.25575215443604,
        37.8121385637487,
        47.57521988004281,
        49.29053940905122,
        47.83697426493374,
        44.686420684392374,
        52.041486290618096,
        44.25738573734647,
        30.251236900440745,
        44.57593968163255,
        30.653786242733894,
        37.814231028282975,
        33.50857236219929,
        44.04850002686916,
        35.758091053158324,
        44.777864887432365,
        35.585997036015044,
        43.99454323963175,
        46.103699433708954,
        49.47712862624927,
        46.019994167529646,
        33.46677170128468,
        36.408527115860565,
        45.480326800473726,
        38.993498615482224,
        40.86866692773125,
        37.31500362994534,
        40.2929854487684,
        41.03407796505484,
        43.03886042862386,
        49.09106235816709,
        50.01873361947236,
        47.141505543436935,
        49.91744300047229,
        44.351588646777486,
        46.13339017427488,
        54.56524928113531,
        45.028694483980864,
        45.43052276432013,
        48.82433787312661,
        41.42500860759412,
        40.724721063929024,
        49.22111228795838,
        45.84451755206382,
        47.933651889482775,
        37.74355678110899,
        52.043546185502194,
        38.25188974400288,
        47.02681673701741,
        42.2167590484349,
        55.19365864634333,
        53.76744336421701,
        45.74159164864662,
        44.52318750957209,
        47.04694862911796,
        53.107118704746576,
        38.850248354795596,
        39.87831346781023,
        43.73099561875394,
        57.571060425816604,
        44.92606926392167,
        41.73240729605754,
        37.963439917297116,
        46.550278095303966,
        54.220742366157985,
        42.08258629125819,
        53.76824707254954,
        42.71338423861471,
        39.889555747343934,
        44.07413889566267,
        52.904149829050326,
        52.547055537635906,
        55.66519559015289,
        44.879433897885804,
        54.562398360477765,
        51.73018223348237,
        62.50138354867661,
        52.11659076410842,
        57.46086949137848,
        63.28721731979535,
        49.246844297019784,
        56.07313539699062,
        54.70688505842704,
        55.99966234974168,
        62.315766544705205,
        52.31975258185139,
        56.362948026689274,
        61.16483526397997,
        59.463358779608186,
        63.12310036439031,
        67.35207834871366,
        51.40859894035337,
        57.54780010828307,
        57.86729210794943,
        54.98115206343173,
        50.55339797078017,
        40.34601121763323,
        38.67442440771582,
        39.687294435880865,
        37.308804992385504,
        36.12153845658488,
        45.982586499903675,
        40.08273726132333,
        37.569701260592765,
        44.84158787569794,
        46.32933919717054,
        37.04490813007253,
        46.63579945817866,
        45.50353448903062,
        27.273853914370115,
        36.57653956398404,
        43.4825267282844,
        36.96407775428608,
        41.93258328758948,
        41.01856005317097,
        44.5010819546483,
        42.66143967273163,
        50.08844595238516,
        56.68991840944207,
        53.76996886003417,
        50.00661788477332,
        34.03202990394338,
        48.88977811431827,
        37.375855574239885,
        50.4168440284546,
        39.58002860977884,
        52.08875926704385,
        56.465658252722875,
        52.508949903368396,
        44.93539931065993,
        52.12729940748905,
        46.76030389421461,
        44.94007236113491,
        44.10423167038626,
        45.03253606318872,
        48.29711955353667,
        49.994194011911006,
        39.876689756605344,
        46.2417488743711,
        46.612339292510995,
        55.52117456219874,
        50.040344795046195,
        48.68032331976441,
        44.27865349580262,
        42.492353277243076,
        45.21083431576382,
        43.05650307444983,
        52.652404499075644,
        43.827859383104915,
        45.86818320161628,
        49.63914004860147,
        48.450009202025356,
        46.19251544502185,
        38.0319021046206,
        44.04390855944839,
        46.82490624555686,
        47.7499674186051,
        50.651596729477895,
        45.72368215699713,
        45.47464352842563,
        43.51137511023261,
        47.70847202164959,
        54.50883342534411,
        45.05085623005207,
        51.36003728298763,
        36.53900147914866,
        52.46706435598412,
        43.771793474850114,
        52.24478180972284,
        35.23644959815349,
        48.74588677413091,
        47.85228475894366,
        43.560632048271486,
        45.0181083558267,
        41.09322131738994,
        45.655622200399236,
        43.726512031734124,
        51.16462552814173,
        43.194507958715015,
        43.14028693552863,
        51.00091880877763,
        38.184999455373244,
        42.16388688727136,
        26.66813094014079,
        43.28905240678868,
        45.100276988071236,
        41.84217266397234,
        44.08185563790686,
        39.480987490336474,
        42.73189723047613,
        43.26412479566872,
        46.376343544471766,
        40.29347117677685,
        43.96054179640494,
        39.71234858383254,
        38.35177555586675,
        41.1736670710711,
        44.13218780768383,
        38.48694640273767,
        36.73488639455037,
        38.45906064050271
      ],
      "random_effects": [
        45.966229548848105,
        47.57847689375506,
        43.97592352828453,
        39.95415072137784,
        46.1191759919247,
        48.205397061770235,
        56.98268449402672,
        40.47884186691517,
        48.13133250378592,
        46.51264614814869,
        45.96525421577447,
        40.70013600862325
      ],
      "group_sizes": [
        18,
        24,
        15,
        22,
        20,
        27,
        19,
        21,
        16,
        25,
        23,
        20
      ],
      "n_groups": 12,
      "group_labels": [
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12
      ],
      "residual_variance": 25.376508171306615,
      "random_intercept_variance": 2125.6258101087055,
      "sigma": 5.037510116248564,
      "icc": 0.9882024728864085,
      "boundary": false,
      "method": "ML",
      "converged": true,
      "n_input": 250,
      "n_observations": 250,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119,
        120,
        121,
        122,
        123,
        124,
        125,
        126,
        127,
        128,
        129,
        130,
        131,
        132,
        133,
        134,
        135,
        136,
        137,
        138,
        139,
        140,
        141,
        142,
        143,
        144,
        145,
        146,
        147,
        148,
        149,
        150,
        151,
        152,
        153,
        154,
        155,
        156,
        157,
        158,
        159,
        160,
        161,
        162,
        163,
        164,
        165,
        166,
        167,
        168,
        169,
        170,
        171,
        172,
        173,
        174,
        175,
        176,
        177,
        178,
        179,
        180,
        181,
        182,
        183,
        184,
        185,
        186,
        187,
        188,
        189,
        190,
        191,
        192,
        193,
        194,
        195,
        196,
        197,
        198,
        199,
        200,
        201,
        202,
        203,
        204,
        205,
        206,
        207,
        208,
        209,
        210,
        211,
        212,
        213,
        214,
        215,
        216,
        217,
        218,
        219,
        220,
        221,
        222,
        223,
        224,
        225,
        226,
        227,
        228,
        229,
        230,
        231,
        232,
        233,
        234,
        235,
        236,
        237,
        238,
        239,
        240,
        241,
        242,
        243,
        244,
        245,
        246,
        247,
        248,
        249
      ],
      "dropped_rows": []
    },
    "python_diagnostics": {
      "backend": "statsmodels MixedLM (ML)",
      "warnings": [],
      "covariance_convention": "plug-in GLS, matching lme4"
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "Python": 2.8797579876282953e-09,
        "phit": 2.8121027728644776e-09
      },
      "covariance": {
        "Python": 9.118761301607492e-11,
        "phit": 8.904529544273565e-11
      },
      "std_errors": {
        "Python": 2.8462174284094033e-10,
        "phit": 2.7793498058592547e-10
      },
      "z_statistics": {
        "Python": 3.5505649975675624e-08,
        "phit": 3.467149944924586e-08
      },
      "p_values": {
        "Python": 4.8440078363259206e-17,
        "phit": 4.729512070535987e-17
      },
      "conf_int": {
        "Python": 3.4376066437857844e-09,
        "phit": 3.3568454682608717e-09
      },
      "fixed_fitted": {
        "Python": 9.917567211914502e-08,
        "phit": 9.68456603800405e-08
      },
      "fitted": {
        "Python": 4.173427470277602e-08,
        "phit": 4.0753775465418585e-08
      },
      "residuals": {
        "Python": 4.173427470277602e-08,
        "phit": 4.0753775465418585e-08
      },
      "marginal_residuals": {
        "Python": 9.917567211914502e-08,
        "phit": 9.68456603800405e-08
      },
      "random_effects": {
        "Python": 7.453904515841714e-08,
        "phit": 7.27878415318628e-08
      },
      "residual_variance": {
        "Python": 9.872439221680906e-08,
        "phit": 9.640497111718105e-08
      },
      "random_intercept_variance": {
        "Python": 0.0001641136273065058,
        "phit": 0.00016025775266825804
      },
      "sigma": {
        "Python": 9.798927891324638e-09,
        "phit": 9.568712933116785e-09
      },
      "icc": {
        "Python": 9.454635963024316e-10,
        "phit": 9.232498099365216e-10
      },
      "log_likelihood": {
        "Python": 0.0,
        "phit": 1.1368683772161603e-13
      },
      "aic": {
        "Python": 0.0,
        "phit": 2.2737367544323206e-13
      },
      "df_residual": {
        "Python": 0.0,
        "phit": 0.0
      }
    },
    "tolerance": {
      "absolute": 1e-07,
      "relative": 1e-06
    },
    "extension_sha256": "2105dd47a15f21b0da6ae81a23461ef385285517e1af0519a0bb22238bc3ffc6"
  },
  {
    "name": "intercept_only",
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "lme4": "2.0.6",
      "statsmodels": "0.15.0",
      "PHP": "8.5.10",
      "Python": "3.14.7"
    },
    "R": {
      "coefficients": [
        71.94807808871924
      ],
      "covariance": [
        [
          2.1259779362403366
        ]
      ],
      "std_errors": [
        1.4580733644917654
      ],
      "z_statistics": [
        49.34462136190101
      ],
      "p_values": [
        0
      ],
      "conf_int": [
        [
          69.09030680749824,
          74.80584936994025
        ]
      ],
      "fixed_fitted": [
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924,
        71.94807808871924
      ],
      "fitted": [
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.73682303590573,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        72.7678634788757,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.61110503272567,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        69.96968505421752,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        72.80188561710925,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        76.24574483116989,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        81.4313429246453,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        65.32560983605146,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        74.29988314157583,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.57891284431334,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        71.30169784469633,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231,
        65.30638342334231
      ],
      "residuals": [
        5.520176964094276,
        -5.494823035905725,
        15.48617696409427,
        -4.190823035905723,
        -12.599823035905729,
        -0.5898230359057237,
        -12.381823035905732,
        -3.0668230359057276,
        9.705176964094264,
        -0.6078230359057244,
        -10.936823035905732,
        -9.029823035905729,
        3.6551769640942666,
        4.341176964094274,
        18.300176964094277,
        1.7201769640942643,
        3.2981769640942673,
        0.02517696409427117,
        -3.59386347887569,
        -13.716863478875695,
        19.315136521124302,
        -8.350863478875695,
        -5.702863478875699,
        8.0351365211243,
        -4.526863478875697,
        -7.1398634788756965,
        13.468136521124308,
        -2.0828634788756943,
        6.6741365211242965,
        -14.687863478875698,
        15.957136521124298,
        -7.899863478875702,
        -15.130863478875696,
        2.7561365211243043,
        -9.527863478875695,
        11.372136521124304,
        10.02513652112431,
        8.947136521124307,
        -7.2718634788757015,
        5.950136521124307,
        -2.8198634788757033,
        3.2291365211243033,
        3.2658949672743205,
        -13.782105032725674,
        -6.9941050327256775,
        -16.975105032725672,
        13.50389496727432,
        -3.62710503272568,
        14.365894967274329,
        -3.968105032725674,
        -21.312105032725675,
        10.422894967274331,
        2.7018949672743275,
        3.084894967274323,
        -3.0761050327256783,
        5.954894967274328,
        7.091894967274328,
        -6.223685054217519,
        13.971314945782481,
        -17.16768505421752,
        -18.11068505421752,
        -12.824685054217518,
        13.105314945782482,
        2.9873149457824724,
        6.604314945782477,
        -1.6726850542175242,
        1.9433149457824754,
        6.218314945782481,
        3.2333149457824817,
        10.418314945782484,
        -14.219685054217521,
        -12.508685054217523,
        3.448314945782485,
        6.993314945782473,
        7.440314945782475,
        0.7073149457824854,
        2.0513149457824795,
        -2.9626850542175163,
        -1.3406850542175164,
        -4.5008856171092475,
        -5.238885617109247,
        -12.333885617109246,
        8.827114382890755,
        2.352114382890747,
        2.613114382890757,
        2.6611143828907444,
        4.9921143828907475,
        12.194114382890746,
        -3.5658856171092452,
        3.132114382890748,
        2.4441143828907457,
        -4.111885617109252,
        6.943114382890755,
        7.266114382890748,
        -7.57288561710925,
        14.207114382890751,
        -9.49388561710925,
        -8.622885617109247,
        -8.777885617109249,
        5.249255168830118,
        13.142255168830118,
        -15.535744831169886,
        -13.767744831169885,
        -7.670744831169884,
        -1.7987448311698842,
        -16.73874483116989,
        -2.5247448311698832,
        3.05925516883012,
        11.321255168830106,
        -2.397744831169888,
        -4.471744831169886,
        -12.248744831169887,
        7.099255168830112,
        13.55325516883012,
        -2.842744831169881,
        8.079255168830116,
        -12.330744831169888,
        -3.2937448311698887,
        0.2862551688301096,
        -3.444744831169885,
        8.55325516883012,
        20.353255168830117,
        9.80125516883011,
        -12.181744831169894,
        8.171255168830115,
        19.760255168830113,
        3.531657075354687,
        9.363657075354695,
        14.763657075354686,
        -10.16134292464531,
        6.825657075354698,
        7.440657075354693,
        -4.570342924645303,
        12.563657075354698,
        -5.02434292464531,
        11.544657075354692,
        5.866657075354695,
        -2.073342924645303,
        10.7456570753547,
        1.4196570753546922,
        -12.656342924645301,
        -5.813342924645312,
        5.105657075354699,
        -11.383342924645305,
        0.4226570753546923,
        -6.636609836051456,
        10.07239016394854,
        -4.558609836051453,
        5.526390163948548,
        -2.2246098360514566,
        13.288390163948549,
        -12.713609836051454,
        -2.0186098360514535,
        -6.2956098360514545,
        -1.9316098360514573,
        -8.926609836051455,
        0.2663901639485431,
        -5.396609836051454,
        -7.031609836051459,
        -1.506609836051453,
        8.44139016394854,
        3.084390163948541,
        -1.6136098360514524,
        -11.769609836051458,
        2.31839016394855,
        3.151390163948548,
        14.78811685842416,
        0.39311685842416466,
        -0.9228831415758378,
        3.054116858424166,
        -18.130883141575836,
        -15.685883141575836,
        -3.3868831415758365,
        6.902116858424165,
        -4.786883141575828,
        13.956116858424167,
        11.675116858424161,
        6.324116858424162,
        1.9351168584241663,
        5.596116858424168,
        -1.3028831415758333,
        -11.005883141575836,
        -15.177912844313333,
        7.20608715568666,
        -2.999912844313343,
        0.4020871556866581,
        -2.16391284431333,
        10.353087155686666,
        -14.201912844313334,
        18.54208715568666,
        -2.8789128443133336,
        12.893087155686658,
        -2.92791284431334,
        -7.142912844313329,
        1.7200871556866701,
        -9.100912844313335,
        2.264087155686667,
        -6.092912844313332,
        2.204087155686665,
        -8.716912844313335,
        6.9990871556866665,
        -6.856912844313342,
        6.483087155686661,
        -5.076912844313341,
        -5.16891284431334,
        3.460087155686665,
        14.504087155686662,
        11.09230215530367,
        13.118302155303667,
        -1.9616978446963316,
        -13.236697844696337,
        9.96130215530367,
        4.102302155303661,
        -8.351697844696332,
        -18.162697844696332,
        -3.8106978446963353,
        -7.720697844696332,
        7.497302155303672,
        -0.8386978446963411,
        -1.3496978446963368,
        -4.537697844696339,
        7.647302155303663,
        -9.812697844696338,
        0.7313021553036663,
        1.6303021553036672,
        -5.536697844696334,
        18.81830215530367,
        -6.400697844696339,
        -10.790697844696332,
        15.32830215530366,
        2.0236165766576875,
        13.079616576657685,
        -12.039383423342308,
        1.9236165766576931,
        14.703616576657694,
        7.019616576657683,
        -6.46238342334231,
        -8.458383423342312,
        -2.3173834233423136,
        -3.2123834233423096,
        16.32161657665769,
        -12.356383423342308,
        -5.33738342334231,
        2.974616576657695,
        -2.9723834233423077,
        -11.851383423342313,
        -4.28838342334231,
        0.4006165766576828,
        -14.620383423342311,
        -1.082383423342307
      ],
      "marginal_residuals": [
        6.308921911280763,
        -4.706078088719238,
        16.274921911280757,
        -3.402078088719236,
        -11.811078088719242,
        0.1989219112807632,
        -11.593078088719245,
        -2.2780780887192407,
        10.49392191128075,
        0.18092191128076252,
        -10.148078088719245,
        -8.241078088719242,
        4.4439219112807535,
        5.129921911280761,
        19.088921911280764,
        2.5089219112807513,
        4.086921911280754,
        0.8139219112807581,
        -2.774078088719236,
        -12.89707808871924,
        20.134921911280756,
        -7.531078088719241,
        -4.883078088719245,
        8.854921911280755,
        -3.7070780887192427,
        -6.320078088719242,
        14.287921911280762,
        -1.26307808871924,
        7.493921911280751,
        -13.868078088719244,
        16.776921911280752,
        -7.080078088719247,
        -14.311078088719242,
        3.5759219112807585,
        -8.70807808871924,
        12.191921911280758,
        10.844921911280764,
        9.766921911280761,
        -6.452078088719247,
        6.769921911280761,
        -2.000078088719249,
        4.0489219112807575,
        0.928921911280753,
        -16.11907808871924,
        -9.331078088719245,
        -19.31207808871924,
        11.166921911280753,
        -5.964078088719248,
        12.028921911280761,
        -6.305078088719242,
        -23.649078088719243,
        8.085921911280764,
        0.36492191128076,
        0.7479219112807556,
        -5.413078088719246,
        3.61792191128076,
        4.754921911280761,
        -8.20207808871924,
        11.99292191128076,
        -19.146078088719243,
        -20.08907808871924,
        -14.80307808871924,
        11.12692191128076,
        1.0089219112807513,
        4.625921911280756,
        -3.6510780887192453,
        -0.03507808871924567,
        4.23992191128076,
        1.2549219112807606,
        8.439921911280763,
        -16.198078088719242,
        -14.487078088719244,
        1.469921911280764,
        5.0149219112807515,
        5.461921911280754,
        -1.2710780887192357,
        0.07292191128075842,
        -4.941078088719237,
        -3.3190780887192375,
        -3.6470780887192404,
        -4.38507808871924,
        -11.480078088719239,
        9.680921911280763,
        3.205921911280754,
        3.466921911280764,
        3.5149219112807515,
        5.845921911280755,
        13.047921911280753,
        -2.712078088719238,
        3.985921911280755,
        3.2979219112807527,
        -3.2580780887192446,
        7.796921911280762,
        8.119921911280755,
        -6.719078088719243,
        15.060921911280758,
        -8.640078088719243,
        -7.76907808871924,
        -7.9240780887192415,
        9.546921911280762,
        17.439921911280763,
        -11.238078088719242,
        -9.47007808871924,
        -3.3730780887192395,
        2.4989219112807604,
        -12.441078088719244,
        1.7729219112807613,
        7.3569219112807644,
        15.61892191128075,
        1.8999219112807566,
        -0.17407808871924146,
        -7.9510780887192425,
        11.396921911280756,
        17.850921911280764,
        1.4549219112807634,
        12.37692191128076,
        -8.033078088719243,
        1.0039219112807558,
        4.583921911280754,
        0.8529219112807596,
        12.850921911280764,
        24.65092191128076,
        14.098921911280755,
        -7.884078088719249,
        12.46892191128076,
        24.057921911280758,
        13.014921911280751,
        18.84692191128076,
        24.24692191128075,
        -0.6780780887192464,
        16.308921911280763,
        16.923921911280758,
        4.912921911280762,
        22.046921911280762,
        4.458921911280754,
        21.027921911280757,
        15.34992191128076,
        7.409921911280762,
        20.228921911280764,
        10.902921911280757,
        -3.1730780887192367,
        3.6699219112807526,
        14.588921911280764,
        -1.9000780887192406,
        9.905921911280757,
        -13.259078088719242,
        3.4499219112807538,
        -11.18107808871924,
        -1.0960780887192385,
        -8.847078088719243,
        6.665921911280762,
        -19.33607808871924,
        -8.64107808871924,
        -12.918078088719241,
        -8.554078088719244,
        -15.549078088719241,
        -6.356078088719244,
        -12.01907808871924,
        -13.654078088719245,
        -8.12907808871924,
        1.8189219112807535,
        -3.538078088719246,
        -8.236078088719239,
        -18.392078088719245,
        -4.304078088719237,
        -3.4710780887192385,
        17.13992191128075,
        2.7449219112807555,
        1.428921911280753,
        5.405921911280757,
        -15.779078088719245,
        -13.334078088719245,
        -1.0350780887192457,
        9.253921911280756,
        -2.435078088719237,
        16.307921911280758,
        14.026921911280752,
        8.675921911280753,
        4.286921911280757,
        7.947921911280758,
        1.0489219112807575,
        -8.654078088719245,
        -15.547078088719239,
        6.836921911280754,
        -3.369078088719249,
        0.03292191128075217,
        -2.533078088719236,
        9.98392191128076,
        -14.57107808871924,
        18.172921911280753,
        -3.2480780887192395,
        12.523921911280752,
        -3.297078088719246,
        -7.512078088719235,
        1.3509219112807642,
        -9.47007808871924,
        1.8949219112807612,
        -6.462078088719238,
        1.8349219112807589,
        -9.08607808871924,
        6.629921911280761,
        -7.226078088719248,
        6.113921911280755,
        -5.446078088719247,
        -5.538078088719246,
        3.090921911280759,
        14.134921911280756,
        10.445921911280763,
        12.47192191128076,
        -2.608078088719239,
        -13.883078088719245,
        9.314921911280763,
        3.455921911280754,
        -8.99807808871924,
        -18.80907808871924,
        -4.457078088719243,
        -8.36707808871924,
        6.850921911280764,
        -1.4850780887192485,
        -1.9960780887192442,
        -5.184078088719247,
        7.000921911280756,
        -10.459078088719245,
        0.08492191128075888,
        0.9839219112807598,
        -6.183078088719242,
        18.171921911280762,
        -7.047078088719246,
        -11.43707808871924,
        14.681921911280753,
        -4.618078088719244,
        6.437921911280753,
        -18.68107808871924,
        -4.718078088719238,
        8.061921911280763,
        0.37792191128075103,
        -13.104078088719241,
        -15.100078088719243,
        -8.959078088719245,
        -9.854078088719241,
        9.679921911280758,
        -18.99807808871924,
        -11.979078088719241,
        -3.6670780887192365,
        -9.61407808871924,
        -18.493078088719244,
        -10.930078088719242,
        -6.241078088719249,
        -21.262078088719242,
        -7.724078088719239
      ],
      "random_effects": [
        0.7887449471864836,
        0.8197853901564481,
        -2.3369730559935706,
        -1.9783930345017258,
        0.8538075283900023,
        4.297666742450651,
        9.483264835926061,
        -6.622468252667788,
        2.351805052856593,
        -0.36916524440590126,
        -0.6463802440229112,
        -6.641694665376938
      ],
      "residual_variance": 85.24170913677762,
      "random_intercept_variance": 21.32255475953557,
      "sigma": 9.232643669977609,
      "icc": 0.20009104346915374,
      "log_likelihood": -921.3206334405859,
      "aic": 1848.6412668811718,
      "df_residual": 249
    },
    "Python": {
      "coefficients": [
        71.94807808865338
      ],
      "covariance": [
        [
          2.1259779704637385
        ]
      ],
      "std_errors": [
        1.4580733762275953
      ],
      "z_statistics": [
        49.34462096468784
      ],
      "p_values": [
        0.0
      ],
      "conf_int": [
        [
          69.09030678443057,
          74.80584939287618
        ]
      ],
      "fixed_fitted": [
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338,
        71.94807808865338
      ],
      "fitted": [
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.73682303879136,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        72.76786348123252,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.61110502277072,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        69.9696850480576,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        72.80188561997349,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        76.24574484236571,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        81.43134295795768,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        65.32560981463166,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        74.29988315106658,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.57891284327543,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        71.30169784275174,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519,
        65.30638340096519
      ],
      "residuals": [
        5.520176961208648,
        -5.494823038791353,
        15.486176961208642,
        -4.1908230387913505,
        -12.599823038791357,
        -0.5898230387913515,
        -12.38182303879136,
        -3.0668230387913553,
        9.705176961208636,
        -0.6078230387913521,
        -10.93682303879136,
        -9.029823038791356,
        3.655176961208639,
        4.341176961208646,
        18.30017696120865,
        1.7201769612086366,
        3.2981769612086396,
        0.025176961208643434,
        -3.5938634812325176,
        -13.716863481232522,
        19.315136518767474,
        -8.350863481232523,
        -5.7028634812325265,
        8.035136518767473,
        -4.526863481232525,
        -7.139863481232524,
        13.46813651876748,
        -2.082863481232522,
        6.674136518767469,
        -14.687863481232526,
        15.95713651876747,
        -7.899863481232529,
        -15.130863481232524,
        2.7561365187674767,
        -9.527863481232522,
        11.372136518767476,
        10.025136518767482,
        8.94713651876748,
        -7.271863481232529,
        5.950136518767479,
        -2.819863481232531,
        3.2291365187674756,
        3.26589497722928,
        -13.782105022770715,
        -6.994105022770718,
        -16.975105022770713,
        13.50389497722928,
        -3.6271050227707207,
        14.365894977229289,
        -3.9681050227707146,
        -21.312105022770716,
        10.42289497722929,
        2.701894977229287,
        3.0848949772292826,
        -3.0761050227707187,
        5.954894977229287,
        7.091894977229288,
        -6.223685048057597,
        13.971314951942404,
        -17.1676850480576,
        -18.110685048057597,
        -12.824685048057596,
        13.105314951942404,
        2.9873149519423947,
        6.604314951942399,
        -1.6726850480576019,
        1.9433149519423978,
        6.2183149519424035,
        3.233314951942404,
        10.418314951942406,
        -14.219685048057599,
        -12.5086850480576,
        3.4483149519424074,
        6.993314951942395,
        7.440314951942398,
        0.7073149519424078,
        2.051314951942402,
        -2.962685048057594,
        -1.340685048057594,
        -4.500885619973488,
        -5.2388856199734875,
        -12.333885619973486,
        8.827114380026515,
        2.3521143800265065,
        2.6131143800265164,
        2.661114380026504,
        4.992114380026507,
        12.194114380026505,
        -3.5658856199734856,
        3.1321143800265077,
        2.4441143800265053,
        -4.111885619973492,
        6.943114380026515,
        7.266114380026508,
        -7.572885619973491,
        14.20711438002651,
        -9.49388561997349,
        -8.622885619973488,
        -8.777885619973489,
        5.249255157634295,
        13.142255157634295,
        -15.535744842365709,
        -13.767744842365708,
        -7.670744842365707,
        -1.798744842365707,
        -16.738744842365712,
        -2.524744842365706,
        3.059255157634297,
        11.321255157634283,
        -2.397744842365711,
        -4.471744842365709,
        -12.24874484236571,
        7.099255157634289,
        13.553255157634297,
        -2.842744842365704,
        8.079255157634293,
        -12.33074484236571,
        -3.2937448423657116,
        0.28625515763428666,
        -3.444744842365708,
        8.553255157634297,
        20.353255157634294,
        9.801255157634287,
        -12.181744842365717,
        8.171255157634292,
        19.76025515763429,
        3.531657042042312,
        9.36365704204232,
        14.763657042042311,
        -10.161342957957686,
        6.825657042042323,
        7.440657042042318,
        -4.570342957957678,
        12.563657042042323,
        -5.0243429579576855,
        11.544657042042317,
        5.86665704204232,
        -2.073342957957678,
        10.745657042042325,
        1.4196570420423171,
        -12.656342957957676,
        -5.813342957957687,
        5.105657042042324,
        -11.38334295795768,
        0.42265704204231724,
        -6.636609814631662,
        10.072390185368334,
        -4.558609814631659,
        5.526390185368342,
        -2.2246098146316626,
        13.288390185368343,
        -12.71360981463166,
        -2.0186098146316596,
        -6.295609814631661,
        -1.9316098146316634,
        -8.92660981463166,
        0.26639018536833703,
        -5.39660981463166,
        -7.031609814631665,
        -1.506609814631659,
        8.441390185368334,
        3.084390185368335,
        -1.6136098146316584,
        -11.769609814631664,
        2.3183901853683437,
        3.151390185368342,
        14.788116848933413,
        0.3931168489334169,
        -0.9228831510665856,
        3.0541168489334183,
        -18.130883151066584,
        -15.685883151066584,
        -3.386883151066584,
        6.902116848933417,
        -4.786883151066576,
        13.95611684893342,
        11.675116848933413,
        6.324116848933414,
        1.9351168489334185,
        5.59611684893342,
        -1.302883151066581,
        -11.005883151066584,
        -15.177912843275429,
        7.206087156724564,
        -2.999912843275439,
        0.4020871567245621,
        -2.163912843275426,
        10.35308715672457,
        -14.20191284327543,
        18.542087156724563,
        -2.8789128432754296,
        12.893087156724562,
        -2.927912843275436,
        -7.142912843275425,
        1.7200871567245741,
        -9.100912843275431,
        2.264087156724571,
        -6.092912843275428,
        2.204087156724569,
        -8.71691284327543,
        6.9990871567245705,
        -6.856912843275438,
        6.483087156724565,
        -5.076912843275437,
        -5.168912843275436,
        3.460087156724569,
        14.504087156724566,
        11.09230215724827,
        13.118302157248266,
        -1.9616978427517324,
        -13.236697842751738,
        9.96130215724827,
        4.1023021572482605,
        -8.351697842751733,
        -18.162697842751733,
        -3.810697842751736,
        -7.720697842751733,
        7.497302157248271,
        -0.838697842751742,
        -1.3496978427517377,
        -4.53769784275174,
        7.647302157248262,
        -9.812697842751739,
        0.7313021572482654,
        1.6303021572482663,
        -5.536697842751735,
        18.81830215724827,
        -6.40069784275174,
        -10.790697842751733,
        15.32830215724826,
        2.02361659903481,
        13.079616599034807,
        -12.039383400965185,
        1.9236165990348155,
        14.703616599034817,
        7.019616599034805,
        -6.462383400965187,
        -8.45838340096519,
        -2.3173834009651912,
        -3.2123834009651873,
        16.32161659903481,
        -12.356383400965186,
        -5.337383400965187,
        2.9746165990348175,
        -2.9723834009651853,
        -11.85138340096519,
        -4.288383400965188,
        0.4006165990348052,
        -14.620383400965189,
        -1.0823834009651847
      ],
      "marginal_residuals": [
        6.30892191134663,
        -4.706078088653371,
        16.274921911346624,
        -3.4020780886533686,
        -11.811078088653375,
        0.1989219113466305,
        -11.593078088653378,
        -2.2780780886533734,
        10.493921911346618,
        0.18092191134662983,
        -10.148078088653378,
        -8.241078088653374,
        4.443921911346621,
        5.129921911346628,
        19.08892191134663,
        2.5089219113466186,
        4.0869219113466215,
        0.8139219113466254,
        -2.7740780886533685,
        -12.897078088653373,
        20.134921911346623,
        -7.5310780886533735,
        -4.883078088653377,
        8.854921911346622,
        -3.7070780886533754,
        -6.320078088653375,
        14.28792191134663,
        -1.2630780886533728,
        7.493921911346618,
        -13.868078088653377,
        16.77692191134662,
        -7.08007808865338,
        -14.311078088653375,
        3.575921911346626,
        -8.708078088653373,
        12.191921911346626,
        10.844921911346631,
        9.766921911346628,
        -6.45207808865338,
        6.7699219113466285,
        -2.0000780886533818,
        4.048921911346625,
        0.9289219113466203,
        -16.119078088653374,
        -9.331078088653378,
        -19.312078088653372,
        11.16692191134662,
        -5.96407808865338,
        12.028921911346629,
        -6.305078088653374,
        -23.649078088653376,
        8.085921911346631,
        0.3649219113466273,
        0.7479219113466229,
        -5.4130780886533785,
        3.6179219113466274,
        4.754921911346628,
        -8.202078088653373,
        11.992921911346627,
        -19.146078088653375,
        -20.089078088653373,
        -14.803078088653372,
        11.126921911346628,
        1.0089219113466186,
        4.625921911346623,
        -3.651078088653378,
        -0.03507808865337836,
        4.239921911346627,
        1.254921911346628,
        8.43992191134663,
        -16.198078088653375,
        -14.487078088653377,
        1.4699219113466313,
        5.014921911346619,
        5.4619219113466215,
        -1.2710780886533684,
        0.07292191134662573,
        -4.94107808865337,
        -3.31907808865337,
        -3.647078088653373,
        -4.385078088653373,
        -11.480078088653372,
        9.68092191134663,
        3.2059219113466213,
        3.466921911346631,
        3.514921911346619,
        5.845921911346622,
        13.04792191134662,
        -2.712078088653371,
        3.9859219113466224,
        3.29792191134662,
        -3.2580780886533773,
        7.7969219113466295,
        8.119921911346623,
        -6.719078088653376,
        15.060921911346625,
        -8.640078088653375,
        -7.769078088653373,
        -7.924078088653374,
        9.54692191134663,
        17.43992191134663,
        -11.238078088653374,
        -9.470078088653374,
        -3.373078088653372,
        2.4989219113466277,
        -12.441078088653377,
        1.7729219113466286,
        7.356921911346632,
        15.618921911346618,
        1.899921911346624,
        -0.17407808865337415,
        -7.951078088653375,
        11.396921911346624,
        17.85092191134663,
        1.4549219113466307,
        12.376921911346628,
        -8.033078088653376,
        1.0039219113466231,
        4.583921911346621,
        0.8529219113466269,
        12.850921911346632,
        24.65092191134663,
        14.098921911346622,
        -7.884078088653382,
        12.468921911346627,
        24.057921911346625,
        13.014921911346619,
        18.846921911346627,
        24.246921911346618,
        -0.678078088653379,
        16.30892191134663,
        16.923921911346625,
        4.912921911346629,
        22.04692191134663,
        4.458921911346621,
        21.027921911346624,
        15.349921911346627,
        7.409921911346629,
        20.22892191134663,
        10.902921911346624,
        -3.1730780886533694,
        3.66992191134662,
        14.588921911346631,
        -1.9000780886533732,
        9.905921911346624,
        -13.259078088653375,
        3.449921911346621,
        -11.181078088653372,
        -1.0960780886533712,
        -8.847078088653376,
        6.665921911346629,
        -19.336078088653373,
        -8.641078088653373,
        -12.918078088653374,
        -8.554078088653377,
        -15.549078088653374,
        -6.356078088653376,
        -12.019078088653373,
        -13.654078088653378,
        -8.129078088653372,
        1.8189219113466208,
        -3.5380780886533785,
        -8.236078088653372,
        -18.392078088653378,
        -4.30407808865337,
        -3.471078088653371,
        17.13992191134662,
        2.744921911346623,
        1.4289219113466203,
        5.405921911346624,
        -15.779078088653378,
        -13.334078088653378,
        -1.0350780886533784,
        9.253921911346623,
        -2.43507808865337,
        16.307921911346625,
        14.02692191134662,
        8.67592191134662,
        4.286921911346624,
        7.947921911346626,
        1.0489219113466248,
        -8.654078088653378,
        -15.547078088653372,
        6.8369219113466215,
        -3.3690780886533815,
        0.03292191134661948,
        -2.533078088653369,
        9.983921911346627,
        -14.571078088653373,
        18.17292191134662,
        -3.248078088653372,
        12.52392191134662,
        -3.297078088653379,
        -7.512078088653368,
        1.3509219113466315,
        -9.470078088653374,
        1.8949219113466285,
        -6.462078088653371,
        1.8349219113466262,
        -9.086078088653373,
        6.629921911346628,
        -7.226078088653381,
        6.1139219113466226,
        -5.44607808865338,
        -5.5380780886533785,
        3.0909219113466264,
        14.134921911346623,
        10.44592191134663,
        12.471921911346627,
        -2.6080780886533717,
        -13.883078088653377,
        9.31492191134663,
        3.4559219113466213,
        -8.998078088653372,
        -18.809078088653372,
        -4.457078088653375,
        -8.367078088653372,
        6.8509219113466315,
        -1.4850780886533812,
        -1.9960780886533769,
        -5.184078088653379,
        7.000921911346623,
        -10.459078088653378,
        0.08492191134662619,
        0.9839219113466271,
        -6.1830780886533745,
        18.17192191134663,
        -7.047078088653379,
        -11.437078088653372,
        14.68192191134662,
        -4.618078088653377,
        6.437921911346621,
        -18.681078088653372,
        -4.718078088653371,
        8.06192191134663,
        0.37792191134661834,
        -13.104078088653374,
        -15.100078088653376,
        -8.959078088653378,
        -9.854078088653374,
        9.679921911346625,
        -18.998078088653372,
        -11.979078088653374,
        -3.667078088653369,
        -9.614078088653372,
        -18.493078088653377,
        -10.930078088653374,
        -6.241078088653381,
        -21.262078088653375,
        -7.724078088653371
      ],
      "random_effects": [
        0.7887449501379855,
        0.8197853925791494,
        -2.336973065882657,
        -1.978393040595774,
        0.8538075313201173,
        4.297666753712341,
        9.483264869304303,
        -6.62246827402171,
        2.351805062413213,
        -0.3691652453779388,
        -0.6463802459016335,
        -6.641694687688185
      ],
      "residual_variance": 85.24170906764847,
      "random_intercept_variance": 21.322555173274118,
      "sigma": 9.232643666233875,
      "icc": 0.20009104670462194,
      "log_likelihood": -921.320633440586,
      "aic": 1848.641266881172,
      "df_residual": 249
    },
    "phit": {
      "coefficients": [
        71.94807808865323
      ],
      "covariance": [
        [
          2.125977970505094
        ]
      ],
      "std_errors": [
        1.4580733762417768
      ],
      "z_statistics": [
        49.344620964207806
      ],
      "p_values": [
        0
      ],
      "conf_int": [
        [
          69.09030678440263,
          74.80584939290384
        ]
      ],
      "fitted": [
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.73682303879484,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        72.76786348123537,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.61110502275868,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        69.96968504805015,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        72.80188561997694,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        76.24574484237924,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        81.43134295799793,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        65.32560981460577,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        74.29988315107805,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.57891284327417,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        71.30169784274938,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815,
        65.30638340093815
      ],
      "residuals": [
        5.520176961205166,
        -5.494823038794834,
        15.48617696120516,
        -4.190823038794832,
        -12.599823038794838,
        -0.5898230387948331,
        -12.381823038794842,
        -3.066823038794837,
        9.705176961205154,
        -0.6078230387948338,
        -10.936823038794842,
        -9.029823038794838,
        3.6551769612051572,
        4.341176961205164,
        18.300176961205167,
        1.720176961205155,
        3.298176961205158,
        0.025176961205161774,
        -3.59386348123536,
        -13.716863481235364,
        19.315136518764632,
        -8.350863481235365,
        -5.702863481235369,
        8.03513651876463,
        -4.526863481235367,
        -7.139863481235366,
        13.468136518764638,
        -2.082863481235364,
        6.674136518764627,
        -14.687863481235368,
        15.957136518764628,
        -7.899863481235371,
        -15.130863481235366,
        2.7561365187646345,
        -9.527863481235364,
        11.372136518764634,
        10.02513651876464,
        8.947136518764637,
        -7.271863481235371,
        5.950136518764637,
        -2.819863481235373,
        3.2291365187646335,
        3.2658949772413166,
        -13.782105022758678,
        -6.994105022758681,
        -16.975105022758676,
        13.503894977241316,
        -3.627105022758684,
        14.365894977241325,
        -3.968105022758678,
        -21.31210502275868,
        10.422894977241327,
        2.7018949772413237,
        3.0848949772413192,
        -3.076105022758682,
        5.954894977241324,
        7.091894977241324,
        -6.22368504805015,
        13.97131495194985,
        -17.167685048050153,
        -18.11068504805015,
        -12.82468504805015,
        13.10531495194985,
        2.987314951949841,
        6.604314951949846,
        -1.6726850480501554,
        1.9433149519498443,
        6.21831495194985,
        3.2333149519498505,
        10.418314951949853,
        -14.219685048050152,
        -12.508685048050154,
        3.448314951949854,
        6.993314951949841,
        7.440314951949844,
        0.7073149519498543,
        2.0513149519498484,
        -2.9626850480501474,
        -1.3406850480501475,
        -4.500885619976941,
        -5.238885619976941,
        -12.33388561997694,
        8.827114380023062,
        2.3521143800230533,
        2.613114380023063,
        2.661114380023051,
        4.992114380023054,
        12.194114380023052,
        -3.565885619976939,
        3.1321143800230544,
        2.444114380023052,
        -4.111885619976945,
        6.9431143800230615,
        7.266114380023055,
        -7.572885619976944,
        14.207114380023057,
        -9.493885619976943,
        -8.622885619976941,
        -8.777885619976942,
        5.249255157620766,
        13.142255157620767,
        -15.535744842379238,
        -13.767744842379237,
        -7.670744842379236,
        -1.7987448423792358,
        -16.73874484237924,
        -2.524744842379235,
        3.0592551576207683,
        11.321255157620755,
        -2.3977448423792396,
        -4.471744842379238,
        -12.248744842379239,
        7.09925515762076,
        13.553255157620768,
        -2.8427448423792328,
        8.079255157620764,
        -12.33074484237924,
        -3.2937448423792404,
        0.2862551576207579,
        -3.4447448423792366,
        8.553255157620768,
        20.353255157620765,
        9.801255157620758,
        -12.181744842379246,
        8.171255157620763,
        19.76025515762076,
        3.5316570420020668,
        9.363657042002075,
        14.763657042002066,
        -10.161342957997931,
        6.825657042002078,
        7.440657042002073,
        -4.570342957997923,
        12.563657042002077,
        -5.024342957997931,
        11.544657042002072,
        5.866657042002075,
        -2.073342957997923,
        10.74565704200208,
        1.419657042002072,
        -12.656342957997921,
        -5.813342957997932,
        5.105657042002079,
        -11.383342957997925,
        0.4226570420020721,
        -6.6366098146057695,
        10.072390185394227,
        -4.5586098146057665,
        5.526390185394234,
        -2.2246098146057705,
        13.288390185394235,
        -12.713609814605768,
        -2.0186098146057674,
        -6.295609814605768,
        -1.9316098146057712,
        -8.926609814605769,
        0.2663901853942292,
        -5.3966098146057675,
        -7.031609814605773,
        -1.506609814605767,
        8.441390185394226,
        3.084390185394227,
        -1.6136098146057662,
        -11.769609814605772,
        2.318390185394236,
        3.1513901853942343,
        14.788116848921945,
        0.39311684892194876,
        -0.9228831510780537,
        3.05411684892195,
        -18.130883151078052,
        -15.685883151078052,
        -3.3868831510780524,
        6.902116848921949,
        -4.786883151078044,
        13.956116848921951,
        11.675116848921945,
        6.324116848921946,
        1.9351168489219503,
        5.596116848921952,
        -1.3028831510780492,
        -11.005883151078052,
        -15.177912843274164,
        7.206087156725829,
        -2.999912843274174,
        0.40208715672582684,
        -2.1639128432741614,
        10.353087156725834,
        -14.201912843274165,
        18.542087156725827,
        -2.878912843274165,
        12.893087156725827,
        -2.9279128432741715,
        -7.142912843274161,
        1.720087156725839,
        -9.100912843274166,
        2.264087156725836,
        -6.0929128432741635,
        2.2040871567258336,
        -8.716912843274166,
        6.999087156725835,
        -6.8569128432741735,
        6.48308715672583,
        -5.076912843274172,
        -5.168912843274171,
        3.460087156725834,
        14.50408715672583,
        11.092302157250629,
        13.118302157250625,
        -1.9616978427493734,
        -13.236697842749379,
        9.961302157250628,
        4.1023021572506195,
        -8.351697842749374,
        -18.162697842749374,
        -3.810697842749377,
        -7.720697842749374,
        7.49730215725063,
        -0.838697842749383,
        -1.3496978427493787,
        -4.537697842749381,
        7.647302157250621,
        -9.81269784274938,
        0.7313021572506244,
        1.6303021572506253,
        -5.536697842749376,
        18.818302157250628,
        -6.400697842749381,
        -10.790697842749374,
        15.328302157250619,
        2.023616599061853,
        13.07961659906185,
        -12.039383400938142,
        1.9236165990618588,
        14.70361659906186,
        7.019616599061848,
        -6.462383400938144,
        -8.458383400938146,
        -2.317383400938148,
        -3.212383400938144,
        16.321616599061855,
        -12.356383400938142,
        -5.337383400938144,
        2.9746165990618607,
        -2.972383400938142,
        -11.851383400938147,
        -4.2883834009381445,
        0.40061659906184843,
        -14.620383400938145,
        -1.0823834009381414
      ],
      "log_likelihood": -921.3206334405859,
      "aic": 1848.6412668811718,
      "df_residual": 249,
      "evaluations": 107,
      "fixed_fitted": [
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323,
        71.94807808865323
      ],
      "marginal_residuals": [
        6.308921911346772,
        -4.7060780886532285,
        16.274921911346766,
        -3.4020780886532265,
        -11.811078088653232,
        0.19892191134677262,
        -11.593078088653236,
        -2.2780780886532312,
        10.49392191134676,
        0.18092191134677194,
        -10.148078088653236,
        -8.241078088653232,
        4.443921911346763,
        5.12992191134677,
        19.088921911346773,
        2.5089219113467607,
        4.086921911346764,
        0.8139219113467675,
        -2.7740780886532264,
        -12.897078088653231,
        20.134921911346765,
        -7.531078088653231,
        -4.883078088653235,
        8.854921911346764,
        -3.7070780886532333,
        -6.320078088653233,
        14.287921911346771,
        -1.2630780886532307,
        7.49392191134676,
        -13.868078088653235,
        16.77692191134676,
        -7.080078088653238,
        -14.311078088653232,
        3.575921911346768,
        -8.708078088653231,
        12.191921911346768,
        10.844921911346773,
        9.76692191134677,
        -6.452078088653238,
        6.769921911346771,
        -2.0000780886532397,
        4.048921911346767,
        0.9289219113467624,
        -16.119078088653232,
        -9.331078088653236,
        -19.31207808865323,
        11.166921911346762,
        -5.964078088653238,
        12.028921911346771,
        -6.305078088653232,
        -23.649078088653233,
        8.085921911346773,
        0.36492191134676943,
        0.747921911346765,
        -5.413078088653236,
        3.6179219113467695,
        4.75492191134677,
        -8.20207808865323,
        11.99292191134677,
        -19.146078088653233,
        -20.08907808865323,
        -14.80307808865323,
        11.12692191134677,
        1.0089219113467607,
        4.625921911346765,
        -3.651078088653236,
        -0.03507808865323625,
        4.239921911346769,
        1.25492191134677,
        8.439921911346772,
        -16.198078088653233,
        -14.487078088653234,
        1.4699219113467734,
        5.014921911346761,
        5.461921911346764,
        -1.2710780886532262,
        0.07292191134676784,
        -4.941078088653228,
        -3.319078088653228,
        -3.647078088653231,
        -4.385078088653231,
        -11.48007808865323,
        9.680921911346772,
        3.2059219113467634,
        3.4669219113467733,
        3.514921911346761,
        5.845921911346764,
        13.047921911346762,
        -2.7120780886532287,
        3.9859219113467645,
        3.297921911346762,
        -3.2580780886532352,
        7.796921911346772,
        8.119921911346765,
        -6.719078088653234,
        15.060921911346767,
        -8.640078088653233,
        -7.769078088653231,
        -7.924078088653232,
        9.546921911346772,
        17.439921911346772,
        -11.238078088653232,
        -9.470078088653231,
        -3.37307808865323,
        2.4989219113467698,
        -12.441078088653235,
        1.7729219113467707,
        7.356921911346774,
        15.61892191134676,
        1.899921911346766,
        -0.17407808865323204,
        -7.951078088653233,
        11.396921911346766,
        17.850921911346774,
        1.4549219113467728,
        12.37692191134677,
        -8.033078088653234,
        1.0039219113467652,
        4.5839219113467635,
        0.852921911346769,
        12.850921911346774,
        24.65092191134677,
        14.098921911346764,
        -7.88407808865324,
        12.468921911346769,
        24.057921911346767,
        13.014921911346761,
        18.84692191134677,
        24.24692191134676,
        -0.6780780886532369,
        16.308921911346772,
        16.923921911346767,
        4.912921911346771,
        22.04692191134677,
        4.4589219113467635,
        21.027921911346766,
        15.349921911346769,
        7.409921911346771,
        20.228921911346774,
        10.902921911346766,
        -3.1730780886532273,
        3.669921911346762,
        14.588921911346773,
        -1.9000780886532311,
        9.905921911346766,
        -13.259078088653233,
        3.449921911346763,
        -11.18107808865323,
        -1.096078088653229,
        -8.847078088653234,
        6.665921911346771,
        -19.33607808865323,
        -8.64107808865323,
        -12.918078088653232,
        -8.554078088653235,
        -15.549078088653232,
        -6.356078088653234,
        -12.019078088653231,
        -13.654078088653236,
        -8.12907808865323,
        1.818921911346763,
        -3.5380780886532364,
        -8.23607808865323,
        -18.392078088653236,
        -4.3040780886532275,
        -3.471078088653229,
        17.13992191134676,
        2.744921911346765,
        1.4289219113467624,
        5.405921911346766,
        -15.779078088653236,
        -13.334078088653236,
        -1.0350780886532363,
        9.253921911346765,
        -2.4350780886532277,
        16.307921911346767,
        14.026921911346761,
        8.675921911346762,
        4.2869219113467665,
        7.947921911346768,
        1.048921911346767,
        -8.654078088653236,
        -15.54707808865323,
        6.836921911346764,
        -3.3690780886532394,
        0.03292191134676159,
        -2.5330780886532267,
        9.98392191134677,
        -14.57107808865323,
        18.172921911346762,
        -3.24807808865323,
        12.523921911346761,
        -3.2970780886532367,
        -7.512078088653226,
        1.3509219113467736,
        -9.470078088653231,
        1.8949219113467706,
        -6.462078088653229,
        1.8349219113467683,
        -9.086078088653231,
        6.62992191134677,
        -7.226078088653239,
        6.113921911346765,
        -5.446078088653238,
        -5.538078088653236,
        3.0909219113467685,
        14.134921911346765,
        10.445921911346773,
        12.471921911346769,
        -2.6080780886532295,
        -13.883078088653235,
        9.314921911346772,
        3.4559219113467634,
        -8.99807808865323,
        -18.80907808865323,
        -4.457078088653233,
        -8.36707808865323,
        6.850921911346774,
        -1.485078088653239,
        -1.9960780886532348,
        -5.184078088653237,
        7.000921911346765,
        -10.459078088653236,
        0.0849219113467683,
        0.9839219113467692,
        -6.183078088653232,
        18.17192191134677,
        -7.047078088653237,
        -11.43707808865323,
        14.681921911346762,
        -4.618078088653235,
        6.437921911346763,
        -18.68107808865323,
        -4.718078088653229,
        8.061921911346772,
        0.37792191134676045,
        -13.104078088653232,
        -15.100078088653234,
        -8.959078088653236,
        -9.854078088653232,
        9.679921911346767,
        -18.99807808865323,
        -11.979078088653232,
        -3.667078088653227,
        -9.61407808865323,
        -18.493078088653235,
        -10.930078088653232,
        -6.241078088653239,
        -21.262078088653233,
        -7.724078088653229
      ],
      "random_effects": [
        0.7887449501416033,
        0.8197853925821305,
        -2.336973065894557,
        -1.9783930406030852,
        0.8538075313237101,
        4.297666753726004,
        9.483264869344689,
        -6.622468274047462,
        2.351805062424811,
        -0.3691652453790595,
        -0.6463802459038505,
        -6.641694687715093
      ],
      "group_sizes": [
        18,
        24,
        15,
        22,
        20,
        27,
        19,
        21,
        16,
        25,
        23,
        20
      ],
      "n_groups": 12,
      "group_labels": [
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12
      ],
      "residual_variance": 85.2417090675649,
      "random_intercept_variance": 21.32255517377406,
      "sigma": 9.232643666229349,
      "icc": 0.20009104670853162,
      "boundary": false,
      "method": "ML",
      "converged": true,
      "n_input": 250,
      "n_observations": 250,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119,
        120,
        121,
        122,
        123,
        124,
        125,
        126,
        127,
        128,
        129,
        130,
        131,
        132,
        133,
        134,
        135,
        136,
        137,
        138,
        139,
        140,
        141,
        142,
        143,
        144,
        145,
        146,
        147,
        148,
        149,
        150,
        151,
        152,
        153,
        154,
        155,
        156,
        157,
        158,
        159,
        160,
        161,
        162,
        163,
        164,
        165,
        166,
        167,
        168,
        169,
        170,
        171,
        172,
        173,
        174,
        175,
        176,
        177,
        178,
        179,
        180,
        181,
        182,
        183,
        184,
        185,
        186,
        187,
        188,
        189,
        190,
        191,
        192,
        193,
        194,
        195,
        196,
        197,
        198,
        199,
        200,
        201,
        202,
        203,
        204,
        205,
        206,
        207,
        208,
        209,
        210,
        211,
        212,
        213,
        214,
        215,
        216,
        217,
        218,
        219,
        220,
        221,
        222,
        223,
        224,
        225,
        226,
        227,
        228,
        229,
        230,
        231,
        232,
        233,
        234,
        235,
        236,
        237,
        238,
        239,
        240,
        241,
        242,
        243,
        244,
        245,
        246,
        247,
        248,
        249
      ],
      "dropped_rows": []
    },
    "python_diagnostics": {
      "backend": "statsmodels MixedLM (ML)",
      "warnings": [],
      "covariance_convention": "plug-in GLS, matching lme4"
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "Python": 6.586731160496129e-11,
        "phit": 6.600942015211331e-11
      },
      "covariance": {
        "Python": 3.422340189018769e-08,
        "phit": 3.4264757253765765e-08
      },
      "std_errors": {
        "Python": 1.1735829863468439e-08,
        "phit": 1.175001140829579e-08
      },
      "z_statistics": {
        "Python": 3.9721317079965957e-07,
        "phit": 3.9769320636651173e-07
      },
      "p_values": {
        "Python": 0.0,
        "phit": 0.0
      },
      "conf_int": {
        "Python": 2.3067670440468646e-08,
        "phit": 2.3095608980838733e-08
      },
      "fixed_fitted": {
        "Python": 6.586731160496129e-11,
        "phit": 6.600942015211331e-11
      },
      "fitted": {
        "Python": 3.331237508064078e-08,
        "phit": 3.335262022119423e-08
      },
      "residuals": {
        "Python": 3.331237508064078e-08,
        "phit": 3.335262022119423e-08
      },
      "marginal_residuals": {
        "Python": 6.586731160496129e-11,
        "phit": 6.600942015211331e-11
      },
      "random_effects": {
        "Python": 3.337824239224574e-08,
        "phit": 3.34186278649895e-08
      },
      "residual_variance": {
        "Python": 6.912914329859632e-08,
        "phit": 6.921271733517642e-08
      },
      "random_intercept_variance": {
        "Python": 4.137385474223265e-07,
        "phit": 4.14238488843921e-07
      },
      "sigma": {
        "Python": 3.743734211525407e-09,
        "phit": 3.748260368752199e-09
      },
      "icc": {
        "Python": 3.235468198914404e-09,
        "phit": 3.239377877051197e-09
      },
      "log_likelihood": {
        "Python": 1.1368683772161603e-13,
        "phit": 0.0
      },
      "aic": {
        "Python": 2.2737367544323206e-13,
        "phit": 0.0
      },
      "df_residual": {
        "Python": 0.0,
        "phit": 0.0
      }
    },
    "tolerance": {
      "absolute": 1e-07,
      "relative": 1e-06
    },
    "extension_sha256": "2105dd47a15f21b0da6ae81a23461ef385285517e1af0519a0bb22238bc3ffc6"
  },
  {
    "name": "singleton_groups",
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "lme4": "2.0.6",
      "statsmodels": "0.15.0",
      "PHP": "8.5.10",
      "Python": "3.14.7"
    },
    "R": {
      "coefficients": [
        46.45576735624861,
        1.6225357589749765,
        0.24465092068056096
      ],
      "covariance": [
        [
          4.818694206935786,
          0.13722040593449444,
          -0.06964094144896787
        ],
        [
          0.13722040593449444,
          0.025685102619538765,
          -0.005156688626768335
        ],
        [
          -0.06964094144896787,
          -0.005156688626768335,
          0.001734061027452028
        ]
      ],
      "std_errors": [
        2.1951524336445947,
        0.16026572503045922,
        0.04164205839595382
      ],
      "z_statistics": [
        21.162889029587095,
        10.124034684687611,
        5.875091916789892
      ],
      "p_values": [
        2.0995587659287498e-99,
        4.3222246872321516e-24,
        4.22608793369812e-09
      ],
      "conf_int": [
        [
          42.15334764572975,
          50.75818706676746
        ],
        [
          1.308420709959077,
          1.936650807990876
        ],
        [
          0.16303398598237773,
          0.3262678553787442
        ]
      ],
      "fixed_fitted": [
        84.16358714140661,
        63.485066504666044,
        81.99696122921968,
        63.5678477657024,
        66.65129823696901,
        72.83955003272473,
        62.671671129781835,
        70.62800031423427,
        83.09199447467802,
        74.94541876514253,
        65.33585218408506,
        61.09763030252333,
        81.9709931030982,
        72.4071856327589,
        83.13794829272585,
        74.36120578904372,
        75.1488277451361,
        68.86351568509822,
        66.1643050320574,
        62.0595356053467,
        85.51636886001282,
        60.61049922485441,
        67.24497273767898,
        67.70503270716799,
        63.79056114170667,
        70.30295523768694,
        84.69870492805828,
        67.90332975780568,
        77.30186401786372,
        57.85078550341134,
        84.48232270207785,
        62.66028745443934,
        60.78886191973209,
        70.31788033642378,
        67.95385758045705,
        82.64020394168591,
        79.55802402725362,
        81.28136132016448,
        71.9352553993414,
        80.32820140508827,
        64.19474888196932,
        66.94258427161306,
        74.61385589911261,
        59.23969173494268,
        70.4665010045665,
        57.72583239281147,
        80.75931688236751,
        77.69059680250808,
        78.42441975966334,
        73.15808831660144,
        56.422329574170064,
        78.27081146864518,
        68.59728950184693,
        70.60442736115324,
        67.77547874983763,
        69.35825396803129,
        78.18306421888113,
        79.04929605286623,
        84.91748232707916,
        67.96275697670325,
        59.88205587469876,
        69.26848189520321,
        84.6241769677771,
        82.8270821165565,
        77.49463002246765,
        78.5951077773688,
        73.54300393233686,
        75.81445939044,
        69.5073315227414,
        80.15147961702132,
        68.2224492347302,
        66.87452533411302,
        73.83370877393308,
        83.56491145154435,
        82.276152590587,
        79.00931660114266,
        77.35550607936067,
        71.55875516073107,
        71.37643485472228,
        64.92563874133178,
        63.3495569552675,
        59.081430970600906,
        77.29224555581241,
        76.64974904170504,
        75.1481735817742,
        66.42812247599137,
        78.22806099549874,
        85.12661156203013,
        66.20580108411127,
        80.16722645389595,
        80.09312017975755,
        65.0545710972105,
        79.61574543689724,
        77.74553912285796,
        73.12077428502694,
        80.79562253634543,
        70.800285970455,
        62.840828980880104,
        67.67009771289221,
        71.9586391434988,
        81.19771505269485,
        60.81809572373333,
        63.543325839062,
        67.42069164655534,
        67.09969878560095,
        66.16219367240241,
        79.44710387640356,
        81.19916675058194,
        75.74055589150211,
        74.75823514273874,
        75.65121907109366,
        71.65896743374827,
        82.46952142238648,
        81.04065994274416,
        76.90916005581138,
        75.97905937267647,
        66.9022506056548,
        78.71185892337982,
        78.0712005928777,
        65.73466288681298,
        77.89029678433138,
        86.40149697014272,
        86.66936406020477,
        55.59406593512137,
        78.45208562716792,
        79.23549843022718,
        78.19217702766358,
        78.99632172100804,
        78.41493917036932,
        67.70511924375894,
        77.78893019308943,
        79.97920752707748,
        66.69438385966728,
        77.43466487881774,
        69.88579974984343,
        82.39542871452493,
        71.90296419106694,
        65.92409574162907,
        74.8975699289171,
        61.30391297627246,
        62.887320723680276,
        63.877516355351524,
        74.43393883401514,
        61.007325803348905,
        77.09229146262226,
        64.43865103482617,
        82.32176576067702,
        66.766516646908,
        79.29912930375187,
        73.00606959622768,
        78.35676637256432,
        58.34916238366544,
        71.52271718439688,
        59.93800657264521,
        62.70532749935243,
        64.9893209510228,
        64.87556780524778,
        60.18138693649146,
        76.60087826160614,
        72.97340253957078,
        75.79704451420089,
        77.02504619538914,
        67.50916602999537,
        58.47286657157873,
        68.97103778371725,
        71.55526250403821,
        84.62509880878272,
        63.64212968248759,
        65.1387472215616,
        72.92641870977863,
        67.79266371832249,
        55.69338606915155,
        79.0961717119197,
        76.68584385261157,
        75.53081026307872,
        81.8538796749816,
        75.13911467862296,
        73.84285678314015,
        77.00286003775197,
        73.50600084670157,
        71.87208948025497,
        64.23271707690571,
        58.137608273655395,
        79.60502949119352,
        66.13669599912517,
        67.5637812686643,
        75.428781440604,
        81.39779088290058,
        56.68784475948713,
        80.38996696245395,
        64.28932193821406,
        81.37220117462637,
        69.92747144454407,
        67.72798669731174,
        73.80756757462969,
        65.11762077768736,
        67.03266985984523,
        67.30874148396096,
        73.71078855426812,
        59.29645353369119,
        75.76971122678326,
        64.32575739707842,
        85.58129192451956,
        68.04500288245215,
        65.21543787766412,
        73.08367659492983,
        81.27040482937078,
        82.25891885540067,
        84.43660942912,
        71.45576929682612,
        56.30773562557437,
        72.19773738399785,
        76.35304563017193,
        57.43620083125504,
        62.39858393962523,
        60.84099287930473,
        65.30019519506303,
        72.32997061818091,
        80.9570272415514,
        66.97028790900711,
        64.46258883947762,
        81.17649400435879,
        62.302545619216524,
        76.57361794450259,
        73.00366085691034,
        67.93706459609636,
        84.40245290468654,
        67.29736587648934,
        63.24968533020811,
        81.36381549951989,
        74.90149783802961,
        82.01543581922172,
        72.33689652752943,
        69.60395103619793,
        80.58393862144897,
        75.95295337379768,
        60.59479565627526,
        63.26798684702825,
        65.91042763344969,
        64.56161709225147,
        80.92827195826527,
        58.603061416420886,
        61.91809495791936,
        74.24226224519275,
        69.74554312265944,
        58.0898107735963,
        62.63677390539553,
        72.89442488116651,
        59.65377625223611,
        71.60658786121479
      ],
      "fitted": [
        81.70374922653788,
        64.13491686127917,
        82.6468115858328,
        64.21769812231551,
        67.30114859358213,
        73.48940038933785,
        63.32152148639495,
        71.27785067084739,
        83.74184483129113,
        75.59526912175565,
        65.98570254069817,
        61.74748065913644,
        82.62084345971131,
        73.05703598937201,
        83.78779864933897,
        75.01105614565684,
        75.79867810174922,
        69.51336604171134,
        67.95451487615469,
        63.849745449443986,
        87.30657870411011,
        62.40070906895169,
        69.03518258177627,
        69.49524255126528,
        65.58077098580395,
        72.09316508178424,
        86.48891477215557,
        69.69353960190297,
        79.09207386196101,
        59.64099534750862,
        86.27253254617514,
        64.45049729853663,
        62.579071763829376,
        72.10809018052107,
        69.74406742455434,
        84.4304137857832,
        81.34823387135091,
        83.07157116426177,
        73.72546524343869,
        82.11841124918556,
        65.98495872606661,
        68.73279411571033,
        73.0001970407424,
        57.626032876572495,
        68.85284214619631,
        56.11217353444128,
        79.14565802399733,
        76.0769379441379,
        76.81076090129315,
        71.54442945823125,
        54.80867071579988,
        76.65715261027499,
        66.98363064347673,
        68.99076850278306,
        66.16181989146745,
        67.7445951096611,
        76.56940536051094,
        73.65277573957992,
        79.52096201379287,
        62.56623666341694,
        54.48553556141245,
        63.8719615819169,
        79.22765665449079,
        77.43056180327021,
        72.09810970918134,
        73.1985874640825,
        68.14648361905056,
        70.41793907715369,
        64.1108112094551,
        74.75495930373502,
        62.8259289214439,
        61.47800502082669,
        68.43718846064678,
        78.16839113825804,
        76.8796322773007,
        73.61279628785636,
        71.95898576607436,
        66.16223484744476,
        65.97991454143597,
        65.35139958870167,
        63.77531780263739,
        59.50719181797079,
        77.7180064031823,
        77.07550988907492,
        75.57393442914409,
        66.85388332336126,
        78.65382184286862,
        85.55237240940004,
        66.63156193148116,
        80.59298730126584,
        80.51888102712743,
        65.48033194458039,
        80.04150628426713,
        78.17129997022785,
        73.54653513239683,
        81.22138338371532,
        71.22604681782488,
        63.26658982824999,
        68.0958585602621,
        74.39160628173626,
        83.63068219093229,
        63.25106286197079,
        65.97629297729947,
        69.8536587847928,
        69.53266592383841,
        68.59516081063987,
        81.88007101464102,
        83.6321338888194,
        78.17352302973957,
        77.19120228097621,
        78.08418620933112,
        74.09193457198575,
        84.90248856062392,
        83.47362708098161,
        79.34212719404884,
        78.41202651091393,
        69.33521774389226,
        81.14482606161728,
        80.50416773111516,
        68.16763002505044,
        80.32326392256884,
        88.83446410838017,
        89.10233119844222,
        58.02703307335882,
        80.88505276540538,
        81.66846556846464,
        88.69611738216439,
        89.50026207550886,
        88.91887952487015,
        78.20905959825976,
        88.29287054759024,
        90.48314788157829,
        77.1983242141681,
        87.93860523331854,
        80.38974010434423,
        92.89936906902574,
        82.40690454556776,
        76.42803609612989,
        85.40151028341792,
        71.80785333077327,
        73.39126107818109,
        74.38145670985233,
        84.93787918851595,
        71.51126615784972,
        87.59623181712307,
        59.515162840903415,
        77.39827756675427,
        61.84302845298525,
        74.37564110982912,
        68.08258140230492,
        73.43327817864157,
        53.425674189742686,
        66.59922899047413,
        55.01451837872246,
        57.78183930542968,
        60.065832757100054,
        59.95207961132503,
        55.2578987425687,
        71.67739006768339,
        68.04991434564805,
        70.87355632027814,
        72.10155800146639,
        62.58567783607262,
        53.54937837765598,
        64.0475495897945,
        66.63177431011546,
        86.9019066642648,
        65.91893753796967,
        67.41555507704368,
        75.2032265652607,
        70.06947157380456,
        57.97019392463363,
        81.37297956740177,
        78.96265170809365,
        77.8076181185608,
        84.13068753046367,
        77.41592253410504,
        76.11966463862223,
        79.27966789323405,
        75.78280870218364,
        74.14889733573705,
        66.50952493238779,
        58.8863389276261,
        80.35376014516423,
        66.88542665309588,
        68.312511922635,
        76.17751209457471,
        82.14652153687129,
        57.43657541345783,
        81.13869761642466,
        65.03805259218477,
        82.12093182859707,
        70.67620209851478,
        68.47671735128245,
        74.55629822860038,
        65.86635143165807,
        67.78140051381594,
        68.05747213793167,
        74.45951920823883,
        60.045184187661896,
        76.51844188075397,
        65.07448805104913,
        86.33002257849026,
        68.79373353642285,
        65.96416853163483,
        73.83240724890054,
        82.01913548334149,
        82.51884997032222,
        84.69654054404155,
        71.71570041174768,
        56.567666740495916,
        72.4576684989194,
        76.61297674509348,
        57.6961319461766,
        62.65851505454679,
        61.100923994226285,
        65.56012630998458,
        72.58990173310248,
        81.21695835647296,
        67.23021902392867,
        64.72251995439917,
        81.43642511928034,
        62.56247673413808,
        76.83354905942414,
        73.26359197183191,
        68.19699571101792,
        84.6623840196081,
        67.5572969914109,
        63.509616445129666,
        81.62374661444144,
        70.20680495328169,
        77.3207429344738,
        67.64220364278151,
        64.90925815144999,
        75.88924573670106,
        71.25826048904976,
        55.900102771527344,
        58.57329396228033,
        61.21573474870177,
        59.86692420750355,
        76.23357907351735,
        53.90836853167297,
        57.22340207317145,
        69.54756936044483,
        65.0508502379115,
        53.39511788884838,
        57.94208102064761,
        68.19973199641859,
        54.9590833674882,
        66.91189497646687
      ],
      "residuals": [
        -3.446749226537875,
        3.1070831387208386,
        5.576188414167206,
        4.3283018776844955,
        -7.1641485935821265,
        -1.3424003893378398,
        -2.966521486394953,
        -1.6078506708473839,
        -1.2998448312911393,
        -3.4662691217556443,
        -4.185702540698173,
        1.959519340863558,
        -6.228843459711314,
        4.020964010627992,
        7.249201350661039,
        -0.554056145656844,
        0.23632189825077887,
        3.2486339582886643,
        1.2194851238453168,
        -4.7987454494439845,
        4.7764212958898895,
        2.01629093104831,
        -1.970182581776271,
        11.30775744873472,
        2.660229014196048,
        -6.465165081784235,
        -0.25291477215556313,
        0.9914603980970327,
        0.3499261380389811,
        -1.560995347508623,
        2.452467453824852,
        0.41750270146336277,
        -4.942071763829375,
        3.4159098194789266,
        -6.504067424554343,
        -0.2904137857832012,
        1.4447661286490927,
        -1.3565711642617657,
        -8.229465243438696,
        -3.4004112491855523,
        3.963041273933385,
        7.264205884289666,
        -0.12319704074241145,
        -1.7970328765724943,
        -6.235842146196312,
        -3.47617353444128,
        3.969341976002667,
        -10.092937944137901,
        7.166239098706853,
        -5.901429458231249,
        -6.509670715799878,
        3.3768473897250146,
        5.329369356523273,
        3.7052314972169427,
        0.37318010853255146,
        7.821404890338897,
        0.13359463948906125,
        -9.90677573957992,
        4.420037986207134,
        -9.764236663416938,
        -2.626535561412446,
        -6.726961581916896,
        3.8473433455092163,
        -4.473561803270215,
        4.475890290818654,
        -4.901587464082496,
        3.76651638094944,
        5.770060922846312,
        9.09218879054491,
        5.633040696264985,
        -7.0759289214438965,
        -4.017005020826694,
        4.980811539353226,
        -1.2053911382580509,
        0.530367722699296,
        -2.9357962878563484,
        0.06201423392563754,
        0.8447651525552402,
        2.6490854585640307,
        2.9496004112983343,
        3.7876821973626136,
        0.9608081820292114,
        3.910993596817704,
        -1.921509889074926,
        -0.1589344291440824,
        8.609116676638735,
        -0.8598218428686266,
        -0.5563724094000406,
        2.6044380685188457,
        -4.658987301265839,
        -5.27288102712744,
        3.2096680554196126,
        -0.29650628426712444,
        1.8967000297721484,
        -8.317535132396827,
        5.78761661628468,
        -7.91804681782488,
        0.912410171750011,
        -4.0718585602621005,
        7.103393718263746,
        5.757317809067715,
        -2.5410628619707865,
        -3.4982929772994638,
        -1.2786587847927962,
        4.914334076161595,
        -9.08816081063987,
        -8.159071014641015,
        -4.3271338888193895,
        9.393476970260423,
        -3.3432022809762145,
        -6.310186209331121,
        -10.094934571985746,
        -1.5574885606239235,
        6.325372919018392,
        -5.939127194048837,
        5.91297348908607,
        -5.420217743892259,
        -8.192826061617282,
        -3.9721677311151637,
        4.633369974949559,
        4.475736077431165,
        7.764535891619829,
        -3.055331198442218,
        6.0369669266411705,
        3.5319472345946252,
        14.33753443153536,
        -3.7331173821643944,
        1.2947379244911446,
        7.276120475129844,
        -6.93905959825976,
        -0.035870547590235446,
        -1.6111478815782903,
        -0.3373242141680919,
        6.056394766681464,
        -3.9827401043442308,
        0.07663093097426099,
        4.8910954544322465,
        2.9299639038701173,
        6.775489716582086,
        11.04314666922673,
        -4.616261078181083,
        1.2365432901476652,
        1.599120811484056,
        -1.4632661578497164,
        -5.74223181712307,
        -0.8261628409034145,
        -2.000277566754278,
        -1.0760284529852484,
        -3.5236411098291143,
        -4.981581402304926,
        5.180721821358432,
        -0.8136741897426845,
        -3.292228990474129,
        4.015481621277544,
        5.612160694570321,
        -3.666832757100053,
        5.639920388674966,
        4.671101257431303,
        -13.383390067683393,
        -4.230914345648046,
        2.8934436797218552,
        -3.6915580014663902,
        1.1263221639273837,
        0.00662162234402075,
        3.596450410205506,
        1.8452256898845434,
        2.186093335735194,
        8.77406246203033,
        5.961444922956318,
        2.1507734347392926,
        -13.900471573804566,
        0.6438060753663706,
        -10.459979567401774,
        2.239348291906353,
        -8.294618118560791,
        4.1253124695363255,
        8.559077465894958,
        4.50433536137777,
        -3.044667893234049,
        4.113191297816357,
        -1.151897335737047,
        -3.215524932387794,
        -2.4853389276260955,
        -1.5687601451642337,
        1.6935733469041168,
        3.668488077364998,
        -6.762512094574703,
        -0.21452153687128828,
        -0.059575413457828574,
        8.98230238357533,
        3.6619474078152336,
        2.351068171402929,
        -2.0252020985147823,
        -4.040717351282439,
        -1.2572982286003764,
        -3.388351431658073,
        6.061599486184065,
        -2.5714721379316643,
        -0.6765192082388296,
        2.816815812338106,
        2.0595581192460344,
        -0.3524880510491357,
        -8.26802257849026,
        -2.2917335364228535,
        0.44583146836517074,
        1.206592751099464,
        4.063864516658512,
        -0.12484997032221656,
        -0.27654054404155204,
        -2.3757004117476725,
        1.4973332595040816,
        8.805331501080602,
        -1.20897674509348,
        5.253868053823403,
        -9.519515054546787,
        6.3900760057737145,
        -1.9791263099845793,
        6.209098266897527,
        -10.753958356472964,
        2.7217809760713294,
        2.041480045600821,
        -2.4874251192803456,
        -1.073476734138083,
        -4.800549059424142,
        -0.33159197183191225,
        -2.431995711017919,
        5.457615980391907,
        -2.6562969914108976,
        -2.998616445129663,
        5.006253385558551,
        -2.8768049532816917,
        1.0652570655261968,
        -14.375203642781507,
        2.320741848550014,
        4.120754263298949,
        1.0677395109502328,
        2.9438972284726574,
        -1.7252939622803325,
        1.773265251298227,
        2.22707579249645,
        5.394420926482653,
        -0.9583685316729671,
        2.7455979268285517,
        -1.2665693604448194,
        -2.716850237911501,
        0.0598821111516159,
        3.0759189793523873,
        -2.4927319964185983,
        -4.273083367488198,
        -2.6878949764668647
      ],
      "marginal_residuals": [
        -5.906587141406604,
        3.7569334953339606,
        6.22603877078032,
        4.978152234297603,
        -6.514298236969012,
        -0.6925500327247249,
        -2.316671129781838,
        -0.958000314234269,
        -0.6499944746780244,
        -2.8164187651425294,
        -3.5358521840850585,
        2.609369697476673,
        -5.578993103098199,
        4.670814367241107,
        7.899051707274154,
        0.09579421095627083,
        0.8861722548638937,
        3.898484314901779,
        3.0096949679426075,
        -3.008535605346701,
        6.56663113998718,
        3.8065007751455937,
        -0.17997273767898037,
        13.09796729283201,
        4.450438858293332,
        -4.6749552376869445,
        1.5372950719417275,
        2.7816702421943234,
        2.1401359821362718,
        0.22921449658866067,
        4.2426772979221425,
        2.2077125455606534,
        -3.1518619197320916,
        5.206119663576217,
        -4.713857580457052,
        1.4997960583140895,
        3.2349759727463834,
        0.43363867983552495,
        -6.4392553993414055,
        -1.6102014050882616,
        5.753251118030676,
        9.054415728386942,
        -1.7368558991126122,
        -3.410691734942681,
        -7.849501004566498,
        -5.089832392811466,
        2.3556831176324806,
        -11.706596802508088,
        5.552580240336667,
        -7.515088316601435,
        -8.123329574170064,
        1.7631885313548281,
        3.715710498153072,
        2.091572638846756,
        -1.240478749837635,
        6.2077460319687106,
        -1.4800642188811253,
        -15.303296052866223,
        -0.9764823270791538,
        -15.160756976703247,
        -8.023055874698755,
        -12.123481895203206,
        -1.5491769677771003,
        -9.870082116556503,
        -0.9206300224676482,
        -10.298107777368799,
        -1.6300039323368622,
        0.3735406095599956,
        3.6956684772586073,
        0.23652038297868216,
        -12.472449234730206,
        -9.413525334113018,
        -0.41570877393307626,
        -6.601911451544353,
        -4.866152590587006,
        -8.33231660114265,
        -5.334506079360665,
        -4.551755160731062,
        -2.747434854722272,
        3.375361258668221,
        4.2134430447325,
        1.386569029399098,
        4.336754444187591,
        -1.4957490417050394,
        0.2668264182258042,
        9.034877524008621,
        -0.43406099549874,
        -0.1306115620301398,
        3.0301989158887324,
        -4.233226453895952,
        -4.847120179757553,
        3.6354289027894993,
        0.12925456310276218,
        2.322460877142035,
        -7.891774285026941,
        6.213377463654567,
        -7.492285970454994,
        1.3381710191198977,
        -3.646097712892214,
        9.536360856501204,
        8.190284947305159,
        -0.10809572373332799,
        -1.0653258390619982,
        1.1543083534446623,
        7.347301214399053,
        -6.655193672402412,
        -5.726103876403556,
        -1.894166750581931,
        11.826444108497881,
        -0.9102351427387418,
        -3.8772190710936627,
        -7.6619674337482735,
        0.8754785776135208,
        8.75834005725585,
        -3.506160055811378,
        8.345940627323529,
        -2.9872506056548005,
        -5.759858923379824,
        -1.5392005928777053,
        7.066337113187018,
        6.908703215668623,
        10.197503029857288,
        -0.6223640602047738,
        8.469934064878622,
        5.964914372832084,
        16.77050156977282,
        6.770822972336418,
        11.798678278991957,
        17.78006082963067,
        3.5648807562410525,
        10.468069806910577,
        8.892792472922523,
        10.16661614033272,
        16.560335121182263,
        6.521200250156568,
        10.580571285475074,
        15.39503580893306,
        13.43390425837093,
        17.279430071082913,
        21.547087023727542,
        5.88767927631973,
        11.74048364464847,
        12.103061165984869,
        9.040674196651096,
        4.761708537377743,
        -5.749651034826165,
        -6.923765760677028,
        -5.999516646907999,
        -8.447129303751865,
        -9.905069596227676,
        0.25723362743568146,
        -5.737162383665435,
        -8.21571718439688,
        -0.9080065726452062,
        0.68867250064757,
        -8.590320951022804,
        0.7164321947522154,
        -0.2523869364914546,
        -18.306878261606144,
        -9.154402539570782,
        -2.0300445142008954,
        -8.61504619538914,
        -3.797166029995367,
        -4.91686657157873,
        -1.3270377837172447,
        -3.0782625040382072,
        4.46290119121727,
        11.050870317512405,
        8.238252778438394,
        4.427581290221369,
        -11.62366371832249,
        2.9206139308484467,
        -8.183171711919698,
        4.516156147388429,
        -6.017810263078715,
        6.402120325018402,
        10.835885321377035,
        6.781143216859846,
        -0.7678600377519729,
        6.389999153298433,
        1.124910519745029,
        -0.9387170769057178,
        -1.736608273655392,
        -0.8200294911935231,
        2.4423040008748274,
        4.417218731335694,
        -6.013781440603992,
        0.5342091170994223,
        0.6891552405128749,
        9.731033037546041,
        4.410678061785944,
        3.0997988253736253,
        -1.2764714445440717,
        -3.291986697311728,
        -0.50856757462968,
        -2.6396207776873624,
        6.810330140154775,
        -1.8227414839609537,
        0.07221144573188099,
        3.5655464663088097,
        2.808288773216745,
        0.39624260292157487,
        -7.519291924519564,
        -1.543002882452157,
        1.1945621223358813,
        1.9553234050701747,
        4.812595170629223,
        0.13508114459934006,
        -0.01660942911999541,
        -2.115769296826116,
        1.757264374425631,
        9.065262616002158,
        -0.9490456301719377,
        5.51379916874496,
        -9.25958393962523,
        6.650007120695271,
        -1.7191951950630227,
        6.469029381819098,
        -10.494027241551407,
        2.981712090992886,
        2.3014111605223775,
        -2.227494004358789,
        -0.8135456192165265,
        -4.540617944502586,
        -0.07166085691034141,
        -2.1720645960963623,
        5.7175470953134635,
        -2.396365876489341,
        -2.7386853302081064,
        5.266184500480108,
        -7.5714978380296145,
        -3.629435819221726,
        -19.06989652752943,
        -2.373951036197923,
        -0.5739386214489599,
        -3.62695337379769,
        -1.7507956562752582,
        -6.419986847028248,
        -2.9214276334496887,
        -2.4676170922514657,
        0.6997280417347298,
        -5.653061416420883,
        -1.9490949579193568,
        -5.961262245192742,
        -7.411543122659438,
        -4.6348107735963,
        -1.6187739053955283,
        -7.187424881166521,
        -8.967776252236114,
        -7.3825878612147875
      ],
      "random_effects": [
        -2.4598379148687424,
        0.6498503566131135,
        1.7902098440972858,
        -1.6136588583701887,
        -5.396520313286308,
        0.42576084736989,
        2.432967138237457,
        10.503940354500807,
        -4.9234881939227515,
        2.2768078554820743,
        0.7487306539707057,
        0.2599311149215574,
        -4.694692884747917
      ],
      "residual_variance": 25.277067130392656,
      "random_intercept_variance": 18.03945805667944,
      "sigma": 5.027630369308453,
      "icc": 0.4164567212806662,
      "log_likelihood": -775.2271156725184,
      "aic": 1560.4542313450368,
      "df_residual": 247
    },
    "Python": {
      "coefficients": [
        46.4557673546889,
        1.622535759145009,
        0.2446509206270583
      ],
      "covariance": [
        [
          4.818694248393039,
          0.1372204057066871,
          -0.06964094135251099
        ],
        [
          0.1372204057066871,
          0.02568510258208957,
          -0.0051566886191656055
        ],
        [
          -0.06964094135251099,
          -0.0051566886191656055,
          0.0017340610249525056
        ]
      ],
      "std_errors": [
        2.1951524430875042,
        0.16026572491362454,
        0.04164205836594183
      ],
      "z_statistics": [
        21.16288893783996,
        10.124034693129033,
        5.875091919739328
      ],
      "p_values": [
        2.0995628515703313e-99,
        4.322224314312645e-24,
        4.2260878584541514e-09
      ],
      "conf_int": [
        [
          42.153347625662285,
          50.75818708371552
        ],
        [
          1.3084207103581011,
          1.9366508079319167
        ],
        [
          0.16303398598769744,
          0.3262678552664191
        ]
      ],
      "fixed_fitted": [
        84.16358713767852,
        63.48506650079934,
        81.99696122514662,
        63.567847762347704,
        66.65129823329166,
        72.83955002828715,
        62.671671126114006,
        70.62800031012289,
        83.09199447108455,
        74.94541876174556,
        65.33585218130422,
        61.09763029844917,
        81.97099309922501,
        72.40718562852611,
        83.13794828905412,
        74.36120578453057,
        75.14882774152142,
        68.86351568120476,
        66.16430502844455,
        62.05953560184423,
        85.5163688559469,
        60.6104992208028,
        67.24497273361985,
        67.70503270295052,
        63.79056113748973,
        70.30295523402981,
        84.69870492410294,
        67.90332975414319,
        77.30186401427682,
        57.85078550032016,
        84.48232269849,
        62.66028745112566,
        60.78886191575695,
        70.31788033330398,
        67.95385757643186,
        82.6402039377871,
        79.55802402359846,
        81.28136131596973,
        71.93525539575243,
        80.32820140205197,
        64.19474887884493,
        66.94258426857006,
        74.61385589521078,
        59.23969173123809,
        70.46650100094706,
        57.72583238950618,
        80.75931687930517,
        77.69059679940828,
        78.4244197558047,
        73.15808831317544,
        56.42232957101862,
        78.27081146544472,
        68.59728949768102,
        70.60442735759813,
        67.77547874684869,
        69.35825396475396,
        78.18306421542694,
        79.04929604880795,
        84.91748232311272,
        67.96275697333743,
        59.88205587127358,
        69.26848189124217,
        84.62417696395877,
        82.82708211281103,
        77.49463001887008,
        78.59510777441758,
        73.54300392842254,
        75.8144593869212,
        69.50733151928974,
        80.151479613756,
        68.22244923179048,
        66.87452533075424,
        73.83370877094193,
        83.5649114477005,
        82.27615258719294,
        79.00931659739756,
        77.35550607552061,
        71.55875515665234,
        71.37643485131849,
        64.92563873758041,
        63.34955695179259,
        59.08143096688369,
        77.29224555181297,
        76.64974903859667,
        75.14817357870552,
        66.4281224716385,
        78.2280609911162,
        85.12661155809668,
        66.20580108064681,
        80.1672264502073,
        80.09312017577543,
        65.05457109302155,
        79.61574543339216,
        77.74553911896933,
        73.12077428114196,
        80.79562253324892,
        70.80028596689903,
        62.840828977002076,
        67.67009770968488,
        71.95863913966852,
        81.19771504874933,
        60.81809572036589,
        63.543325834857136,
        67.42069164344454,
        67.09969878203547,
        66.16219366796074,
        79.44710387252073,
        81.19916674679882,
        75.74055588803095,
        74.75823513956115,
        75.65121906716442,
        71.65896742980509,
        82.46952141879265,
        81.04065993840786,
        76.90916005183274,
        75.97905936811918,
        66.90225060188583,
        78.71185891963678,
        78.07120058900183,
        65.73466288348828,
        77.89029678053707,
        86.40149696591473,
        86.66936405609664,
        55.59406593248697,
        78.45208562381235,
        79.23549842676852,
        78.19217702288475,
        78.99632171731301,
        78.4149391661401,
        67.70511923994036,
        77.78893018918082,
        79.9792075239128,
        66.69438385634265,
        77.43466487541174,
        69.88579974645594,
        82.39542871129372,
        71.90296418761625,
        65.92409573895577,
        74.89756992576676,
        61.30391297276203,
        62.88732071923573,
        63.87751635189237,
        74.43393883058829,
        61.00732580029173,
        77.09229145933313,
        64.43865103235176,
        82.3217657568216,
        66.76651664308999,
        79.29912930037902,
        73.00606959366421,
        78.35676636907215,
        58.3491623801556,
        71.52271718099261,
        59.938006568924365,
        62.70532749530983,
        64.98932094700034,
        64.87556780218446,
        60.181386932796116,
        76.60087825759518,
        72.97340253600672,
        75.79704450994583,
        77.0250461913799,
        67.50916602633511,
        58.472866568461725,
        68.97103778041435,
        71.55526250047986,
        84.62509880505867,
        63.64212967845532,
        65.13874721719154,
        72.92641870569997,
        67.79266371441652,
        55.693386066101795,
        79.0961717078774,
        76.68584384968425,
        75.53081025910758,
        81.85387967141746,
        75.13911467475323,
        73.84285677958013,
        77.00286003416223,
        73.50600084316798,
        71.87208947634915,
        64.2327170736943,
        58.13760827021282,
        79.60502948815267,
        66.13669599586477,
        67.56378126448821,
        75.42878143762091,
        81.39779087939942,
        56.68784475629862,
        80.38996695921522,
        64.28932193416098,
        81.37220117069518,
        69.92747144033395,
        67.72798669383981,
        73.80756757104065,
        65.11762077387303,
        67.03266985655684,
        67.3087414800296,
        73.71078855093644,
        59.29645353105541,
        75.76971122296456,
        64.32575739358947,
        85.58129192056016,
        68.04500287831779,
        65.21543787362894,
        73.08367659158307,
        81.27040482631213,
        82.25891885151177,
        84.43660942493855,
        71.45576929288536,
        56.30773562247423,
        72.19773737944871,
        76.35304562757457,
        57.436200827818894,
        62.3985839361116,
        60.840992875827304,
        65.30019519055794,
        72.32997061475756,
        80.95702723812039,
        66.9702879054542,
        64.46258883516094,
        81.17649400112649,
        62.30254561581312,
        76.5736179406708,
        73.00366085333441,
        67.93706459301434,
        84.4024529003551,
        67.29736587235578,
        63.249685326980725,
        81.36381549611015,
        74.90149783458449,
        82.01543581602115,
        72.3368965239786,
        69.60395103234723,
        80.58393861782139,
        75.95295336939832,
        60.59479565284642,
        63.26798684387559,
        65.91042762950396,
        64.56161708854823,
        80.92827195465162,
        58.60306141334365,
        61.91809495477324,
        74.24226224145616,
        69.74554311915043,
        58.08981077004346,
        62.63677390172483,
        72.89442487740976,
        59.65377624835174,
        71.6065878580021
      ],
      "fitted": [
        81.70374917603512,
        64.13491686260178,
        82.64681158694906,
        64.21769812415015,
        67.30114859509409,
        73.48940039008959,
        63.32152148791645,
        71.27785067192532,
        83.74184483288698,
        75.595269123548,
        65.98570254310665,
        61.74748066025161,
        82.62084346102745,
        73.05703599032854,
        83.78779865085656,
        75.011056146333,
        75.79867810332385,
        69.5133660430072,
        67.95451487934056,
        63.84974545274025,
        87.30657870684291,
        62.40070907169882,
        69.03518258451587,
        69.49524255384654,
        65.58077098838575,
        72.09316508492583,
        86.48891477499896,
        69.6935396050392,
        79.09207386517284,
        59.640995351216176,
        86.27253254938601,
        64.45049730202167,
        62.579071766652966,
        72.1080901842,
        69.74406742732788,
        84.43041378868313,
        81.34823387449448,
        83.07157116686575,
        73.72546524664845,
        82.118411252948,
        65.98495872974095,
        68.73279411946608,
        73.00019703535573,
        57.62603287138304,
        68.85284214109201,
        56.11217352965113,
        79.14565801945012,
        76.07693793955323,
        76.81076089594966,
        71.54442945332039,
        54.80867071116357,
        76.65715260558967,
        66.98363063782597,
        68.99076849774308,
        66.16181988699364,
        67.7445951048989,
        76.56940535557189,
        73.65277572800285,
        79.52096200230763,
        62.56623665253233,
        54.48553555046848,
        63.87196157043707,
        79.22765664315368,
        77.43056179200593,
        72.09810969806499,
        73.19858745361249,
        68.14648360761744,
        70.4179390661161,
        64.11081119848464,
        74.7549592929509,
        62.825928910985375,
        61.478005009949136,
        68.43718845013683,
        78.1683911268954,
        76.87963226638784,
        73.61279627659246,
        71.95898575471551,
        66.16223483584724,
        65.9799145305134,
        65.35139958935261,
        63.77531780356479,
        59.50719181865588,
        77.71800640358516,
        77.07550989036886,
        75.57393443047772,
        66.8538833234107,
        78.65382184288839,
        85.55237240986888,
        66.631561932419,
        80.59298730197949,
        80.51888102754762,
        65.48033194479375,
        80.04150628516436,
        78.17129997074153,
        73.54653513291416,
        81.22138338502111,
        71.22604681867122,
        63.26658982877427,
        68.09585856145708,
        74.39160628551785,
        83.63068219459866,
        63.251062866215214,
        65.97629298070646,
        69.85365878929387,
        69.5326659278848,
        68.59516081381007,
        81.88007101837006,
        83.63213389264816,
        78.17352303388029,
        77.19120228541048,
        78.08418621301375,
        74.09193457565442,
        84.90248856464198,
        83.47362708425719,
        79.34212719768207,
        78.41202651396851,
        69.33521774773516,
        81.14482606548611,
        80.50416773485117,
        68.16763002933762,
        80.3232639263864,
        88.83446411176406,
        89.10233120194597,
        58.027033078336295,
        80.88505276966168,
        81.66846557261785,
        88.69611740497868,
        89.50026209940694,
        88.91887954823403,
        78.20905962203429,
        88.29287057127475,
        90.48314790600674,
        77.19832423843658,
        87.93860525750567,
        80.38974012854987,
        92.89936909338765,
        82.40690456971018,
        76.4280361210497,
        85.40151030786069,
        71.80785335485595,
        73.39126110132966,
        74.3814567339863,
        84.93787921268222,
        71.51126618238567,
        87.59623184142706,
        59.51516283138676,
        77.39827755585661,
        61.84302844212499,
        74.37564109941403,
        68.08258139269921,
        73.43327816810715,
        53.4256741791906,
        66.59922898002762,
        55.01451836795937,
        57.781839294344834,
        60.06583274603534,
        59.95207960121947,
        55.25789873183112,
        71.67739005663019,
        68.04991433504172,
        70.87355630898084,
        72.1015579904149,
        62.58567782537011,
        53.54937836749673,
        64.04754957944935,
        66.63177429951486,
        86.90190667012314,
        65.91893754351979,
        67.415555082256,
        75.20322657076444,
        70.06947157948099,
        57.970193931166264,
        81.37297957294187,
        78.96265171474872,
        77.80761812417205,
        84.13068753648193,
        77.4159225398177,
        76.1196646446446,
        79.2796678992267,
        75.78280870823245,
        74.14889734141362,
        66.50952493875877,
        58.88633892888979,
        80.35376014682963,
        66.88542665454173,
        68.31251192316518,
        76.17751209629787,
        82.14652153807639,
        57.436575414975586,
        81.13869761789218,
        65.03805259283794,
        82.12093182937214,
        70.67620209901091,
        68.47671735251677,
        74.55629822971761,
        65.86635143254999,
        67.7814005152338,
        68.05747213870656,
        74.4595192096134,
        60.04518418973238,
        76.51844188164152,
        65.07448805226643,
        86.33002257923712,
        68.79373353699475,
        65.9641685323059,
        73.83240725026003,
        82.01913548498909,
        82.5188499703841,
        84.69654054381088,
        71.7157004117577,
        56.567666741346564,
        72.45766849832104,
        76.6129767464469,
        57.696131946691224,
        62.65851505498393,
        61.100923994699635,
        65.56012630943027,
        72.58990173362989,
        81.21695835699272,
        67.23021902432653,
        64.72251995403327,
        81.43642511999882,
        62.562476734685454,
        76.83354905954313,
        73.26359197220674,
        68.19699571188667,
        84.66238401922743,
        67.55729699122811,
        63.509616445853055,
        81.62374661498248,
        70.20680494282718,
        77.32074292426384,
        67.64220363222128,
        64.90925814058991,
        75.88924572606408,
        71.258260477641,
        55.90010276108911,
        58.57329395211828,
        61.215734737746644,
        59.86692419679092,
        76.23357906289431,
        53.90836852158634,
        57.223402063015925,
        69.54756934969885,
        65.05085022739311,
        53.39511787828614,
        57.94208100996752,
        68.19973198565245,
        54.95908335659443,
        66.91189496624479
      ],
      "residuals": [
        -3.4467491760351123,
        3.10708313739822,
        5.576188413050943,
        4.32830187584986,
        -7.16414859509409,
        -1.3424003900895798,
        -2.9665214879164523,
        -1.6078506719253198,
        -1.2998448328869898,
        -3.4662691235479883,
        -4.1857025431066575,
        1.9595193397483897,
        -6.228843461027452,
        4.020964009671459,
        7.249201349143448,
        -0.5540561463330107,
        0.23632189667614512,
        3.248633956992805,
        1.2194851206594421,
        -4.798745452740249,
        4.776421293157085,
        2.0162909283011814,
        -1.970182584515868,
        11.30775744615346,
        2.6602290116142484,
        -6.465165084925829,
        -0.2529147749989562,
        0.9914603949607965,
        0.3499261348271574,
        -1.560995351216178,
        2.4524674506139803,
        0.4175026979783212,
        -4.942071766652965,
        3.4159098158000063,
        -6.504067427327875,
        -0.29041378868312506,
        1.4447661255055237,
        -1.3565711668657485,
        -8.22946524664846,
        -3.4004112529479897,
        3.9630412702590405,
        7.264205880533922,
        -0.12319703535573012,
        -1.7970328713830384,
        -6.235842141092014,
        -3.4761735296511276,
        3.9693419805498706,
        -10.092937939553238,
        7.166239104050348,
        -5.9014294533203895,
        -6.509670711163572,
        3.3768473944103334,
        5.329369362174035,
        3.7052315022569218,
        0.3731801130063559,
        7.821404895101097,
        0.13359464442811486,
        -9.906775728002849,
        4.420037997692376,
        -9.764236652532333,
        -2.626535550468475,
        -6.726961570437069,
        3.8473433568463236,
        -4.473561792005938,
        4.47589030193501,
        -4.901587453612493,
        3.766516392382556,
        5.770060933883897,
        9.092188801515363,
        5.633040707049105,
        -7.075928910985375,
        -4.017005009949138,
        4.980811549863176,
        -1.2053911268954067,
        0.5303677336121524,
        -2.9357962765924555,
        0.0620142452844874,
        0.8447651641527614,
        2.6490854694866073,
        2.949600410647392,
        3.787682196435213,
        0.9608081813441203,
        3.9109935964148406,
        -1.921509890368867,
        -0.15893443047771427,
        8.609116676589295,
        -0.8598218428883939,
        -0.5563724098688851,
        2.6044380675810004,
        -4.658987301979494,
        -5.272881027547626,
        3.209668055206251,
        -0.2965062851643552,
        1.8967000292584686,
        -8.31753513291416,
        5.787616614978887,
        -7.918046818671222,
        0.91241017122573,
        -4.071858561457077,
        7.103393714482152,
        5.7573178054013425,
        -2.5410628662152135,
        -3.4982929807064593,
        -1.2786587892938712,
        4.914334072115196,
        -9.08816081381007,
        -8.159071018370057,
        -4.327133892648149,
        9.393476966119707,
        -3.3432022854104844,
        -6.3101862130137505,
        -10.09493457565442,
        -1.5574885646419858,
        6.325372915742818,
        -5.939127197682069,
        5.91297348603149,
        -5.420217747735158,
        -8.192826065486116,
        -3.972167734851169,
        4.633369970662386,
        4.475736073613604,
        7.76453588823594,
        -3.0553312019459753,
        6.036966921663698,
        3.531947230338318,
        14.337534427382153,
        -3.7331174049786853,
        1.2947379005930628,
        7.276120451765962,
        -6.939059622034293,
        -0.03587057127474225,
        -1.6111479060067353,
        -0.33732423843657955,
        6.056394742494334,
        -3.982740128549878,
        0.07663090661235117,
        4.891095430289823,
        2.9299638789503035,
        6.775489692139317,
        11.043146645144049,
        -4.6162611013296555,
        1.2365432660136975,
        1.599120787317787,
        -1.4632661823856665,
        -5.742231841427056,
        -0.8261628313867604,
        -2.000277555856613,
        -1.0760284421249864,
        -3.5236410994140215,
        -4.981581392699212,
        5.180721831892853,
        -0.813674179190599,
        -3.292228980027616,
        4.015481632040633,
        5.612160705655164,
        -3.6668327460353396,
        5.639920398780532,
        4.671101268168883,
        -13.38339005663019,
        -4.230914335041717,
        2.893443691019158,
        -3.691557990414907,
        1.126322174629891,
        0.006621632503268415,
        3.596450420550653,
        1.8452257004851447,
        2.1860933298768543,
        8.774062456480209,
        5.961444917743989,
        2.1507734292355565,
        -13.900471579480993,
        0.643806068833733,
        -10.459979572941876,
        2.239348285251282,
        -8.294618124172047,
        4.125312463518071,
        8.559077460182294,
        4.504335355355394,
        -3.0446678992266953,
        4.113191291767549,
        -1.1518973414136155,
        -3.215524938758776,
        -2.4853389288897887,
        -1.5687601468296322,
        1.6935733454582618,
        3.6684880768348194,
        -6.762512096297868,
        -0.21452153807638297,
        -0.059575414975583385,
        8.982302382107818,
        3.66194740716206,
        2.3510681706278547,
        -2.0252020990109116,
        -4.040717352516765,
        -1.2572982297176054,
        -3.388351432549989,
        6.061599484766205,
        -2.571472138706554,
        -0.676519209613403,
        2.81681581026762,
        2.0595581183584812,
        -0.35248805226643753,
        -8.268022579237126,
        -2.291733536994755,
        0.44583146769409154,
        1.2065927497399684,
        4.063864515010906,
        -0.12484997038409062,
        -0.27654054381088145,
        -2.375700411757691,
        1.497333258653434,
        8.805331501678964,
        -1.2089767464469077,
        5.2538680533087785,
        -9.519515054983927,
        6.390076005300365,
        -1.9791263094302707,
        6.20909826637012,
        -10.753958356992726,
        2.721780975673468,
        2.041480045966722,
        -2.487425119998818,
        -1.0734767346854568,
        -4.80054905954313,
        -0.33159197220673775,
        -2.431995711886671,
        5.457615980772573,
        -2.6562969912281176,
        -2.9986164458530524,
        5.006253385017516,
        -2.876804942827178,
        1.065257075736156,
        -14.375203632221279,
        2.3207418594100915,
        4.12075427393593,
        1.0677395223589912,
        2.9438972389108926,
        -1.7252939521182782,
        1.7732652622533536,
        2.2270758032090825,
        5.394420937105693,
        -0.9583685215863369,
        2.745597936984076,
        -1.266569349698841,
        -2.7168502273931097,
        0.059882121713854986,
        3.075918990032484,
        -2.492731985652455,
        -4.273083356594427,
        -2.6878949662447837
      ],
      "marginal_residuals": [
        -5.906587137678514,
        3.756933499200663,
        6.226038774853379,
        4.978152237652303,
        -6.514298233291655,
        -0.692550028287144,
        -2.3166711261140094,
        -0.958000310122884,
        -0.649994471084554,
        -2.8164187617455525,
        -3.5358521813042216,
        2.6093697015508326,
        -5.578993099225016,
        4.670814371473895,
        7.8990517109458835,
        0.09579421546942513,
        0.8861722584785809,
        3.8984843187952407,
        3.0096949715554615,
        -3.0085356018442297,
        6.566631144053105,
        3.8065007791972008,
        -0.17997273361984867,
        13.097967297049479,
        4.450438862510268,
        -4.6749552340298095,
        1.5372950758970632,
        2.781670245856816,
        2.1401359857231768,
        0.2292144996798413,
        4.24267730151,
        2.2077125488743334,
        -3.151861915756946,
        5.206119666696026,
        -4.713857576431856,
        1.4997960622128943,
        3.234975976401543,
        0.43363868403027084,
        -6.43925539575244,
        -1.6102014020519704,
        5.75325112115506,
        9.054415731429941,
        -1.7368558952107804,
        -3.4106917312380887,
        -7.849501000947065,
        -5.089832389506178,
        2.3556831206948203,
        -11.706596799408288,
        5.552580244195298,
        -7.51508831317544,
        -8.123329571018623,
        1.7631885345552831,
        3.7157105023189843,
        2.0915726424018715,
        -1.2404787468486944,
        6.207746035246046,
        -1.4800642154269354,
        -15.303296048807944,
        -0.9764823231127195,
        -15.160756973337435,
        -8.023055871273577,
        -12.123481891242172,
        -1.5491769639587716,
        -9.870082112811033,
        -0.9206300188700851,
        -10.298107774417588,
        -1.6300039284225392,
        0.37354061307880215,
        3.6956684807102675,
        0.23652038624400973,
        -12.472449231790478,
        -9.41352533075424,
        -0.4157087709419187,
        -6.601911447700502,
        -4.866152587192943,
        -8.33231659739755,
        -5.334506075520608,
        -4.551755156652334,
        -2.747434851318488,
        3.375361262419588,
        4.2134430482074094,
        1.3865690331163165,
        4.336754448187037,
        -1.4957490385966707,
        0.266826421294482,
        9.034877528361491,
        -0.43406099111619767,
        -0.1306115580966889,
        3.0301989193531966,
        -4.233226450207297,
        -4.84712017577543,
        3.635428906978447,
        0.12925456660784107,
        2.322460881030665,
        -7.891774281141963,
        6.2133774667510835,
        -7.492285966899026,
        1.3381710229979262,
        -3.646097709684881,
        9.536360860331484,
        8.190284951250675,
        -0.10809572036588833,
        -1.0653258348571342,
        1.154308356555461,
        7.347301217964528,
        -6.655193667960738,
        -5.726103872520724,
        -1.8941667467988168,
        11.826444111969039,
        -0.9102351395611521,
        -3.877219067164418,
        -7.661967429805088,
        0.8754785812073465,
        8.75834006159215,
        -3.5061600518327367,
        8.345940631880822,
        -2.987250601885826,
        -5.759858919636784,
        -1.5392005890018368,
        7.066337116511718,
        6.908703219462936,
        10.197503034085273,
        -0.622364056096643,
        8.469934067513023,
        5.96491437618765,
        16.770501573231485,
        6.770822977115245,
        11.798678282686993,
        17.780060833859892,
        3.564880760059637,
        10.468069810819188,
        8.892792476087195,
        10.16661614365735,
        16.560335124588264,
        6.521200253544052,
        10.580571288706281,
        15.395035812383753,
        13.433904261044233,
        17.279430074233247,
        21.54708702723797,
        5.887679280764274,
        11.740483648107627,
        12.103061169411717,
        9.04067419970827,
        4.7617085406668735,
        -5.749651032351757,
        -6.923765756821609,
        -5.999516643089983,
        -8.447129300379018,
        -9.905069593664209,
        0.2572336309278569,
        -5.7371623801555955,
        -8.215717180992613,
        -0.9080065689243639,
        0.6886725046901674,
        -8.590320947000336,
        0.7164321978155357,
        -0.2523869327961137,
        -18.306878257595187,
        -9.154402536006714,
        -2.0300445099458386,
        -8.615046191379903,
        -3.7971660263351055,
        -4.916866568461728,
        -1.3270377804143436,
        -3.078262500479852,
        4.462901194941324,
        11.050870321544679,
        8.238252782808459,
        4.427581294300026,
        -11.623663714416523,
        2.9206139338982027,
        -8.183171707877406,
        4.5161561503157515,
        -6.017810259107577,
        6.402120328582541,
        10.835885325246764,
        6.781143220419864,
        -0.7678600341622257,
        6.389999156832019,
        1.124910523650854,
        -0.9387170736943062,
        -1.7366082702128196,
        -0.8200294881526702,
        2.4423040041352237,
        4.417218735511781,
        -6.0137814376209064,
        0.534209120600579,
        0.6891552437013857,
        9.73103304078478,
        4.410678065839022,
        3.0997988293048166,
        -1.2764714403339497,
        -3.291986693839803,
        -0.5085675710406434,
        -2.639620773873027,
        6.810330143443167,
        -1.8227414800295918,
        0.07221144906355903,
        3.5655464689445893,
        2.808288777035443,
        0.39624260641052444,
        -7.519291920560164,
        -1.5430028783177931,
        1.1945621263710535,
        1.9553234084169304,
        4.812595173687868,
        0.13508114848823993,
        -0.016609424938550887,
        -2.1157692928853606,
        1.7572643775257646,
        9.065262620551295,
        -0.9490456275745771,
        5.513799172181109,
        -9.259583936111596,
        6.650007124172696,
        -1.7191951905579401,
        6.46902938524245,
        -10.494027238120395,
        2.9817120945457987,
        2.3014111648390525,
        -2.2274940011264874,
        -0.8135456158131262,
        -4.540617940670799,
        -0.07166085333440719,
        -2.1720645930143405,
        5.717547099644904,
        -2.396365872355787,
        -2.738685326980722,
        5.266184503889846,
        -7.571497834584491,
        -3.6294358160211573,
        -19.069896523978592,
        -2.3739510323472217,
        -0.5739386178213834,
        -3.626953369398322,
        -1.7507956528464206,
        -6.419986843875591,
        -2.9214276295039596,
        -2.4676170885482307,
        0.6997280453483796,
        -5.65306141334365,
        -1.949094954773237,
        -5.961262241456154,
        -7.411543119150423,
        -4.634810770043458,
        -1.618773901724829,
        -7.187424877409768,
        -8.96777624835174,
        -7.382587858002097
      ],
      "random_effects": [
        -2.4598379616433954,
        0.6498503618024409,
        1.790209850896017,
        -1.6136588598550512,
        -5.3965203208051005,
        0.4257608517721928,
        2.432967145849326,
        10.50394038209393,
        -4.9234882009649965,
        2.2768078650644687,
        0.7487306586769661,
        0.25993111887233067,
        -4.694692891757315
      ],
      "residual_variance": 25.277067090778434,
      "random_intercept_variance": 18.03945863575373,
      "sigma": 5.027630365368802,
      "icc": 0.4164567294625901,
      "log_likelihood": -775.2271156725185,
      "aic": 1560.454231345037,
      "df_residual": 247
    },
    "phit": {
      "coefficients": [
        46.45576735468992,
        1.62253575914493,
        0.24465092062708269
      ],
      "covariance": [
        [
          4.818694248372385,
          0.13722040570680075,
          -0.0696409413525591
        ],
        [
          0.13722040570680072,
          0.025685102582108252,
          -0.005156688619169396
        ],
        [
          -0.06964094135255909,
          -0.005156688619169396,
          0.0017340610249537516
        ]
      ],
      "std_errors": [
        2.1951524430828,
        0.16026572491368282,
        0.04164205836595679
      ],
      "z_statistics": [
        21.162888937885775,
        10.12403469312486,
        5.875091919737803
      ],
      "p_values": [
        2.0995628493816492e-99,
        4.322224314723402e-24,
        4.226087858596827e-09
      ],
      "conf_int": [
        [
          42.153347625672524,
          50.75818708370731
        ],
        [
          1.3084207103579082,
          1.936650807931952
        ],
        [
          0.16303398598769253,
          0.32626785526647284
        ]
      ],
      "fitted": [
        81.70374917606037,
        64.13491686260114,
        82.6468115869485,
        64.21769812414927,
        67.30114859509337,
        73.4894003900892,
        63.3215214879157,
        71.27785067192481,
        83.74184483288622,
        75.59526912354714,
        65.98570254310552,
        61.74748066025105,
        82.62084346102681,
        73.05703599032806,
        83.7877986508558,
        75.01105614633266,
        75.7986781033231,
        69.51336604300657,
        67.95451487933899,
        63.849745452738624,
        87.30657870684153,
        62.40070907169744,
        69.0351825845145,
        69.49524255384524,
        65.58077098838444,
        72.09316508492425,
        86.48891477499753,
        69.69353960503766,
        79.09207386517124,
        59.640995351214364,
        86.27253254938442,
        64.45049730201997,
        62.57907176665156,
        72.10809018419819,
        69.74406742732648,
        84.43041378868166,
        81.3482338744929,
        83.07157116686443,
        73.72546524664686,
        82.11841125294615,
        65.98495872973915,
        68.73279411946424,
        73.00019703535841,
        57.62603287138564,
        68.85284214109456,
        56.11217352965354,
        79.14565801945241,
        76.07693793955553,
        76.81076089595231,
        71.54442945332283,
        54.80867071116592,
        76.65715260559205,
        66.98363063782878,
        68.99076849774559,
        66.16181988699589,
        67.7445951049013,
        76.56940535557436,
        73.6527757280086,
        79.52096200231334,
        62.56623665253778,
        54.485535550473955,
        63.87196157044279,
        79.22765664315932,
        77.43056179201155,
        72.09810969807053,
        73.19858745361773,
        68.14648360762313,
        70.41793906612162,
        64.11081119849013,
        74.75495929295629,
        62.825928910990626,
        61.478005009954586,
        68.4371884501421,
        78.16839112690106,
        76.87963226639329,
        73.61279627659806,
        71.95898575472116,
        66.162234835853,
        65.97991453051885,
        65.3513995893523,
        63.77531780356434,
        59.507191818655556,
        77.71800640358495,
        77.07550989036824,
        75.5739344304771,
        66.85388332341066,
        78.65382184288833,
        85.55237240986864,
        66.63156193241855,
        80.59298730197914,
        80.5188810275474,
        65.48033194479362,
        80.04150628516392,
        78.17129997074126,
        73.5465351329139,
        81.22138338502049,
        71.22604681867081,
        63.26658982877402,
        68.09585856145651,
        74.39160628551598,
        83.63068219459683,
        63.251062866213125,
        65.97629298070477,
        69.85365878929166,
        69.53266592788282,
        68.59516081380848,
        81.8800710183682,
        83.63213389264624,
        78.17352303387824,
        77.1912022854083,
        78.08418621301192,
        74.09193457565259,
        84.90248856464,
        83.47362708425554,
        79.34212719768026,
        78.41202651396696,
        69.33521774773325,
        81.1448260654842,
        80.5041677348493,
        68.16763002933551,
        80.32326392638451,
        88.83446411176236,
        89.10233120194421,
        58.027033078333886,
        80.88505276965958,
        81.6684655726158,
        88.69611740496725,
        89.50026209939503,
        88.91887954822238,
        78.20905962202244,
        88.29287057126294,
        90.48314790599458,
        77.19832423842452,
        87.93860525749362,
        80.38974012853784,
        92.89936909337553,
        82.40690456969817,
        76.42803612103734,
        85.40151030784854,
        71.80785335484397,
        73.39126110131811,
        74.38145673397429,
        84.93787921267018,
        71.51126618237348,
        87.59623184141496,
        59.51516283139155,
        77.39827755586202,
        61.84302844213039,
        74.37564109941923,
        68.08258139270404,
        73.4332781681124,
        53.42567417919587,
        66.59922898003283,
        55.01451836796473,
        57.78183929435035,
        60.06583274604084,
        59.95207960122451,
        55.25789873183648,
        71.67739005663569,
        68.04991433504702,
        70.87355630898645,
        72.10155799042039,
        62.58567782537544,
        53.54937836750182,
        64.04754957945454,
        66.63177429952015,
        86.90190667012024,
        65.91893754351703,
        67.4155550822534,
        75.20322657076169,
        70.06947157947816,
        57.97019393116305,
        81.37297957293912,
        78.96265171474545,
        77.80761812416925,
        84.13068753647893,
        77.41592253981486,
        76.11966464464163,
        79.27966789922372,
        75.78280870822945,
        74.14889734141079,
        66.50952493875563,
        58.88633892888918,
        80.35376014682883,
        66.88542665454102,
        68.31251192316489,
        76.17751209629705,
        82.14652153807579,
        57.436575414974854,
        81.13869761789144,
        65.0380525928376,
        82.12093182937174,
        70.67620209901065,
        68.47671735251616,
        74.55629822971706,
        65.86635143254955,
        67.78140051523312,
        68.05747213870617,
        74.45951920961274,
        60.045184189731394,
        76.51844188164108,
        65.07448805226583,
        86.33002257923673,
        68.79373353699445,
        65.96416853230556,
        73.83240725025937,
        82.01913548498828,
        82.51884997038404,
        84.69654054381097,
        71.7157004117577,
        56.56766674134617,
        72.4576684983213,
        76.61297674644628,
        57.69613194669099,
        62.65851505498373,
        61.10092399469942,
        65.56012630943052,
        72.58990173362965,
        81.21695835699249,
        67.23021902432635,
        64.72251995403346,
        81.43642511999847,
        62.5624767346852,
        76.83354905954307,
        73.26359197220657,
        68.19699571188627,
        84.6623840192276,
        67.5572969912282,
        63.50961644585273,
        81.62374661498224,
        70.20680494283239,
        77.32074292426893,
        67.64220363222654,
        64.90925814059531,
        75.88924572606938,
        71.25826047764666,
        55.900102761094324,
        58.573293952123365,
        61.2157347377521,
        59.86692419679625,
        76.2335790628996,
        53.908368521591385,
        57.22340206302101,
        69.5475693497042,
        65.05085022739837,
        53.39511787829142,
        57.942081009972846,
        68.19973198565782,
        54.959083356599855,
        66.9118949662499
      ],
      "residuals": [
        -3.446749176060365,
        3.1070831373988597,
        5.576188413051497,
        4.328301875850741,
        -7.164148595093366,
        -1.342400390089196,
        -2.9665214879157062,
        -1.6078506719248082,
        -1.2998448328862224,
        -3.4662691235471357,
        -4.185702543105521,
        1.959519339748951,
        -6.228843461026813,
        4.020964009671943,
        7.249201349144201,
        -0.5540561463326696,
        0.2363218966768983,
        3.24863395699343,
        1.2194851206610196,
        -4.798745452738622,
        4.776421293158464,
        2.01629092830256,
        -1.9701825845145038,
        11.307757446154753,
        2.660229011615556,
        -6.4651650849242515,
        -0.2529147749975209,
        0.9914603949623455,
        0.349926134828749,
        -1.5609953512143662,
        2.452467450615572,
        0.4175026979800265,
        -4.942071766651559,
        3.415909815801811,
        -6.504067427326483,
        -0.29041378868166134,
        1.4447661255071012,
        -1.356571166864427,
        -8.229465246646868,
        -3.4004112529461423,
        3.9630412702608453,
        7.264205880535755,
        -0.12319703535841597,
        -1.797032871385639,
        -6.235842141094558,
        -3.4761735296535363,
        3.9693419805475827,
        -10.09293793955554,
        7.1662391040476905,
        -5.901429453322834,
        -6.509670711165917,
        3.3768473944079602,
        5.329369362171221,
        3.7052315022544065,
        0.3731801130041106,
        7.821404895098709,
        0.13359464442564217,
        -9.906775728008604,
        4.420037997686663,
        -9.764236652537782,
        -2.626535550473953,
        -6.726961570442789,
        3.847343356840682,
        -4.473561792011552,
        4.475890301929468,
        -4.901587453617736,
        3.7665163923768716,
        5.7700609338783835,
        9.092188801509877,
        5.633040707043719,
        -7.075928910990626,
        -4.0170050099545875,
        4.980811549857904,
        -1.2053911269010626,
        0.5303677336067096,
        -2.9357962765980545,
        0.06201424527884569,
        0.844765164147006,
        2.6490854694811503,
        2.9496004106477045,
        3.787682196435661,
        0.9608081813444471,
        3.9109935964150537,
        -1.9215098903682417,
        -0.158934430477089,
        8.609116676589338,
        -0.8598218428883371,
        -0.5563724098686436,
        2.604438067581455,
        -4.658987301979138,
        -5.272881027547399,
        3.2096680552063788,
        -0.29650628516391464,
        1.8967000292587386,
        -8.317535132913903,
        5.7876166149795125,
        -7.91804681867081,
        0.9124101712259787,
        -4.071858561456509,
        7.103393714484028,
        5.757317805403176,
        -2.5410628662131245,
        -3.4982929807047682,
        -1.2786587892916543,
        4.914334072117185,
        -9.088160813808479,
        -8.159071018368195,
        -4.327133892646231,
        9.393476966121753,
        -3.343202285408296,
        -6.310186213011917,
        -10.094934575652587,
        -1.5574885646399963,
        6.325372915744467,
        -5.93912719768025,
        5.912973486033039,
        -5.420217747733254,
        -8.192826065484198,
        -3.9721677348493074,
        4.633369970664489,
        4.475736073615494,
        7.764535888237646,
        -3.055331201944213,
        6.036966921666107,
        3.531947230340421,
        14.337534427384199,
        -3.7331174049672597,
        1.2947379006049715,
        7.276120451777615,
        -6.939059622022441,
        -0.035870571262933026,
        -1.611147905994585,
        -0.33732423842451453,
        6.056394742506384,
        -3.9827401285378414,
        0.07663090662447303,
        4.8910954303018315,
        2.929963878962667,
        6.775489692151467,
        11.043146645156028,
        -4.616261101318102,
        1.2365432660257056,
        1.5991207873298237,
        -1.4632661823734736,
        -5.742231841414963,
        -0.8261628313915494,
        -2.000277555862027,
        -1.0760284421303865,
        -3.5236410994192227,
        -4.981581392704044,
        5.18072183188761,
        -0.8136741791958713,
        -3.2922289800328315,
        4.015481632035268,
        5.61216070564965,
        -3.666832746040839,
        5.639920398775487,
        4.671101268163525,
        -13.38339005663569,
        -4.230914335047018,
        2.8934436910135446,
        -3.6915579904203923,
        1.126322174624562,
        0.006621632498180929,
        3.596450420545466,
        1.8452257004798582,
        2.1860933298797534,
        8.774062456482966,
        5.96144491774659,
        2.1507734292383134,
        -13.900471579478165,
        0.6438060688369447,
        -10.459979572939119,
        2.2393482852545503,
        -8.294618124169247,
        4.12531246352107,
        8.559077460185136,
        4.504335355358364,
        -3.0446678992237253,
        4.113191291770548,
        -1.1518973414107876,
        -3.2155249387556353,
        -2.4853389288891776,
        -1.5687601468288364,
        1.6935733454589723,
        3.6684880768351036,
        -6.762512096297044,
        -0.2145215380757861,
        -0.059575414974851526,
        8.982302382108557,
        3.661947407162401,
        2.3510681706282526,
        -2.025202099010656,
        -4.040717352516154,
        -1.2572982297170512,
        -3.3883514325495483,
        6.061599484766887,
        -2.57147213870617,
        -0.676519209612735,
        2.816815810268608,
        2.0595581183589218,
        -0.3524880522658407,
        -8.268022579236728,
        -2.2917335369944567,
        0.4458314676944326,
        1.2065927497406363,
        4.063864515011716,
        -0.12484997038403378,
        -0.2765405438109667,
        -2.375700411757691,
        1.4973332586538248,
        8.805331501678708,
        -1.2089767464462824,
        5.253868053309013,
        -9.519515054983728,
        6.390076005300578,
        -1.9791263094305123,
        6.209098266370361,
        -10.753958356992499,
        2.721780975673653,
        2.041480045966537,
        -2.487425119998477,
        -1.073476734685201,
        -4.800549059543073,
        -0.3315919722065672,
        -2.431995711886273,
        5.4576159807724025,
        -2.656296991228203,
        -2.9986164458527256,
        5.006253385017757,
        -2.8768049428323934,
        1.0652570757310684,
        -14.375203632226537,
        2.3207418594046914,
        4.120754273930629,
        1.0677395223533352,
        2.9438972389056772,
        -1.7252939521233657,
        1.7732652622478966,
        2.2270758032037534,
        5.394420937100406,
        -0.9583685215913818,
        2.7455979369789887,
        -1.2665693497041985,
        -2.7168502273983677,
        0.05988212170857565,
        3.075918990027155,
        -2.4927319856578265,
        -4.273083356599855,
        -2.6878949662498997
      ],
      "log_likelihood": -775.2271156725184,
      "aic": 1560.4542313450368,
      "df_residual": 247,
      "evaluations": 107,
      "fixed_fitted": [
        84.16358713768051,
        63.48506650080141,
        81.99696122514877,
        63.56784776234954,
        66.65129823329363,
        72.83955002828947,
        62.671671126115974,
        70.62800031012507,
        83.09199447108648,
        74.9454187617474,
        65.33585218130578,
        61.09763029845132,
        81.97099309922707,
        72.40718562852832,
        83.13794828905607,
        74.36120578453293,
        75.14882774152336,
        68.86351568120683,
        66.16430502844649,
        62.05953560184613,
        85.51636885594904,
        60.61049922080495,
        67.244972733622,
        67.70503270295275,
        63.79056113749195,
        70.30295523403176,
        84.69870492410503,
        67.90332975414516,
        77.30186401427875,
        57.85078550032187,
        84.48232269849193,
        62.66028745112747,
        60.788861915759064,
        70.3178803333057,
        67.95385757643399,
        82.64020393778917,
        79.55802402360041,
        81.28136131597194,
        71.93525539575437,
        80.32820140205365,
        64.19474887884665,
        66.94258426857175,
        74.61385589521285,
        59.239691731240086,
        70.46650100094901,
        57.725832389507985,
        80.75931687930685,
        77.69059679940999,
        78.42441975580675,
        73.15808831317729,
        56.42232957102036,
        78.27081146544649,
        68.59728949768322,
        70.60442735760003,
        67.77547874685034,
        69.35825396475575,
        78.1830642154288,
        79.04929604881009,
        84.91748232311483,
        67.96275697333927,
        59.88205587127544,
        69.26848189124428,
        84.6241769639608,
        82.82708211281303,
        77.49463001887202,
        78.59510777441922,
        73.54300392842461,
        75.8144593869231,
        69.50733151929161,
        80.15147961375777,
        68.22244923179211,
        66.87452533075607,
        73.83370877094359,
        83.56491144770254,
        82.27615258719477,
        79.00931659739955,
        77.35550607552264,
        71.55875515665448,
        71.37643485132034,
        64.92563873758243,
        63.34955695179447,
        59.081430966885684,
        77.29224555181509,
        76.64974903859837,
        75.14817357870723,
        66.42812247164079,
        78.22806099111847,
        85.12661155809877,
        66.20580108064868,
        80.16722645020927,
        80.09312017577753,
        65.05457109302375,
        79.61574543339405,
        77.7455391189714,
        73.12077428114404,
        80.79562253325062,
        70.80028596690094,
        62.84082897700415,
        67.67009770968664,
        71.95863913967057,
        81.19771504875142,
        60.81809572036772,
        63.54332583485936,
        67.42069164344625,
        67.09969878203741,
        66.16219366796307,
        79.44710387252279,
        81.19916674680083,
        75.74055588803283,
        74.75823513956288,
        75.65121906716651,
        71.65896742980718,
        82.46952141879459,
        81.04065993841013,
        76.90916005183485,
        75.97905936812155,
        66.90225060188784,
        78.71185891963879,
        78.0712005890039,
        65.7346628834901,
        77.8902967805391,
        86.40149696591695,
        86.6693640560988,
        55.59406593248848,
        78.45208562381417,
        79.23549842677039,
        78.19217702288721,
        78.99632171731498,
        78.41493916614233,
        67.70511923994239,
        77.78893018918289,
        79.97920752391454,
        66.69438385634447,
        77.43466487541357,
        69.88579974645779,
        82.39542871129548,
        71.90296418761812,
        65.92409573895729,
        74.8975699257685,
        61.303912972763925,
        62.88732071923806,
        63.87751635189424,
        74.43393883059014,
        61.00732580029343,
        77.09229145933492,
        64.43865103235318,
        82.32176575682365,
        66.76651664309202,
        79.29912930038086,
        73.00606959366567,
        78.35676636907402,
        58.3491623801575,
        71.52271718099446,
        59.93800656892636,
        62.70532749531198,
        64.98932094700247,
        64.87556780218614,
        60.181386932798105,
        76.60087825759732,
        72.97340253600865,
        75.79704450994808,
        77.02504619138202,
        67.50916602633707,
        58.472866568463445,
        68.97103778041617,
        71.55526250048177,
        84.62509880506067,
        63.642129678457465,
        65.13874721719384,
        72.92641870570212,
        67.7926637144186,
        55.693386066103486,
        79.09617170787955,
        76.68584384968588,
        75.53081025910969,
        81.85387967141936,
        75.13911467475529,
        73.84285677958206,
        77.00286003416416,
        73.50600084316989,
        71.87208947635122,
        64.23271707369607,
        58.1376082702147,
        79.60502948815436,
        66.13669599586655,
        67.56378126449042,
        75.42878143762258,
        81.39779087940131,
        56.68784475630037,
        80.38996695921696,
        64.28932193416313,
        81.37220117069727,
        69.92747144033618,
        67.72798669384169,
        73.80756757104258,
        65.11762077387507,
        67.03266985655864,
        67.3087414800317,
        73.71078855093826,
        59.29645353105691,
        75.7697112229666,
        64.32575739359136,
        85.58129192056225,
        68.04500287831998,
        65.21543787363109,
        73.08367659158489,
        81.27040482631381,
        82.25891885151381,
        84.43660942494074,
        71.45576929288747,
        56.307735622475946,
        72.19773737945107,
        76.35304562757605,
        57.43620082782076,
        62.3985839361135,
        60.840992875829194,
        65.30019519056029,
        72.32997061475942,
        80.95702723812227,
        66.97028790545612,
        64.46258883516323,
        81.17649400112825,
        62.30254561581497,
        76.57361794067285,
        73.00366085333634,
        67.93706459301605,
        84.40245290035737,
        67.29736587235797,
        63.2496853269825,
        81.36381549611201,
        74.90149783458635,
        82.01543581602289,
        72.3368965239805,
        69.60395103234927,
        80.58393861782334,
        75.95295336940062,
        60.59479565284828,
        63.267986843877324,
        65.91042762950606,
        64.56161708855021,
        80.92827195465355,
        58.603061413345344,
        61.91809495477497,
        74.24226224145816,
        69.74554311915233,
        58.08981077004538,
        62.636773901726805,
        72.89442487741178,
        59.653776248353815,
        71.60658785800386
      ],
      "marginal_residuals": [
        -5.9065871376805035,
        3.7569334991985954,
        6.226038774851233,
        4.97815223765047,
        -6.51429823329363,
        -0.6925500282894603,
        -2.3166711261159776,
        -0.9580003101250725,
        -0.6499944710864867,
        -2.8164187617474,
        -3.535852181305785,
        2.6093697015486796,
        -5.578993099227077,
        4.670814371471678,
        7.899051710943937,
        0.09579421546706612,
        0.8861722584766341,
        3.898484318793166,
        3.0096949715535146,
        -3.008535601846127,
        6.566631144050959,
        3.806500779195055,
        -0.17997273362200872,
        13.097967297047248,
        4.450438862508051,
        -4.674955234031756,
        1.5372950758949742,
        2.7816702458548406,
        2.140135985721244,
        0.2292144996781289,
        4.242677301508067,
        2.2077125488725216,
        -3.1518619157590635,
        5.206119666694306,
        -4.713857576433988,
        1.4997960622108337,
        3.234975976399596,
        0.43363868402806816,
        -6.439255395754373,
        -1.6102014020536473,
        5.75325112115334,
        9.05441573142825,
        -1.7368558952128552,
        -3.4106917312400853,
        -7.849501000949012,
        -5.089832389507983,
        2.3556831206931435,
        -11.706596799409994,
        5.552580244193251,
        -7.515088313177287,
        -8.123329571020363,
        1.763188534553521,
        3.7157105023167816,
        2.091572642399967,
        -1.2404787468503429,
        6.207746035244256,
        -1.480064215428797,
        -15.30329604881009,
        -0.9764823231148227,
        -15.160756973339268,
        -8.023055871275439,
        -12.123481891244275,
        -1.5491769639608037,
        -9.870082112813037,
        -0.9206300188720178,
        -10.298107774419222,
        -1.630003928424614,
        0.3735406130768979,
        3.6956684807083917,
        0.23652038624223337,
        -12.472449231792112,
        -9.413525330756073,
        -0.4157087709435814,
        -6.601911447702548,
        -4.866152587194776,
        -8.33231659739954,
        -5.33450607552264,
        -4.55175515665448,
        -2.7474348513203353,
        3.37536126241757,
        4.213443048205534,
        1.38656903311432,
        4.336754448184919,
        -1.495749038598376,
        0.26682642129277667,
        9.034877528359203,
        -0.4340609911184714,
        -0.1306115580987779,
        3.030198919351321,
        -4.233226450209273,
        -4.847120175777533,
        3.6354289069762444,
        0.12925456660595103,
        2.3224608810286043,
        -7.891774281144038,
        6.213377466749378,
        -7.492285966900944,
        1.3381710229958514,
        -3.646097709686643,
        9.536360860329438,
        8.190284951248586,
        -0.10809572036772153,
        -1.0653258348593582,
        1.1543083565537557,
        7.347301217962595,
        -6.6551936679630685,
        -5.726103872522785,
        -1.8941667468008205,
        11.826444111967163,
        -0.9102351395628858,
        -3.877219067166507,
        -7.661967429807177,
        0.8754785812054138,
        8.758340061589877,
        -3.50616005183484,
        8.345940631878449,
        -2.987250601887844,
        -5.759858919638788,
        -1.5392005890038973,
        7.066337116509899,
        6.908703219460904,
        10.197503034083056,
        -0.6223640560988031,
        8.46993406751151,
        5.964914376185831,
        16.77050157322961,
        6.770822977112786,
        11.798678282685017,
        17.78006083385766,
        3.564880760057605,
        10.468069810817113,
        8.89279247608546,
        10.166616143655531,
        16.56033512458643,
        6.5212002535422045,
        10.580571288704519,
        15.395035812381877,
        13.433904261042713,
        17.279430074231513,
        21.547087027236074,
        5.887679280761944,
        11.740483648105752,
        12.10306116940987,
        9.040674199706572,
        4.761708540665083,
        -5.749651032353178,
        -6.923765756823656,
        -5.999516643092015,
        -8.447129300380851,
        -9.905069593665672,
        0.25723363092598106,
        -5.7371623801575,
        -8.21571718099446,
        -0.9080065689263606,
        0.6886725046880215,
        -8.590320947002468,
        0.7164321978138588,
        -0.2523869327981032,
        -18.30687825759732,
        -9.154402536008647,
        -2.030044509948084,
        -8.61504619138202,
        -3.7971660263370666,
        -4.916866568463448,
        -1.3270377804161626,
        -3.0782625004817703,
        4.46290119493932,
        11.050870321542533,
        8.238252782806157,
        4.42758129429788,
        -11.623663714418598,
        2.9206139338965116,
        -8.183171707879552,
        4.516156150314117,
        -6.01781025910968,
        6.4021203285806365,
        10.835885325244703,
        6.781143220417931,
        -0.7678600341641584,
        6.389999156830115,
        1.1249105236487793,
        -0.9387170736960684,
        -1.7366082702146954,
        -0.8200294881543613,
        2.4423040041334474,
        4.417218735509579,
        -6.013781437622569,
        0.534209120598689,
        0.6891552436996307,
        9.731033040783032,
        4.410678065836876,
        3.0997988293027277,
        -1.2764714403361808,
        -3.291986693841679,
        -0.5085675710425761,
        -2.639620773875073,
        6.810330143441362,
        -1.822741480031695,
        0.07221144906174004,
        3.56554646894309,
        2.808288777033397,
        0.3962426064086344,
        -7.519291920562253,
        -1.5430028783199816,
        1.1945621263689077,
        1.9553234084151114,
        4.812595173686191,
        0.13508114848619357,
        -0.01660942494073936,
        -2.115769292887464,
        1.7572643775240522,
        9.065262620548936,
        -0.949045627576055,
        5.51379917217924,
        -9.2595839361135,
        6.650007124170806,
        -1.719195190560285,
        6.469029385240589,
        -10.494027238122271,
        2.98171209454388,
        2.3014111648367646,
        -2.2274940011282496,
        -0.8135456158149736,
        -4.5406179406728455,
        -0.07166085333633987,
        -2.172064593016046,
        5.71754709964263,
        -2.3963658723579755,
        -2.7386853269824982,
        5.266184503887985,
        -7.571497834586353,
        -3.629435816022891,
        -19.069896523980496,
        -2.373951032349268,
        -0.5739386178233303,
        -3.626953369400624,
        -1.7507956528482822,
        -6.419986843877325,
        -2.921427629506063,
        -2.467617088550206,
        0.699728045346447,
        -5.653061413345341,
        -1.9490949547749707,
        -5.961262241458158,
        -7.411543119152327,
        -4.634810770045384,
        -1.6187739017268044,
        -7.187424877411786,
        -8.967776248353815,
        -7.382587858003859
      ],
      "random_effects": [
        -2.459837961620144,
        0.6498503617997307,
        1.7902098508924962,
        -1.6136588598544463,
        -5.396520320801488,
        0.4257608517698696,
        2.432967145845404,
        10.503940382080046,
        -4.923488200961626,
        2.2768078650595647,
        0.7487306586744811,
        0.2599311188702266,
        -4.694692891753957
      ],
      "group_sizes": [
        1,
        17,
        24,
        15,
        22,
        20,
        27,
        19,
        21,
        16,
        25,
        23,
        20
      ],
      "n_groups": 13,
      "group_labels": [
        99,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12
      ],
      "residual_variance": 25.27706709079817,
      "random_intercept_variance": 18.03945863546519,
      "sigma": 5.027630365370765,
      "icc": 0.4164567294585133,
      "boundary": false,
      "method": "ML",
      "converged": true,
      "n_input": 250,
      "n_observations": 250,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119,
        120,
        121,
        122,
        123,
        124,
        125,
        126,
        127,
        128,
        129,
        130,
        131,
        132,
        133,
        134,
        135,
        136,
        137,
        138,
        139,
        140,
        141,
        142,
        143,
        144,
        145,
        146,
        147,
        148,
        149,
        150,
        151,
        152,
        153,
        154,
        155,
        156,
        157,
        158,
        159,
        160,
        161,
        162,
        163,
        164,
        165,
        166,
        167,
        168,
        169,
        170,
        171,
        172,
        173,
        174,
        175,
        176,
        177,
        178,
        179,
        180,
        181,
        182,
        183,
        184,
        185,
        186,
        187,
        188,
        189,
        190,
        191,
        192,
        193,
        194,
        195,
        196,
        197,
        198,
        199,
        200,
        201,
        202,
        203,
        204,
        205,
        206,
        207,
        208,
        209,
        210,
        211,
        212,
        213,
        214,
        215,
        216,
        217,
        218,
        219,
        220,
        221,
        222,
        223,
        224,
        225,
        226,
        227,
        228,
        229,
        230,
        231,
        232,
        233,
        234,
        235,
        236,
        237,
        238,
        239,
        240,
        241,
        242,
        243,
        244,
        245,
        246,
        247,
        248,
        249
      ],
      "dropped_rows": []
    },
    "python_diagnostics": {
      "backend": "statsmodels MixedLM (ML)",
      "warnings": [],
      "covariance_convention": "plug-in GLS, matching lme4"
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "Python": 1.5597052538396383e-09,
        "phit": 1.5586891777275014e-09
      },
      "covariance": {
        "Python": 4.145725363002839e-08,
        "phit": 4.1436599040878264e-08
      },
      "std_errors": {
        "Python": 9.44290956539362e-09,
        "phit": 9.438205328393678e-09
      },
      "z_statistics": {
        "Python": 9.174713611059815e-08,
        "phit": 9.170132031499634e-08
      },
      "p_values": {
        "Python": 7.524396826018393e-17,
        "phit": 7.510129283940833e-17
      },
      "conf_int": {
        "Python": 2.006746768756784e-08,
        "phit": 2.005722876674554e-08
      },
      "fixed_fitted": {
        "Python": 4.77882622362813e-09,
        "phit": 4.7763677457624e-09
      },
      "fitted": {
        "Python": 5.0502762860560324e-08,
        "phit": 5.047751017173141e-08
      },
      "residuals": {
        "Python": 5.0502762860560324e-08,
        "phit": 5.047751017173141e-08
      },
      "marginal_residuals": {
        "Python": 4.77882622362813e-09,
        "phit": 4.7763677457624e-09
      },
      "random_effects": {
        "Python": 4.677465303970507e-08,
        "phit": 4.675140141685574e-08
      },
      "residual_variance": {
        "Python": 3.961422123666125e-08,
        "phit": 3.9594485912175514e-08
      },
      "random_intercept_variance": {
        "Python": 5.790742889644207e-07,
        "phit": 5.787857517702832e-07
      },
      "sigma": {
        "Python": 3.93965127187812e-09,
        "phit": 3.937688397570582e-09
      },
      "icc": {
        "Python": 8.181923916161793e-09,
        "phit": 8.177847121704218e-09
      },
      "log_likelihood": {
        "Python": 1.1368683772161603e-13,
        "phit": 0.0
      },
      "aic": {
        "Python": 2.2737367544323206e-13,
        "phit": 0.0
      },
      "df_residual": {
        "Python": 0.0,
        "phit": 0.0
      }
    },
    "tolerance": {
      "absolute": 1e-07,
      "relative": 1e-06
    },
    "extension_sha256": "2105dd47a15f21b0da6ae81a23461ef385285517e1af0519a0bb22238bc3ffc6"
  },
  {
    "name": "boundary",
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "lme4": "2.0.6",
      "statsmodels": "0.15.0",
      "PHP": "8.5.10",
      "Python": "3.14.7"
    },
    "R": {
      "coefficients": [
        0
      ],
      "covariance": [
        [
          0.055555555555555566
        ]
      ],
      "std_errors": [
        0.23570226039551587
      ],
      "z_statistics": [
        0
      ],
      "p_values": [
        1
      ],
      "conf_int": [
        [
          -0.4619679414498925,
          0.4619679414498925
        ]
      ],
      "fixed_fitted": [
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      "fitted": [
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      "residuals": [
        -1,
        0,
        1,
        -1,
        0,
        1,
        -1,
        0,
        1,
        -1,
        0,
        1
      ],
      "marginal_residuals": [
        -1,
        0,
        1,
        -1,
        0,
        1,
        -1,
        0,
        1,
        -1,
        0,
        1
      ],
      "random_effects": [
        0,
        0,
        0,
        0
      ],
      "residual_variance": 0.6666666666666666,
      "random_intercept_variance": 0,
      "sigma": 0.816496580927726,
      "icc": 0,
      "log_likelihood": -14.594471749807088,
      "aic": 35.188943499614176,
      "df_residual": 11
    },
    "Python": {
      "coefficients": [
        7.137232641435784e-19
      ],
      "covariance": [
        [
          0.055555555555555566
        ]
      ],
      "std_errors": [
        0.23570226039551587
      ],
      "z_statistics": [
        3.02807135979913e-18
      ],
      "p_values": [
        1.0
      ],
      "conf_int": [
        [
          -0.46196794144989267,
          0.46196794144989267
        ]
      ],
      "fixed_fitted": [
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19
      ],
      "fitted": [
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19,
        7.137232641435784e-19
      ],
      "residuals": [
        -1.0,
        -7.137232641435784e-19,
        1.0,
        -1.0,
        -7.137232641435784e-19,
        1.0,
        -1.0,
        -7.137232641435784e-19,
        1.0,
        -1.0,
        -7.137232641435784e-19,
        1.0
      ],
      "marginal_residuals": [
        -1.0,
        -7.137232641435784e-19,
        1.0,
        -1.0,
        -7.137232641435784e-19,
        1.0,
        -1.0,
        -7.137232641435784e-19,
        1.0,
        -1.0,
        -7.137232641435784e-19,
        1.0
      ],
      "random_effects": [
        0.0,
        0.0,
        0.0,
        0.0
      ],
      "residual_variance": 0.6666666666666666,
      "random_intercept_variance": 0.0,
      "sigma": 0.816496580927726,
      "icc": 0.0,
      "log_likelihood": -14.594471749807086,
      "aic": 35.18894349961417,
      "df_residual": 11
    },
    "phit": {
      "coefficients": [
        -6.409875621278547e-17
      ],
      "covariance": [
        [
          0.05555555555555556
        ]
      ],
      "std_errors": [
        0.23570226039551584
      ],
      "z_statistics": [
        -2.719479911021037e-16
      ],
      "p_values": [
        0.9999999999999998
      ],
      "conf_int": [
        [
          -0.4619679414498926,
          0.4619679414498925
        ]
      ],
      "fitted": [
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17
      ],
      "residuals": [
        -0.9999999999999999,
        6.409875621278547e-17,
        1,
        -0.9999999999999999,
        6.409875621278547e-17,
        1,
        -0.9999999999999999,
        6.409875621278547e-17,
        1,
        -0.9999999999999999,
        6.409875621278547e-17,
        1
      ],
      "log_likelihood": -14.594471749807084,
      "aic": 35.18894349961417,
      "df_residual": 11,
      "evaluations": 66,
      "fixed_fitted": [
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17,
        -6.409875621278547e-17
      ],
      "marginal_residuals": [
        -0.9999999999999999,
        6.409875621278547e-17,
        1,
        -0.9999999999999999,
        6.409875621278547e-17,
        1,
        -0.9999999999999999,
        6.409875621278547e-17,
        1,
        -0.9999999999999999,
        6.409875621278547e-17,
        1
      ],
      "random_effects": [
        0,
        0,
        0,
        0
      ],
      "group_sizes": [
        3,
        3,
        3,
        3
      ],
      "n_groups": 4,
      "group_labels": [
        1,
        2,
        3,
        4
      ],
      "residual_variance": 0.6666666666666666,
      "random_intercept_variance": 0,
      "sigma": 0.816496580927726,
      "icc": 0,
      "boundary": true,
      "method": "ML",
      "converged": true,
      "n_input": 12,
      "n_observations": 12,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11
      ],
      "dropped_rows": []
    },
    "python_diagnostics": {
      "backend": "NumPy exact zero-random-variance limit",
      "warnings": [],
      "covariance_convention": "plug-in GLS, matching lme4"
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "Python": 7.137232641435784e-19,
        "phit": 6.409875621278547e-17
      },
      "covariance": {
        "Python": 0.0,
        "phit": 6.938893903907228e-18
      },
      "std_errors": {
        "Python": 0.0,
        "phit": 2.7755575615628914e-17
      },
      "z_statistics": {
        "Python": 3.02807135979913e-18,
        "phit": 2.719479911021037e-16
      },
      "p_values": {
        "Python": 0.0,
        "phit": 2.220446049250313e-16
      },
      "conf_int": {
        "Python": 1.6653345369377348e-16,
        "phit": 1.1102230246251565e-16
      },
      "fixed_fitted": {
        "Python": 7.137232641435784e-19,
        "phit": 6.409875621278547e-17
      },
      "fitted": {
        "Python": 7.137232641435784e-19,
        "phit": 6.409875621278547e-17
      },
      "residuals": {
        "Python": 7.137232641435784e-19,
        "phit": 1.1102230246251565e-16
      },
      "marginal_residuals": {
        "Python": 7.137232641435784e-19,
        "phit": 1.1102230246251565e-16
      },
      "random_effects": {
        "Python": 0.0,
        "phit": 0.0
      },
      "residual_variance": {
        "Python": 0.0,
        "phit": 0.0
      },
      "random_intercept_variance": {
        "Python": 0.0,
        "phit": 0.0
      },
      "sigma": {
        "Python": 0.0,
        "phit": 0.0
      },
      "icc": {
        "Python": 0.0,
        "phit": 0.0
      },
      "log_likelihood": {
        "Python": 1.7763568394002505e-15,
        "phit": 3.552713678800501e-15
      },
      "aic": {
        "Python": 7.105427357601002e-15,
        "phit": 7.105427357601002e-15
      },
      "df_residual": {
        "Python": 0.0,
        "phit": 0.0
      }
    },
    "tolerance": {
      "absolute": 1e-07,
      "relative": 1e-06
    },
    "extension_sha256": "2105dd47a15f21b0da6ae81a23461ef385285517e1af0519a0bb22238bc3ffc6"
  },
  {
    "name": "listwise_missing",
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "lme4": "2.0.6",
      "statsmodels": "0.15.0",
      "PHP": "8.5.10",
      "Python": "3.14.7"
    },
    "R": {
      "coefficients": [
        46.73918013856852,
        1.6197573851579952,
        0.24377706155692883
      ],
      "covariance": [
        [
          4.883909781460102,
          0.13854801243377363,
          -0.07000064270240346
        ],
        [
          0.13854801243377363,
          0.02598473993649854,
          -0.005192953204181321
        ],
        [
          -0.07000064270240346,
          -0.005192953204181321,
          0.0017462920909786872
        ]
      ],
      "std_errors": [
        2.2099569637122127,
        0.1611978285725293,
        0.04178865983707407
      ],
      "z_statistics": [
        21.149362139639855,
        10.048258090705001,
        5.833569741345346
      ],
      "p_values": [
        2.796980247393099e-99,
        9.350558798562494e-24,
        5.425391479360668e-09
      ],
      "conf_int": [
        [
          42.407744082309094,
          51.07061619482795
        ],
        [
          1.3038154467697762,
          1.935699323546214
        ],
        [
          0.16187279331406823,
          0.3256813297997894
        ]
      ],
      "fixed_fitted": [
        84.3472508288954,
        82.18365712976876,
        63.80133200849584,
        73.0453478197981,
        62.90542980540528,
        70.84079232027436,
        75.15232358362019,
        65.56854265109045,
        61.33269678237797,
        82.15889808469149,
        72.61516135616138,
        83.32430994822201,
        74.5630468113496,
        75.35401037241996,
        69.08164471369902,
        66.39029517817048,
        62.29566176999966,
        85.69495923111775,
        60.84682293350475,
        67.46589604931476,
        67.92398086761096,
        64.01857338032298,
        70.51911074163344,
        84.87982365838604,
        68.12500912118182,
        77.5022225422124,
        58.09901815342828,
        84.66605474985676,
        62.89610824707052,
        61.02521230330295,
        70.53709014160576,
        68.17333500936567,
        82.8264125277617,
        79.75276771118455,
        81.46901418195361,
        72.14802440363543,
        80.52471977033441,
        64.42810589006803,
        67.170048621437,
        74.81862620559454,
        59.48118331651601,
        70.68249473955076,
        57.9731234926102,
        80.9546875858062,
        77.89285546485353,
        78.62061781581457,
        73.36896355237992,
        56.67352233040677,
        78.47114853968756,
        68.8144686812604,
        70.82047152009832,
        68.001325810612,
        69.57877945631616,
        78.38214581961631,
        79.24290008581133,
        85.09803081181657,
        68.1860041625111,
        60.12366669966984,
        69.48528512466947,
        84.8062558343232,
        83.01373952623895,
        77.69448103932908,
        78.79612693719909,
        73.75018113700855,
        76.01865233927886,
        69.72650991006013,
        80.34709048764526,
        68.44754456660954,
        67.10033200885948,
        74.04551976674342,
        83.7492954891143,
        82.46610536745915,
        79.20481335235968,
        77.55428513633088,
        71.76958033407213,
        71.59156194025904,
        65.1536998945185,
        63.5828554309603,
        59.32321629877394,
        77.49025492803361,
        76.85436777335512,
        75.35649632824148,
        66.6492480745673,
        78.42170195134601,
        85.30686563097231,
        66.43254814168426,
        80.36036740007958,
        80.28474573505687,
        65.27981838496976,
        79.8112182485499,
        77.94313623285126,
        73.32909758354165,
        80.99071270609562,
        71.01587191753134,
        63.07298780558709,
        67.89493331471849,
        72.16996692990966,
        81.38699421074755,
        61.05787169364287,
        63.77197979996301,
        67.64665946011789,
        67.32379604244275,
        66.38342434412189,
        79.64079554435912,
        81.38937602395481,
        75.9451938392985,
        74.96683436867198,
        75.85343055783251,
        71.87033979235959,
        82.65787838304001,
        81.22805622993384,
        77.1081757044158,
        76.17690173479652,
        67.125635083615,
        78.90805610028681,
        78.2681172210969,
        65.96330398152426,
        78.08810094373224,
        86.57710681244055,
        86.84504293198823,
        55.850148077228525,
        78.65111145037804,
        79.4321182344918,
        78.38362299009673,
        79.1921364270119,
        78.60902894982326,
        67.92636009008413,
        77.98631197423074,
        80.17579578152883,
        66.92080380376477,
        77.63575589639046,
        70.10447108882173,
        82.58604160915786,
        72.11660280973801,
        66.15604277870852,
        75.10600335119025,
        61.541742477496285,
        63.11611536176064,
        64.10968330802827,
        74.64185597116045,
        61.248447325784795,
        77.29484675839824,
        64.67517977049556,
        82.50896090879358,
        66.98993338292634,
        79.49609507611488,
        73.22225483764765,
        78.55522753332173,
        58.59383481244879,
        71.7375027956799,
        60.17778831621642,
        62.936853990036795,
        65.2156762618559,
        65.10769986213363,
        60.42075192399012,
        76.80042180123579,
        73.18391163376161,
        75.99704555745438,
        77.22361774380497,
        67.73177055570022,
        58.71951082510193,
        69.19231276373716,
        71.76908708033396,
        84.80771746039889,
        63.871547056279766,
        65.36275854330741,
        73.13407852503023,
        68.01319964511303,
        55.94685062953631,
        79.28975916645126,
        76.89141981412448,
        75.73305961053804,
        82.04383220275567,
        75.3428536212903,
        74.05137663398268,
        77.20389433998136,
        73.71545236130406,
        72.08318333228905,
        64.46548590308478,
        58.38315702829578,
        79.8031956255342,
        66.36477604598414,
        67.7832943016087,
        75.6369466823803,
        81.58916129961491,
        56.93820981628978,
        80.58517855418783,
        64.51712156380987,
        81.5611588023412,
        70.14131743509672,
        67.95116732036735,
        74.01600227671985,
        65.34487551374696,
        67.25851508403237,
        67.53025163912532,
        73.92092663197852,
        59.54395759323193,
        75.97228392164298,
        64.55671551780902,
        85.76034433214237,
        68.2636418462242,
        65.44119672713316,
        73.29517967088627,
        81.46461375932182,
        82.44606694505872,
        84.61703509490862,
        71.66762608307987,
        56.55948855041913,
        72.40437942939414,
        76.56128867907447,
        57.68341012827904,
        62.633861122537205,
        61.08008364402211,
        65.5230565983167,
        72.54277796186689,
        81.14982114986833,
        67.19475689057423,
        64.68847222733459,
        81.3699220442362,
        62.53867874444753,
        76.774254496757,
        73.21403170160585,
        68.16200261380877,
        84.58209544324153,
        67.5177399952683,
        63.48463788590265,
        81.55579000737187,
        75.10822765510912,
        82.2071042858564,
        72.54895502915119,
        69.8206120009957,
        80.77646608823288,
        76.15176394153178,
        60.83473563230702,
        63.50332659704398,
        66.13509194137887,
        64.79079745431197,
        81.12008242094568,
        58.84963285485868,
        62.15659693009562,
        74.44884256840295,
        69.96384048022776,
        58.334836321580156,
        62.87059688708654,
        73.10400923312605,
        59.893275874629694,
        71.82228073754659
      ],
      "fitted": [
        84.73262777850131,
        82.56903407937467,
        64.18670895810175,
        73.43072476940401,
        63.29080675501118,
        71.22616926988027,
        75.5377005332261,
        65.95391960069635,
        61.71807373198388,
        82.5442750342974,
        73.0005383057673,
        83.70968689782792,
        74.9484237609555,
        75.73938732202588,
        69.46702166330493,
        67.97794056486174,
        63.88330715669093,
        87.28260461780903,
        62.43446832019602,
        69.05354143600603,
        69.51162625430223,
        65.60621876701424,
        72.1067561283247,
        86.46746904507731,
        69.71265450787308,
        79.08986792890364,
        59.686663540119554,
        86.25370013654802,
        64.4837536337618,
        62.61285768999422,
        72.12473552829702,
        69.76098039605694,
        84.41405791445297,
        81.34041309787581,
        83.05665956864487,
        73.73566979032668,
        82.11236515702568,
        66.01575127675929,
        68.75769400812825,
        73.00712271789038,
        57.66967982881186,
        68.8709912518466,
        56.16162000490605,
        79.14318409810204,
        76.08135197714937,
        76.80911432811041,
        71.55746006467577,
        54.86201884270262,
        76.6596450519834,
        67.00296519355624,
        69.00896803239416,
        66.18982232290784,
        67.767275968612,
        76.57064233191215,
        73.65364621572044,
        79.50877694172569,
        62.596750292420204,
        54.53441282957895,
        63.89603125457858,
        79.21700196423231,
        77.42448565614806,
        72.10522716923818,
        73.2068730671082,
        68.16092726691767,
        70.42939846918797,
        64.13725603996924,
        74.75783661755437,
        62.858290696518644,
        61.51107813876859,
        68.45626589665254,
        78.16004161902342,
        76.87685149736826,
        73.6155594822688,
        71.96503126623998,
        66.18032646398125,
        66.00230807016816,
        65.38251458010518,
        63.811670116546985,
        59.55203098436063,
        77.71906961362029,
        77.0831824589418,
        75.58531101382816,
        66.87806276015398,
        78.6505166369327,
        85.535680316559,
        66.66136282727095,
        80.58918208566627,
        80.51356042064356,
        65.50863307055644,
        80.04003293413659,
        78.17195091843794,
        73.55791226912834,
        81.2195273916823,
        71.24468660311803,
        63.301802491173774,
        68.12374800030517,
        74.40684773134812,
        83.623875012186,
        63.294752495081326,
        66.00886060140147,
        69.88354026155635,
        69.56067684388121,
        68.62030514556035,
        81.87767634579758,
        83.62625682539327,
        78.18207464073696,
        77.20371517011044,
        78.09031135927096,
        74.10722059379805,
        84.89475918447847,
        83.4649370313723,
        79.34505650585426,
        78.41378253623499,
        69.36251588505345,
        81.14493690172527,
        80.50499802253536,
        68.20018478296272,
        80.3249817451707,
        88.81398761387901,
        89.08192373342669,
        58.087028878666985,
        80.8879922518165,
        81.66899903593026,
        88.68976683485091,
        89.49828027176609,
        88.91517279457744,
        78.23250393483832,
        88.29245581898493,
        90.48193962628302,
        77.22694764851896,
        87.94189974114465,
        80.41061493357591,
        92.89218545391205,
        82.42274665449222,
        76.46218662346271,
        85.41214719594443,
        71.84788632225047,
        73.42225920651484,
        74.41582715278246,
        84.94799981591464,
        71.55459117053898,
        87.60099060315243,
        59.54627519603763,
        77.38005633433565,
        61.861028808468404,
        74.36719050165696,
        68.09335026318972,
        73.42632295886379,
        53.464930237990856,
        66.60859822122197,
        55.04888374175849,
        57.80794941557886,
        60.08677168739797,
        59.97879528767568,
        55.291847349532176,
        71.67151722677785,
        68.05500705930366,
        70.86814098299645,
        72.09471316934703,
        62.60286598124229,
        53.59060625064399,
        64.06340818927923,
        66.64018250587603,
        86.89056291004775,
        65.95439250592862,
        67.44560399295628,
        75.21692397467909,
        70.09604509476189,
        58.02969607918517,
        81.37260461610012,
        78.97426526377333,
        77.81590506018688,
        84.12667765240452,
        77.42569907093916,
        76.13422208363154,
        79.28673978963022,
        75.79829781095292,
        74.16602878193791,
        66.54833135273364,
        58.927599562725014,
        80.34763815996344,
        66.90921858041338,
        68.32773683603794,
        76.18138921680952,
        82.13360383404415,
        57.482652350719015,
        81.12962108861707,
        65.0615640982391,
        82.10560133677043,
        70.68575996952596,
        68.49560985479658,
        74.56044481114908,
        65.8893180481762,
        67.80295761846162,
        68.07469417355456,
        74.46536916640775,
        60.08840012766117,
        76.51672645607222,
        65.10115805223826,
        86.3047868665716,
        68.80808438065344,
        65.9856392615624,
        73.83962220531551,
        82.00905629375106,
        82.50359427136742,
        84.67456242121732,
        71.72515340938857,
        56.61701587672784,
        72.46190675570284,
        76.61881600538317,
        57.74093745458775,
        62.69138844884591,
        61.13761097033082,
        65.5805839246254,
        72.60030528817558,
        81.20734847617702,
        67.25228421688293,
        64.74599955364329,
        81.4274493705449,
        62.59620607075624,
        76.8317818230657,
        73.27155902791455,
        68.21952994011747,
        84.63962276955023,
        67.575267321577,
        63.54216521221136,
        81.61331733368057,
        70.20821260888987,
        77.30708923963715,
        67.64893998293194,
        64.92059695477644,
        75.87645104201361,
        71.25174889531252,
        55.934720586087764,
        58.60331155082473,
        61.23507689515962,
        59.89078240809272,
        76.22006737472641,
        53.94961780863943,
        57.256581883876365,
        69.5488275221837,
        65.0638254340085,
        53.4348212753609,
        57.97058184086729,
        68.2039941869068,
        54.99326082841044,
        66.92226569132735
      ],
      "residuals": [
        -6.475627778501305,
        5.653965920625325,
        4.35929104189826,
        -1.283724769404003,
        -2.9358067550111855,
        -1.5561692698802716,
        -3.408700533226096,
        -4.153919600696355,
        1.9889262680161224,
        -6.1522750342974035,
        4.07746169423271,
        7.327313102172084,
        -0.491423760955513,
        0.2956126779741197,
        3.294978336695067,
        1.1960594351382667,
        -4.832307156690931,
        4.80039538219097,
        1.9825316798039836,
        -1.988541436006031,
        11.291373745697769,
        2.634781232985759,
        -6.478756128324704,
        -0.23146904507730426,
        0.9723454921269195,
        0.35213207109634936,
        -1.6066635401195555,
        2.471299863451975,
        0.38424636623820163,
        -4.975857689994221,
        3.3992644717029776,
        -6.520980396056935,
        -0.27405791445296757,
        1.452586902124196,
        -1.3416595686448716,
        -8.239669790326687,
        -3.3943651570256748,
        3.932248723240704,
        7.2393059918717455,
        -0.1301227178903872,
        -1.840679828811858,
        -6.253991251846607,
        -3.5256200049060453,
        3.971815901897955,
        -10.097351977149373,
        7.167885671889593,
        -5.914460064675765,
        -6.563018842702618,
        3.3743549480166024,
        5.310034806443767,
        3.687031967605833,
        0.34517767709215263,
        7.798724031388005,
        0.13235766808784888,
        -9.90764621572044,
        4.432223058274317,
        -9.794750292420204,
        -2.6754128295789457,
        -6.751031254578578,
        3.857998035767693,
        -4.467485656148071,
        4.4687728307618215,
        -4.909873067108208,
        3.752072733082329,
        5.7586015308120295,
        9.065743960030758,
        5.63016338244563,
        -7.108290696518644,
        -4.0500781387685905,
        4.961734103347467,
        -1.1970416190234232,
        0.5331485026317324,
        -2.9385594822687864,
        0.0559687337600252,
        0.8266735360187596,
        2.62669192983185,
        2.9184854198948216,
        3.7513298834530175,
        0.9159690156393765,
        3.9099303863797132,
        -1.9291824589418098,
        -0.1703110138281545,
        8.584937239846013,
        -0.856516636932696,
        -0.5396803165590001,
        2.574637172729055,
        -4.655182085666269,
        -5.267560420643562,
        3.1813669294435556,
        -0.2950329341365858,
        1.8960490815620545,
        -8.328912269128338,
        5.789472608317695,
        -7.9366866031180265,
        0.877197508826228,
        -4.099748000305169,
        7.088152268651882,
        5.764124987814,
        -2.584752495081325,
        -3.5308606014014643,
        -1.3085402615563453,
        4.886323156118792,
        -9.113305145560354,
        -8.156676345797578,
        -4.321256825393263,
        9.384925359263036,
        -3.355715170110443,
        -6.316311359270955,
        -10.110220593798047,
        -1.549759184478475,
        6.3340629686277055,
        -5.942056505854254,
        5.911217463765013,
        -5.4475158850534555,
        -8.192936901725275,
        -3.9729980225353643,
        4.60081521703728,
        4.4740182548293035,
        7.7850123861209966,
        -3.0349237334266945,
        5.976971121333008,
        3.5290077481835027,
        14.337000964069745,
        -3.7267668348509204,
        1.29671972823391,
        7.279827205422549,
        -6.962503934838324,
        -0.035455818984928555,
        -1.6099396262830226,
        -0.36594764851895434,
        6.053100258855352,
        -4.003614933575918,
        0.08381454608795025,
        4.875253345507787,
        2.8958133765372907,
        6.764852804055579,
        11.003113677749525,
        -4.647259206514832,
        1.2021728472175397,
        1.5890001840853643,
        -1.5065911705389823,
        -5.746990603152426,
        -0.8572751960376266,
        -1.9820563343356525,
        -1.0940288084684013,
        -3.51519050165696,
        -4.992350263189721,
        5.187677041136212,
        -0.8529302379908543,
        -3.3015982212219654,
        3.9811162582415136,
        5.586050584421137,
        -3.6877716873979693,
        5.613204712324318,
        4.637152650467826,
        -13.377517226777854,
        -4.23600705930366,
        2.898859017003545,
        -3.6847131693470345,
        1.1091340187577146,
        -0.034606250643989256,
        3.580591810720776,
        1.8368174941239772,
        2.1974370899522455,
        8.738607494071374,
        5.931396007043716,
        2.1370760253209085,
        -13.927045094761894,
        0.5843039208148255,
        -10.459604616100123,
        2.2277347362266653,
        -8.302905060186873,
        4.129322347595476,
        8.549300929060834,
        4.489777916368453,
        -3.0517397896302185,
        4.097702189047084,
        -1.1690287819379108,
        -3.2543313527336437,
        -2.5265995627250106,
        -1.5626381599634414,
        1.669781419586613,
        3.653263163962052,
        -6.7663892168095146,
        -0.20160383404414972,
        -0.10565235071901213,
        8.991378911382924,
        3.6384359017609,
        2.3663986632295604,
        -2.0347599695259646,
        -4.059609854796577,
        -1.261444811149076,
        -3.4113180481761916,
        6.040042381538385,
        -2.5886941735545577,
        -0.6823691664077529,
        2.773599872338835,
        2.0612735439277827,
        -0.3791580522382674,
        -8.242786866571606,
        -2.306084380653445,
        0.42436073843759914,
        1.1993777946844943,
        4.07394370624894,
        -0.1095942713674134,
        -0.2545624212173152,
        -2.3851534093885647,
        1.4479841232721569,
        8.801093244297164,
        -1.2148160053831702,
        5.209062545412252,
        -9.55238844884591,
        6.353389029669181,
        -1.999583924625398,
        6.19869471182443,
        -10.744348476177024,
        2.699715783117071,
        2.0180004463567087,
        -2.478449370544908,
        -1.1072060707562414,
        -4.798781823065696,
        -0.3395590279145466,
        -2.4545299401174674,
        5.4803772304497755,
        -2.6742673215770054,
        -3.0311652122113557,
        5.016682666319426,
        -2.878212608889868,
        1.0789107603628452,
        -14.381939982931932,
        2.3094030452235614,
        4.133548957986392,
        1.0742511046874768,
        2.9092794139122375,
        -1.7553115508247288,
        1.753923104840375,
        2.2032175919072827,
        5.407932625273588,
        -0.9996178086394281,
        2.7124181161236365,
        -1.267827522183694,
        -2.7298254340085037,
        0.02017872463909498,
        3.047418159132711,
        -2.4969941869068037,
        -4.307260828410442,
        -2.69826569132735
      ],
      "marginal_residuals": [
        -6.0902508288953925,
        6.039342870231238,
        4.744667991504166,
        -0.8983478197980901,
        -2.5504298054052796,
        -1.1707923202743586,
        -3.023323583620183,
        -3.7685426510904563,
        2.3743032176220282,
        -5.766898084691491,
        4.462838643838623,
        7.712690051777997,
        -0.10604681134960003,
        0.6809896275800327,
        3.68035528630098,
        2.783704821829531,
        -3.2446617699996594,
        6.388040768882249,
        3.570177066495255,
        -0.40089604931476686,
        12.879019132389033,
        4.222426619677023,
        -4.89111074163344,
        1.3561763416139598,
        2.5599908788181835,
        1.9397774577875992,
        -0.01901815342828428,
        4.058945250143239,
        1.9718917529294728,
        -3.38821230330295,
        4.986909858394242,
        -4.9333350093656705,
        1.3135874722382965,
        3.04023228881546,
        0.24598581804639252,
        -6.652024403635437,
        -1.8067197703344107,
        5.519894109931968,
        8.826951378562995,
        -1.9416262055945452,
        -3.652183316516009,
        -8.065494739550765,
        -5.337123492610196,
        2.160312414193797,
        -11.90885546485353,
        5.356382184185435,
        -7.725963552379923,
        -8.37452233040677,
        1.5628514603124444,
        3.4985313187396088,
        1.875528479901675,
        -1.4663258106120054,
        5.987220543683847,
        -1.6791458196163092,
        -15.496900085811326,
        -1.1570308118165684,
        -15.384004162511097,
        -8.264666699669839,
        -12.340285124669471,
        -1.7312558343231927,
        -10.056739526238957,
        -1.1204810393290785,
        -10.499126937199094,
        -1.8371811370085567,
        0.1693476607211437,
        3.4764900899398725,
        0.04090951235474449,
        -12.697544566609537,
        -9.639332008859483,
        -0.6275197667434185,
        -6.786295489114309,
        -5.056105367459153,
        -8.527813352359672,
        -5.533285136330875,
        -4.762580334072126,
        -2.962561940259036,
        3.1473001054815057,
        3.9801445690397017,
        1.1447837012260607,
        4.138745071966397,
        -1.7003677733551257,
        0.05850367175852966,
        8.813751925432697,
        -0.6277019513460118,
        -0.3108656309723159,
        2.8034518583157393,
        -4.4263674000795845,
        -5.038745735056878,
        3.4101816150302398,
        -0.06621824854990166,
        2.1248637671487387,
        -8.100097583541654,
        6.018287293904379,
        -7.707871917531342,
        1.1060121944129122,
        -3.870933314718485,
        9.325033070090342,
        8.00100578925246,
        -0.3478716936428725,
        -1.2939797999630116,
        0.9283405398821145,
        7.123203957557251,
        -6.876424344121894,
        -5.919795544359118,
        -2.0843760239548033,
        11.621806160701496,
        -1.1188343686719833,
        -4.079430557832509,
        -7.873339792359587,
        0.6871216169599847,
        8.570943770066165,
        -3.705175704415794,
        8.148098265203487,
        -3.2106350836149957,
        -5.9560561002868155,
        -1.7361172210969045,
        6.837696018475739,
        6.710899056267763,
        10.021893187559456,
        -0.7980429319882347,
        8.213851922771468,
        5.7658885496219625,
        16.573881765508204,
        6.5793770099032685,
        11.602863572988099,
        17.585971050176738,
        3.343639909915865,
        10.27068802576926,
        8.696204218471166,
        9.940196196235235,
        16.35924410360954,
        6.302528911178271,
        10.38995839084214,
        15.18139719026199,
        13.20195722129148,
        17.070996648809754,
        21.309257522503714,
        5.658884638239364,
        11.508316691971729,
        11.895144028839553,
        8.799552674215207,
        4.559153241601763,
        -5.986179770495561,
        -7.1109609087935866,
        -6.222933382926335,
        -8.64409507611488,
        -10.121254837647655,
        0.058772466678277624,
        -5.981834812448788,
        -8.4305027956799,
        -1.1477883162164204,
        0.4571460099632034,
        -8.816676261855903,
        0.48430013786637005,
        -0.49175192399011536,
        -18.50642180123579,
        -9.364911633761608,
        -2.230045557454389,
        -8.813617743804969,
        -4.0197705557002195,
        -5.16351082510193,
        -1.548312763737158,
        -3.292087080333957,
        4.280282539601103,
        10.821452943720232,
        8.014241456692588,
        4.219921474969766,
        -11.844199645113036,
        2.66714937046369,
        -8.376759166451265,
        4.310580185875523,
        -6.22005961053803,
        6.212167797244334,
        10.632146378709692,
        6.572623366017311,
        -0.968894339981361,
        6.180547638695941,
        0.9138166677109467,
        -1.1714859030847862,
        -1.9821570282957737,
        -1.0181956255342044,
        2.21422395401585,
        4.197705698391289,
        -6.221946682380292,
        0.34283870038508724,
        0.4387901837102248,
        9.53582144581216,
        4.182878436190137,
        2.9108411976587973,
        -1.4903174350967276,
        -3.5151673203673397,
        -0.717002276719839,
        -2.8668755137469546,
        6.584484915967636,
        -2.0442516391253207,
        -0.13792663197851596,
        3.318042406768072,
        2.6057160783570197,
        0.16528448219096958,
        -7.698344332142369,
        -1.761641846224208,
        0.9688032728668361,
        1.7438203291137313,
        4.618386240678177,
        -0.05206694505871212,
        -0.19703509490861393,
        -2.3276260830798634,
        1.5055114495808652,
        8.858620570605865,
        -1.157288679074469,
        5.26658987172096,
        -9.494861122537202,
        6.410916355977889,
        -1.9420565983166966,
        6.256222038133117,
        -10.686821149868337,
        2.7572431094257723,
        2.07552777266541,
        -2.4209220442362067,
        -1.049678744447533,
        -4.741254496756994,
        -0.28203170160584534,
        -2.397002613808766,
        5.537904556758477,
        -2.616739995268304,
        -2.9736378859026473,
        5.074209992628127,
        -7.77822765510912,
        -3.821104285856407,
        -19.281955029151185,
        -2.5906120009956908,
        -0.7664660882328747,
        -3.8257639415317897,
        -1.9907356323070218,
        -6.655326597043981,
        -3.1460919413788773,
        -2.6967974543119695,
        0.5079175790543218,
        -5.89963285485868,
        -2.1875969300956157,
        -6.167842568402946,
        -7.629840480227756,
        -4.879836321580157,
        -1.8525968870865412,
        -7.397009233126056,
        -9.207275874629694,
        -7.598280737546588
      ],
      "random_effects": [
        0.3853769496059075,
        1.5876453866912699,
        -1.8115034877041523,
        -5.58925387009089,
        0.2288146855866856,
        2.236880801438461,
        10.306143844754194,
        -5.128904574457938,
        2.0828454496488638,
        0.5444425344292373,
        0.05752732630870798,
        -4.900015046219253
      ],
      "residual_variance": 25.41820764267751,
      "random_intercept_variance": 18.143292075602435,
      "sigma": 5.041647314388176,
      "icc": 0.4164983343764188,
      "log_likelihood": -766.4872381433804,
      "aic": 1542.9744762867608,
      "df_residual": 244
    },
    "Python": {
      "coefficients": [
        46.73918014483284,
        1.619757385333327,
        0.24377706143482647
      ],
      "covariance": [
        [
          4.8839098662774845,
          0.1385480120582385,
          -0.07000064251461847
        ],
        [
          0.1385480120582385,
          0.025984739864136585,
          -0.0051929531898876015
        ],
        [
          -0.07000064251461847,
          -0.0051929531898876015,
          0.0017462920862542323
        ]
      ],
      "std_errors": [
        2.2099569829020393,
        0.16119782834807853,
        0.04178865978054611
      ],
      "z_statistics": [
        21.14936195882716,
        10.048258105783807,
        5.833569746314575
      ],
      "p_values": [
        2.7969909670771057e-99,
        9.350557368039032e-24,
        5.425391317704554e-09
      ],
      "conf_int": [
        [
          42.40774405096204,
          51.070616238703636
        ],
        [
          1.3038154473850232,
          1.9356993232816306
        ],
        [
          0.1618727933027586,
          0.32568132956689433
        ]
      ],
      "fixed_fitted": [
        84.3472508277479,
        82.1836571281658,
        63.801332009874514,
        73.0453478183226,
        62.90542980627565,
        70.84079231960706,
        75.15232358391111,
        65.5685426533895,
        61.33269678262521,
        82.15889808346597,
        72.61516135510854,
        83.32430994727113,
        74.56304680959735,
        75.35401037228428,
        69.08164471359713,
        66.3902951788345,
        62.29566177123466,
        85.69495922921628,
        60.846822933837494,
        67.4658960490454,
        67.92398086700364,
        64.01857338006356,
        70.51911074184751,
        84.87982365676456,
        68.12500912159855,
        77.50222254193801,
        58.099018155808245,
        84.6660547489442,
        62.89610824860661,
        61.02521230376341,
        70.53709014282707,
        68.17333500909716,
        82.82641252642877,
        79.75276771058209,
        81.46901418018567,
        72.14802440383279,
        80.52471977082526,
        64.4281058918234,
        67.17004862310162,
        74.81862620496732,
        59.48118331762157,
        70.68249473982112,
        57.97312349459938,
        80.95468758620993,
        77.89285546545892,
        78.62061781493068,
        73.3689635527748,
        56.67352233280023,
        78.47114854005262,
        68.81446868067076,
        70.82047152047718,
        68.00132581230424,
        69.57877945732682,
        78.38214581951291,
        79.24290008449736,
        85.09803081015488,
        68.1860041634794,
        60.1236667012429,
        69.48528512440488,
        84.8062558329655,
        83.01373952517726,
        77.69448103901759,
        78.79612693800324,
        73.75018113645277,
        76.01865233926412,
        69.7265099107304,
        80.3470904877219,
        68.44754456835453,
        67.10033200993746,
        74.04551976789459,
        83.74929548780257,
        82.46610536710585,
        79.20481335163704,
        77.55428513557656,
        71.76958033338363,
        71.59156194085352,
        65.15369989503235,
        63.58285543213268,
        59.32321629986983,
        77.49025492698578,
        76.85436777403669,
        75.35649632913064,
        66.64924807381901,
        78.4217019494962,
        85.30686562935401,
        66.43254814262312,
        80.36036739936026,
        80.28474573379333,
        65.27981838465087,
        79.81121824822404,
        77.94313623197125,
        73.32909758307838,
        80.99071270643198,
        71.01587191789126,
        63.07298780604796,
        67.89493331601017,
        72.16996692965205,
        81.38699420945481,
        61.05787169524132,
        63.77197979974818,
        67.64665946161286,
        67.3237960431128,
        66.38342434323049,
        79.64079554333918,
        81.38937602296674,
        75.94519383937974,
        74.96683436939126,
        75.85343055706188,
        71.87033979191659,
        82.65787838229468,
        81.22805622792154,
        77.10817570344096,
        76.17690173281805,
        67.12563508392059,
        78.9080560995944,
        78.26811722021199,
        65.96330398276721,
        78.08810094301643,
        86.57710681015641,
        86.84504292990535,
        55.85014808066584,
        78.65111145043592,
        79.43211823428675,
        78.38362298750627,
        79.1921364263844,
        78.60902894824467,
        67.92636009022543,
        77.98631197330938,
        80.17579578180965,
        66.92080380492278,
        77.63575589644385,
        70.10447108957894,
        82.5860416090997,
        72.11660281019778,
        66.1560427811573,
        75.10600335194836,
        61.54174247878332,
        63.11611536115408,
        64.10968330918344,
        74.64185597144066,
        61.24844732794884,
        77.29484675870131,
        64.67517977344927,
        82.50896090757033,
        66.98993338315191,
        79.49609507606525,
        73.22225483967487,
        78.55522753313164,
        58.593834813998804,
        71.73750279626049,
        60.177788317229584,
        62.93685399020079,
        65.21567626185526,
        65.10769986394325,
        60.420751925029585,
        76.80042180022764,
        73.18391163391371,
        75.99704555605932,
        77.22361774276244,
        67.73177055615606,
        58.71951082737829,
        69.1923127647342,
        71.76908708062246,
        84.80771745921807,
        63.871547056380116,
        65.36275854264112,
        73.13407852422066,
        68.0131996450826,
        55.94685063218521,
        79.28975916516316,
        76.89141981514268,
        75.73305960969944,
        82.04383220212057,
        75.34285362067675,
        74.05137663406535,
        77.20389433972814,
        73.71545236146618,
        72.08318333189732,
        64.46548590467346,
        58.383157029990784,
        79.8031956260806,
        66.36477604731213,
        67.78329430109157,
        75.63694668340526,
        81.58916129913848,
        56.938209818590124,
        80.58517855429321,
        64.51712156381379,
        81.56115880105989,
        70.14131743430622,
        67.95116732115727,
        74.01600227675115,
        65.34487551412559,
        67.25851508522844,
        67.53025163909011,
        73.92092663250143,
        59.54395759633851,
        75.97228392106936,
        64.55671551886854,
        85.76034433043506,
        68.26364184574274,
        65.44119672708861,
        73.29517967143649,
        81.46461375968721,
        82.44606694377816,
        84.617035092886,
        71.66762608265948,
        56.55948855291904,
        72.4043794277661,
        76.56128868074146,
        57.68341013004828,
        62.6338611237212,
        61.08008364541211,
        65.52305659738265,
        72.54277796234011,
        81.14982114956263,
        67.19475689127931,
        64.68847222682844,
        81.36992204428397,
        62.53867874584693,
        76.77425449608754,
        73.21403170173299,
        68.16200261531199,
        84.58209544094042,
        67.51773999485458,
        63.48463788754847,
        81.55579000707003,
        75.1082276553136,
        82.20710428588936,
        72.54895502938453,
        69.82061200090847,
        80.77646608759125,
        76.15176393985203,
        60.83473563381004,
        63.50332659882844,
        66.13509194144063,
        64.79079745494839,
        81.12008242029968,
        58.84963285719814,
        62.15659693201198,
        74.4488425681188,
        69.96384048076929,
        58.33483632307244,
        62.87059688795463,
        73.10400923292352,
        59.89327587536111,
        71.82228073847936
      ],
      "fitted": [
        84.73262777980086,
        82.56903408021877,
        64.18670896192748,
        73.43072477037556,
        63.29080675832861,
        71.22616927166003,
        75.53770053596408,
        65.95391960544247,
        61.71807373467817,
        82.54427503551894,
        73.0005383071615,
        83.7096868993241,
        74.94842376165032,
        75.73938732433724,
        69.4670216656501,
        67.97794057111157,
        63.883307163511724,
        87.28260462149335,
        62.434468326114555,
        69.05354144132247,
        69.5116262592807,
        65.60621877234063,
        72.10675613412458,
        86.46746904904163,
        69.71265451387562,
        79.08986793421508,
        59.686663548085306,
        86.25370014122127,
        64.48375364088368,
        62.61285769604047,
        72.12473553510414,
        69.76098040137423,
        84.41405791870584,
        81.34041310285916,
        83.05665957246273,
        73.73566979610986,
        82.11236516310233,
        66.01575128410047,
        68.75769401537869,
        73.00712270668856,
        57.66967981934281,
        68.87099124154237,
        56.16161999632062,
        79.14318408793117,
        76.08135196718017,
        76.80911431665193,
        71.55746005449605,
        54.86201883452147,
        76.65964504177387,
        67.002965182392,
        69.00896802219843,
        66.18982231402549,
        67.76727595904806,
        76.57064232123416,
        73.65364619272057,
        79.50877691837809,
        62.596750271702604,
        54.534412809466104,
        63.89603123262809,
        79.21700194118871,
        77.42448563340047,
        72.1052271472408,
        73.20687304622645,
        68.16092724467597,
        70.42939844748733,
        64.13725601895361,
        74.75783659594511,
        62.85829067657774,
        61.51107811816067,
        68.4562658761178,
        78.16004159602578,
        76.87685147532906,
        73.61555945986025,
        71.96503124379977,
        66.18032644160684,
        66.00230804907673,
        65.3825145816629,
        63.81167011876324,
        59.552030986500384,
        77.71906961361634,
        77.08318246066725,
        75.58531101576119,
        66.87806276044957,
        78.65051663612675,
        85.53568031598456,
        66.66136282925368,
        80.58918208599081,
        80.51356042042389,
        65.50863307128142,
        80.0400329348546,
        78.17195091860181,
        73.55791226970894,
        81.21952739306253,
        71.24468660452182,
        63.30180249267852,
        68.12374800264072,
        74.40684773857716,
        83.62387501837992,
        63.294752504166425,
        66.00886060867329,
        69.88354027053796,
        69.5606768520379,
        68.6203051521556,
        81.87767635226429,
        83.62625683189185,
        78.18207464830485,
        77.20371517831637,
        78.09031136598699,
        74.1072206008417,
        84.89475919121979,
        83.46493703684665,
        79.34505651236607,
        78.41378254174316,
        69.36251589284569,
        81.14493690851951,
        80.5049980291371,
        68.20018479169232,
        80.32498175194154,
        88.81398761908152,
        89.08192373883045,
        58.08702888959095,
        80.88799225936103,
        81.66899904321185,
        88.689766878044,
        89.49828031692212,
        88.9151728387824,
        78.23250398076316,
        88.29245586384711,
        90.48193967234738,
        77.22694769546051,
        87.94189978698158,
        80.41061498011666,
        92.89218549963742,
        82.4227467007355,
        76.46218667169502,
        85.41214724248609,
        71.84788636932105,
        73.4222592516918,
        74.41582719972116,
        84.94799986197839,
        71.55459121848656,
        87.60099064923904,
        59.54627517765884,
        77.3800563117799,
        61.86102878736148,
        74.36719048027481,
        68.09335024388444,
        73.42632293734121,
        53.46493021820837,
        66.60859820047006,
        55.048883721439154,
        57.80794939441036,
        60.086771666064834,
        59.97879526815282,
        55.291847329239154,
        71.67151720443721,
        68.05500703812328,
        70.86814096026889,
        72.09471314697201,
        62.602865960365634,
        53.59060623158786,
        64.06340816894377,
        66.64018248483202,
        86.89056291983496,
        65.954392516997,
        67.44560400325801,
        75.21692398483755,
        70.09604510569949,
        58.029696092802105,
        81.37260462578006,
        78.97426527575958,
        77.81590507031633,
        84.12667766273746,
        77.42569908129364,
        76.13422209468224,
        79.28673980034503,
        75.79829782208307,
        74.16602879251421,
        66.54833136529035,
        58.92759956595415,
        80.34763816204396,
        66.9092185832755,
        68.32773683705494,
        76.18138921936863,
        82.13360383510185,
        57.48265235455349,
        81.12962109025658,
        65.06156409977716,
        82.10560133702326,
        70.68575997026959,
        68.49560985712064,
        74.56044481271452,
        65.88931805008896,
        67.80295762119181,
        68.07469417505348,
        74.4653691684648,
        60.08840013230187,
        76.51672645703273,
        65.10115805483191,
        86.30478686639843,
        68.80808438170611,
        65.98563926305198,
        73.83962220739986,
        82.00905629565058,
        82.50359427015297,
        84.67456241926081,
        71.72515340903429,
        56.61701587929386,
        72.46190675414091,
        76.61881600711627,
        57.7409374564231,
        62.69138845009602,
        61.13761097178693,
        65.58058392375746,
        72.60030528871492,
        81.20734847593744,
        67.25228421765412,
        64.74599955320325,
        81.42744937065878,
        62.59620607222175,
        76.83178182246235,
        73.2715590281078,
        68.2195299416868,
        84.63962276731523,
        67.57526732122939,
        63.54216521392329,
        81.61331733344484,
        70.20821258778084,
        77.3070892183566,
        67.64893996185177,
        64.9205969333757,
        75.87645102005848,
        71.25174887231927,
        55.93472056627728,
        58.603311531295674,
        61.23507687390787,
        59.890782387415626,
        76.22006735276692,
        53.949617789665375,
        57.256581864479216,
        69.54882750058604,
        65.06382541323653,
        53.434821255539674,
        57.97058182042187,
        68.20399416539075,
        54.99326080782835,
        66.9222656709466
      ],
      "residuals": [
        -6.47562777980086,
        5.653965919781228,
        4.359291038072527,
        -1.2837247703755565,
        -2.93580675832861,
        -1.5561692716600248,
        -3.4087005359640727,
        -4.153919605442468,
        1.9889262653218296,
        -6.15227503551894,
        4.077461692838497,
        7.327313100675909,
        -0.4914237616503243,
        0.2956126756627526,
        3.2949783343499064,
        1.1960594288884323,
        -4.832307163511722,
        4.80039537850665,
        1.9825316738854468,
        -1.988541441322468,
        11.291373740719294,
        2.6347812276593743,
        -6.4787561341245805,
        -0.23146904904162113,
        0.9723454861243823,
        0.3521320657849145,
        -1.606663548085308,
        2.471299858778721,
        0.3842463591163181,
        -4.975857696040471,
        3.3992644648958645,
        -6.520980401374224,
        -0.27405791870583585,
        1.452586897140847,
        -1.3416595724627314,
        -8.239669796109865,
        -3.3943651631023215,
        3.9322487158995187,
        7.239305984621311,
        -0.1301227066885673,
        -1.8406798193428102,
        -6.253991241542373,
        -3.5256199963206143,
        3.97181591206882,
        -10.097351967180174,
        7.167885683348075,
        -5.914460054496047,
        -6.563018834521472,
        3.374354958226135,
        5.310034817607999,
        3.687031977801567,
        0.34517768597450527,
        7.798724040951939,
        0.13235767876584248,
        -9.90764619272057,
        4.432223081621913,
        -9.794750271702604,
        -2.6754128094661027,
        -6.751031232628087,
        3.8579980588112903,
        -4.467485633400472,
        4.468772852759201,
        -4.909873046226451,
        3.752072755324022,
        5.758601552512673,
        9.065743981046396,
        5.630163404054898,
        -7.108290676577738,
        -4.05007811816067,
        4.961734123882209,
        -1.1970415960257839,
        0.5331485246709349,
        -2.938559459860244,
        0.055968756200229564,
        0.8266735583931677,
        2.6266919509232736,
        2.9184854183370987,
        3.7513298812367637,
        0.9159690134996197,
        3.909930386383664,
        -1.9291824606672492,
        -0.170311015761186,
        8.584937239550428,
        -0.8565166361267558,
        -0.5396803159845689,
        2.5746371707463283,
        -4.655182085990816,
        -5.267560420423891,
        3.1813669287185746,
        -0.29503293485458926,
        1.8960490813981892,
        -8.328912269708937,
        5.789472606937466,
        -7.936686604521817,
        0.8771975073214833,
        -4.099748002640723,
        7.088152261422849,
        5.7641249816200855,
        -2.584752504166424,
        -3.5308606086732865,
        -1.3085402705379607,
        4.886323147962102,
        -9.113305152155597,
        -8.156676352264284,
        -4.321256831891844,
        9.384925351695145,
        -3.3557151783163732,
        -6.316311365986991,
        -10.1102206008417,
        -1.5497591912197919,
        6.334062963153357,
        -5.942056512366065,
        5.911217458256843,
        -5.4475158928456935,
        -8.192936908519513,
        -3.972998029137102,
        4.600815208307679,
        4.474018248058471,
        7.785012380918488,
        -3.0349237388304573,
        5.976971110409046,
        3.529007740638974,
        14.337000956788145,
        -3.7267668780440033,
        1.2967196830778818,
        7.279827161217597,
        -6.9625039807631595,
        -0.03545586384710475,
        -1.6099396723473802,
        -0.36594769546050543,
        6.053100213018425,
        -4.003614980116666,
        0.08381450036257831,
        4.8752532992645,
        2.895813328304982,
        6.764852757513921,
        11.003113630678953,
        -4.647259251691793,
        1.2021728002788308,
        1.5890001380216177,
        -1.5065912184865624,
        -5.746990649239038,
        -0.8572751776588419,
        -1.9820563117798997,
        -1.0940287873614736,
        -3.5151904802748106,
        -4.992350243884445,
        5.187677062658793,
        -0.8529302182083711,
        -3.3015982004700533,
        3.9811162785608474,
        5.586050605589641,
        -3.687771666064833,
        5.613204731847176,
        4.637152670760848,
        -13.377517204437211,
        -4.236007038123276,
        2.898859039731107,
        -3.6847131469720154,
        1.1091340396343696,
        -0.034606231587865466,
        3.580591831056239,
        1.8368175151679793,
        2.197437080165031,
        8.738607483002994,
        5.931395996741983,
        2.1370760151624495,
        -13.927045105699492,
        0.5843039071978922,
        -10.45960462578006,
        2.2277347242404204,
        -8.302905070316328,
        4.129322337262536,
        8.54930091870635,
        4.489777905317752,
        -3.0517398003450324,
        4.097702177916929,
        -1.1690287925142115,
        -3.254331365290355,
        -2.526599565954143,
        -1.5626381620439673,
        1.66978141672449,
        3.653263162945052,
        -6.7663892193686195,
        -0.20160383510184943,
        -0.10565235455348443,
        8.991378909743418,
        3.638435900222845,
        2.366398662976735,
        -2.03475997026959,
        -4.059609857120634,
        -1.2614448127145153,
        -3.4113180500889584,
        6.040042378808195,
        -2.588694175053476,
        -0.6823691684648026,
        2.773599867698131,
        2.061273542967271,
        -0.3791580548319189,
        -8.242786866398433,
        -2.306084381706114,
        0.42436073694801735,
        1.1993777926001457,
        4.073943704349418,
        -0.10959427015296797,
        -0.25456241926080736,
        -2.385153409034288,
        1.4479841207061384,
        8.801093245859093,
        -1.2148160071162692,
        5.209062543576906,
        -9.552388450096018,
        6.353389028213073,
        -1.9995839237574558,
        6.198694711285086,
        -10.744348475937443,
        2.6997157823458764,
        2.018000446796748,
        -2.4784493706587796,
        -1.10720607222175,
        -4.798781822462345,
        -0.33955902810780003,
        -2.4545299416868005,
        5.4803772326847735,
        -2.6742673212293937,
        -3.0311652139232876,
        5.016682666555155,
        -2.878212587780837,
        1.0789107816434012,
        -14.381939961851764,
        2.3094030666242986,
        4.133548979941523,
        1.074251127680725,
        2.9092794337227232,
        -1.7553115312956749,
        1.7539231260921255,
        2.2032176125843748,
        5.407932647233082,
        -0.999617789665372,
        2.7124181355207853,
        -1.267827500586037,
        -2.729825413236526,
        0.020178744460324083,
        3.0474181795781305,
        -2.4969941653907597,
        -4.307260807828349,
        -2.698265670946597
      ],
      "marginal_residuals": [
        -6.090250827747894,
        6.039342871834194,
        4.7446679901254925,
        -0.8983478183225913,
        -2.550429806275652,
        -1.1707923196070595,
        -3.0233235839111074,
        -3.7685426533895026,
        2.3743032173747878,
        -5.766898083465975,
        4.4628386448914625,
        7.712690052728874,
        -0.10604680959735902,
        0.6809896277157179,
        3.6803552864028717,
        2.7837048211655,
        -3.244661771234661,
        6.388040770783718,
        3.5701770661625076,
        -0.4008960490454001,
        12.879019132996362,
        4.222426619936442,
        -4.891110741847513,
        1.3561763432354468,
        2.5599908784014502,
        1.9397774580619824,
        -0.019018155808247172,
        4.058945251055789,
        1.971891751393386,
        -3.38821230376341,
        4.9869098571729324,
        -4.933335009097156,
        1.313587473571232,
        3.040232289417915,
        0.24598581981433654,
        -6.652024403832797,
        -1.8067197708252536,
        5.519894108176587,
        8.826951376898378,
        -1.9416262049673207,
        -3.652183317621571,
        -8.065494739821126,
        -5.337123494599375,
        2.1603124137900664,
        -11.908855465458927,
        5.356382185069322,
        -7.7259635527748,
        -8.374522332800233,
        1.5628514599473817,
        3.4985313193292455,
        1.8755284795228135,
        -1.4663258123042482,
        5.987220542673185,
        -1.679145819512911,
        -15.496900084497362,
        -1.157030810154879,
        -15.384004163479396,
        -8.264666701242895,
        -12.340285124404879,
        -1.731255832965502,
        -10.056739525177264,
        -1.1204810390175908,
        -10.499126938003243,
        -1.8371811364527701,
        0.16934766073588037,
        3.4764900892696033,
        0.04090951227810535,
        -12.69754456835453,
        -9.639332009937462,
        -0.627519767894583,
        -6.786295487802576,
        -5.056105367105857,
        -8.527813351637036,
        -5.533285135576563,
        -4.7625803333836245,
        -2.9625619408535186,
        3.1473001049676554,
        3.9801445678673204,
        1.1447837001301764,
        4.138745073014221,
        -1.7003677740366925,
        0.058503670869370694,
        8.813751926180984,
        -0.6277019494961991,
        -0.3108656293540122,
        2.803451857376885,
        -4.4263673993602595,
        -5.038745733793334,
        3.4101816153491313,
        -0.06621824822403255,
        2.124863768028746,
        -8.10009758307838,
        6.018287293568022,
        -7.707871917891261,
        1.10601219395204,
        -3.8709333160101664,
        9.325033070347956,
        8.001005790545193,
        -0.34787169524131656,
        -1.293979799748179,
        0.9283405383871468,
        7.12320395688721,
        -6.8764243432304895,
        -5.919795543339177,
        -2.0843760229667367,
        11.621806160620253,
        -1.1188343693912657,
        -4.079430557061883,
        -7.873339791916592,
        0.6871216177053157,
        8.570943772078465,
        -3.7051757034409576,
        8.14809826718195,
        -3.210635083920586,
        -5.956056099594406,
        -1.7361172202119945,
        6.837696017232787,
        6.710899056983578,
        10.021893189843595,
        -0.7980429299053498,
        8.213851919334154,
        5.765888549564082,
        16.573881765713253,
        6.5793770124937225,
        11.602863573615608,
        17.585971051755322,
        3.3436399097745664,
        10.270688026690621,
        8.696204218190346,
        9.94019619507722,
        16.35924410355615,
        6.30252891042106,
        10.389958390900304,
        15.181397189802226,
        13.201957218842708,
        17.070996648051647,
        21.30925752121668,
        5.658884638845926,
        11.508316690816557,
        11.895144028559343,
        8.799552672051163,
        4.559153241298688,
        -5.9861797734492725,
        -7.11096090757033,
        -6.222933383151904,
        -8.644095076065241,
        -10.121254839674876,
        0.05877246686836202,
        -5.981834813998802,
        -8.430502796260484,
        -1.1477883172295833,
        0.45714600979921016,
        -8.816676261855264,
        0.4843001360567456,
        -0.49175192502958254,
        -18.506421800227642,
        -9.364911633913707,
        -2.2300455560593235,
        -8.813617742762446,
        -4.019770556156061,
        -5.163510827378296,
        -1.5483127647341917,
        -3.2920870806224514,
        4.280282540781926,
        10.821452943619882,
        8.014241457358878,
        4.219921475779344,
        -11.844199645082597,
        2.667149367814787,
        -8.376759165163165,
        4.310580184857315,
        -6.220059609699433,
        6.212167797879431,
        10.632146379323245,
        6.572623365934646,
        -0.9688943397281378,
        6.180547638533824,
        0.9138166681026831,
        -1.1714859046734603,
        -1.9821570299907805,
        -1.0181956260805975,
        2.2142239526878598,
        4.197705698908422,
        -6.22194668340525,
        0.34283870086152035,
        0.43879018140987824,
        9.535821445706787,
        4.182878436186215,
        2.910841198940105,
        -1.4903174343062204,
        -3.5151673211572643,
        -0.7170022767511455,
        -2.8668755141255886,
        6.584484914771565,
        -2.044251639090106,
        -0.13792663250143278,
        3.3180424036614937,
        2.605716078930641,
        0.1652844811314509,
        -7.698344330435063,
        -1.7616418457427443,
        0.9688032729113871,
        1.7438203285635154,
        4.6183862403127875,
        -0.05206694377815779,
        -0.1970350928859972,
        -2.327626082659478,
        1.5055114470809556,
        8.858620572233903,
        -1.157288680741459,
        5.266589869951723,
        -9.4948611237212,
        6.41091635458789,
        -1.9420565973826456,
        6.256222037659896,
        -10.686821149562633,
        2.7572431087206866,
        2.075527773171558,
        -2.4209220442839694,
        -1.0496787458469328,
        -4.741254496087535,
        -0.28203170173298986,
        -2.3970026153119903,
        5.537904559059584,
        -2.6167399948545835,
        -2.9736378875484704,
        5.0742099929299656,
        -7.7782276553136,
        -3.821104285889362,
        -19.281955029384527,
        -2.5906120009084646,
        -0.7664660875912404,
        -3.825763939852038,
        -1.99073563381004,
        -6.655326598828438,
        -3.1460919414406376,
        -2.6967974549483884,
        0.5079175797003188,
        -5.899632857198135,
        -2.187596932011978,
        -6.1678425681188,
        -7.629840480769289,
        -4.879836323072439,
        -1.8525968879546326,
        -7.397009232923523,
        -9.207275875361113,
        -7.59828073847936
      ],
      "random_effects": [
        0.38537695205295897,
        1.5876453922770637,
        -1.8115034982787581,
        -5.589253891776794,
        0.22881468663055432,
        2.2368808089251084,
        10.306143890537724,
        -5.1289045957904325,
        2.082845460616893,
        0.5444425359633648,
        0.057527326374816216,
        -4.900015067532761
      ],
      "residual_variance": 25.41820756765191,
      "random_intercept_variance": 18.143293201846124,
      "sigma": 5.041647306947592,
      "icc": 0.4164983501796647,
      "log_likelihood": -766.4872381433808,
      "aic": 1542.9744762867615,
      "df_residual": 244
    },
    "phit": {
      "coefficients": [
        46.73918014483013,
        1.6197573853332452,
        0.24377706143487915
      ],
      "covariance": [
        [
          4.883909866241514,
          0.13854801205839748,
          -0.07000064251469805
        ],
        [
          0.13854801205839748,
          0.02598473986416728,
          -0.005192953189893667
        ],
        [
          -0.07000064251469805,
          -0.005192953189893666,
          0.0017462920862562359
        ]
      ],
      "std_errors": [
        2.209956982893901,
        0.16119782834817373,
        0.04178865978057009
      ],
      "z_statistics": [
        21.14936195890382,
        10.048258105777366,
        5.833569746312489
      ],
      "p_values": [
        2.7969909623345792e-99,
        9.3505573691399e-24,
        5.425391317905695e-09
      ],
      "conf_int": [
        [
          42.40774405097528,
          51.07061623868498
        ],
        [
          1.303815447384755,
          1.9356993232817354
        ],
        [
          0.16187279330276433,
          0.32568132956699397
        ]
      ],
      "fitted": [
        84.73262777980027,
        82.56903408021837,
        64.18670896192585,
        73.43072477037515,
        63.29080675832722,
        71.22616927165929,
        75.53770053596288,
        65.95391960544043,
        61.718073734677056,
        82.54427503551838,
        73.00053830716091,
        83.70968689932343,
        74.94842376165003,
        75.73938732433623,
        69.4670216656491,
        67.97794057110893,
        63.883307163508846,
        87.28260462149176,
        62.43446832611207,
        69.05354144132023,
        69.51162625927861,
        65.6062187723384,
        72.10675613412212,
        86.46746904903992,
        69.71265451387308,
        79.0898679342128,
        59.68666354808194,
        86.25370014121927,
        64.48375364088066,
        62.612857696037935,
        72.12473553510124,
        69.76098040137198,
        84.41405791870402,
        81.34041310285701,
        83.05665957246111,
        73.7356697961074,
        82.11236516309971,
        66.01575128409735,
        68.7576940153756,
        73.0071227066933,
        57.66967981934686,
        68.87099124154673,
        56.161619996324276,
        79.14318408793545,
        76.08135196718436,
        76.80911431665677,
        71.55746005450034,
        54.86201883452496,
        76.65964504177816,
        67.00296518239675,
        69.00896802220275,
        66.18982231402924,
        67.7672759590521,
        76.57064232123867,
        73.65364619273033,
        79.50877691838798,
        62.59675027171139,
        54.53441280947465,
        63.896031232637405,
        79.21700194119848,
        77.4244856334101,
        72.10522714725013,
        73.20687304623527,
        68.16092724468542,
        70.42939844749654,
        64.13725601896253,
        74.75783659595426,
        62.858290676586186,
        61.5110781181694,
        68.4562658761265,
        78.16004159603551,
        76.8768514753384,
        73.61555945986974,
        71.96503124380929,
        66.18032644161634,
        66.00230804908568,
        65.38251458166226,
        63.8116701187623,
        59.552030986499496,
        77.71906961361634,
        77.08318246066649,
        75.58531101576037,
        66.87806276044947,
        78.6505166361271,
        85.53568031598479,
        66.66136282925285,
        80.58918208599067,
        80.51356042042397,
        65.50863307128114,
        80.04003293485427,
        78.17195091860174,
        73.5579122697087,
        81.21952739306194,
        71.24468660452122,
        63.30180249267789,
        68.12374800263972,
        74.40684773857411,
        83.62387501837729,
        63.29475250416259,
        66.00886060867023,
        69.88354027053414,
        69.56067685203446,
        68.62030515215284,
        81.87767635226153,
        83.62625683188908,
        78.18207464830164,
        77.20371517831288,
        78.09031136598415,
        74.10722060083873,
        84.89475919121692,
        83.46493703684433,
        79.34505651236331,
        78.41378254174084,
        69.36251589284241,
        81.14493690851663,
        80.50499802913428,
        68.20018479168863,
        80.32498175193865,
        88.8139876190793,
        89.08192373882815,
        58.087028889586314,
        80.88799225935782,
        81.66899904320876,
        88.6897668780257,
        89.49828031690296,
        88.91517283876365,
        78.2325039807437,
        88.29245586382808,
        90.48193967232783,
        77.2269476954406,
        87.94189978696214,
        80.41061498009692,
        92.89218549961798,
        82.42274670071589,
        76.46218667167456,
        85.41214724246633,
        71.8478863693011,
        73.42225925167268,
        74.41582719970127,
        84.94799986195885,
        71.55459121846623,
        87.60099064921947,
        59.546275177666615,
        77.38005631178943,
        61.86102878737043,
        74.36719048028385,
        68.09335024389259,
        73.42632293735032,
        53.46493021821678,
        66.60859820047884,
        55.04888372144779,
        57.80794939441936,
        60.086771666073886,
        59.97879526816109,
        55.29184732924777,
        71.67151720444667,
        68.05500703813225,
        70.86814096027852,
        72.09471314698149,
        62.60286596037449,
        53.59060623159595,
        64.06340816895238,
        66.64018248484093,
        86.89056291983078,
        65.95439251699234,
        67.44560400325368,
        75.21692398483326,
        70.09604510569487,
        58.029696092796335,
        81.37260462577594,
        78.97426527575446,
        77.81590507031204,
        84.12667766273306,
        77.42569908128925,
        76.13422209467754,
        79.28673980034048,
        75.79829782207835,
        74.16602879250974,
        66.54833136528502,
        58.92759956595279,
        80.34763816204304,
        66.90921858327428,
        68.32773683705453,
        76.1813892193675,
        82.13360383510137,
        57.482652354551874,
        81.12962109025585,
        65.06156409977652,
        82.10560133702313,
        70.68575997026929,
        68.49560985711965,
        74.56044481271385,
        65.88931805008815,
        67.80295762119064,
        68.07469417505287,
        74.46536916846392,
        60.0884001322999,
        76.51672645703232,
        65.10115805483082,
        86.30478686639849,
        68.80808438170567,
        65.98563926305137,
        73.83962220739896,
        82.00905629564974,
        82.50359427015347,
        84.67456241926162,
        71.72515340903445,
        56.61701587929278,
        72.4619067541416,
        76.6188160071155,
        57.74093745642234,
        62.6913884500955,
        61.13761097178632,
        65.58058392375786,
        72.60030528871468,
        81.20734847593751,
        67.2522842176538,
        64.74599955320346,
        81.42744937065869,
        62.596206072221136,
        76.83178182246259,
        73.27155902810772,
        68.21952994168612,
        84.63962276731617,
        67.57526732122956,
        63.54216521392258,
        81.61331733344491,
        70.20821258778977,
        77.30708921836559,
        67.6489399618607,
        64.92059693338477,
        75.87645102006779,
        71.25174887232902,
        55.93472056628569,
        58.60331153130396,
        61.235076873916896,
        59.89078238742441,
        76.2200673527762,
        53.949617789673425,
        57.25658186448745,
        69.54882750059518,
        65.06382541324534,
        53.4348212555481,
        57.97058182043056,
        68.20399416539988,
        54.99326080783711,
        66.92226567095524
      ],
      "residuals": [
        -6.475627779800263,
        5.653965919781626,
        4.359291038074161,
        -1.2837247703751444,
        -2.9358067583272245,
        -1.5561692716592859,
        -3.408700535962879,
        -4.153919605440436,
        1.9889262653229451,
        -6.152275035518386,
        4.077461692839094,
        7.327313100676577,
        -0.4914237616500401,
        0.2956126756637616,
        3.294978334350901,
        1.1960594288910755,
        -4.832307163508844,
        4.800395378508242,
        1.9825316738879337,
        -1.988541441320237,
        11.291373740721383,
        2.6347812276616054,
        -6.478756134122122,
        -0.23146904903991583,
        0.9723454861269261,
        0.35213206578718825,
        -1.60666354808194,
        2.471299858780725,
        0.3842463591193308,
        -4.975857696037934,
        3.3992644648987635,
        -6.520980401371979,
        -0.27405791870401686,
        1.452586897142993,
        -1.3416595724611113,
        -8.239669796107407,
        -3.3943651630997067,
        3.932248715902645,
        7.239305984624394,
        -0.1301227066932995,
        -1.8406798193468603,
        -6.253991241546736,
        -3.5256199963242736,
        3.9718159120645424,
        -10.097351967184366,
        7.167885683343229,
        -5.9144600545003385,
        -6.563018834524961,
        3.3743549582218435,
        5.310034817603253,
        3.687031977797247,
        0.3451776859707536,
        7.798724040947903,
        0.13235767876133764,
        -9.907646192730333,
        4.4322230816120225,
        -9.794750271711393,
        -2.6754128094746505,
        -6.751031232637402,
        3.8579980588015275,
        -4.4674856334101065,
        4.468772852749865,
        -4.909873046235276,
        3.752072755314572,
        5.758601552503464,
        9.065743981037471,
        5.630163404045746,
        -7.108290676586186,
        -4.050078118169402,
        4.961734123873512,
        -1.1970415960355183,
        0.5331485246615983,
        -2.9385594598697367,
        0.05596875619070829,
        0.8266735583836606,
        2.6266919509143207,
        2.9184854183377382,
        3.7513298812377016,
        0.9159690135005079,
        3.909930386383664,
        -1.929182460666496,
        -0.17031101576036178,
        8.584937239550527,
        -0.8565166361270968,
        -0.5396803159847963,
        2.5746371707471525,
        -4.655182085990674,
        -5.267560420423976,
        3.181366928718859,
        -0.2950329348542624,
        1.8960490813982602,
        -8.328912269708695,
        5.789472606938062,
        -7.9366866045212205,
        0.8771975073221085,
        -4.099748002639714,
        7.08815226142589,
        5.7641249816227145,
        -2.584752504162587,
        -3.530860608670231,
        -1.308540270534138,
        4.886323147965541,
        -9.11330515215284,
        -8.156676352261528,
        -4.321256831889073,
        9.384925351698357,
        -3.3557151783128774,
        -6.3163113659841486,
        -10.11022060083873,
        -1.5497591912169213,
        6.334062963155674,
        -5.942056512363308,
        5.911217458259159,
        -5.447515892842411,
        -8.192936908516629,
        -3.9729980291342883,
        4.600815208311374,
        4.4740182480613555,
        7.785012380920705,
        -3.034923738828155,
        5.976971110413679,
        3.529007740642186,
        14.337000956791243,
        -3.7267668780256997,
        1.296719683097038,
        7.279827161236341,
        -6.962503980743705,
        -0.03545586382807642,
        -1.609939672327826,
        -0.365947695440596,
        6.053100213037865,
        -4.003614980096927,
        0.08381450038201876,
        4.875253299284111,
        2.8958133283254455,
        6.764852757533674,
        11.003113630698905,
        -4.647259251672679,
        1.202172800298726,
        1.5890001380411576,
        -1.5065912184662267,
        -5.74699064921947,
        -0.8572751776666152,
        -1.9820563117894352,
        -1.0940287873704264,
        -3.5151904802838487,
        -4.992350243892588,
        5.1876770626496835,
        -0.8529302182167768,
        -3.3015982004788356,
        3.9811162785522143,
        5.586050605580638,
        -3.6877716660738855,
        5.613204731838906,
        4.637152670752229,
        -13.377517204446676,
        -4.236007038132243,
        2.898859039721472,
        -3.684713146981494,
        1.1091340396255163,
        -0.03460623159595144,
        3.5805918310476272,
        1.836817515159069,
        2.197437080169209,
        8.738607483007655,
        5.931395996746318,
        2.137076015166741,
        -13.927045105694873,
        0.5843039072036618,
        -10.459604625775938,
        2.2277347242455363,
        -8.302905070312036,
        4.129322337266942,
        8.549300918710742,
        4.489777905322455,
        -3.051739800340485,
        4.097702177921647,
        -1.1690287925097351,
        -3.254331365285026,
        -2.526599565952786,
        -1.5626381620430436,
        1.6697814167257121,
        3.653263162945464,
        -6.766389219367497,
        -0.20160383510136626,
        -0.1056523545518715,
        8.991378909744142,
        3.6384359002234845,
        2.366398662976863,
        -2.034759970269292,
        -4.059609857119639,
        -1.2614448127138473,
        -3.4113180500881484,
        6.0400423788093605,
        -2.588694175052865,
        -0.6823691684639215,
        2.7735998677000993,
        2.061273542967683,
        -0.37915805483082465,
        -8.24278686639849,
        -2.3060843817056735,
        0.4243607369486284,
        1.199377792601041,
        4.073943704350256,
        -0.10959427015346535,
        -0.2545624192616174,
        -2.3851534090344444,
        1.4479841207072184,
        8.80109324585841,
        -1.2148160071155019,
        5.209062543577666,
        -9.5523884500955,
        6.353389028213677,
        -1.9995839237578537,
        6.198694711285327,
        -10.744348475937514,
        2.6997157823462032,
        2.0180004467965347,
        -2.4784493706586943,
        -1.107206072221139,
        -4.798781822462587,
        -0.33955902810771477,
        -2.4545299416861184,
        5.480377232683836,
        -2.6742673212295642,
        -3.031165213922577,
        5.016682666555084,
        -2.8782125877897755,
        1.0789107816344057,
        -14.381939961860702,
        2.309403066615232,
        4.133548979932215,
        1.0742511276709763,
        2.9092794337143104,
        -1.7553115313039598,
        1.7539231260831016,
        2.2032176125755925,
        5.407932647223802,
        -0.9996177896734224,
        2.71241813551255,
        -1.2678275005951747,
        -2.7298254132453366,
        0.020178744451897046,
        3.0474181795694406,
        -2.496994165399883,
        -4.30726080783711,
        -2.6982656709552373
      ],
      "log_likelihood": -766.4872381433806,
      "aic": 1542.9744762867613,
      "df_residual": 244,
      "evaluations": 107,
      "fixed_fitted": [
        84.34725082774831,
        82.18365712816642,
        63.80133200987389,
        73.0453478183232,
        62.90542980627526,
        70.84079231960733,
        75.15232358391093,
        65.56854265338848,
        61.33269678262509,
        82.15889808346643,
        72.61516135510895,
        83.32430994727147,
        74.56304680959808,
        75.35401037228428,
        69.08164471359714,
        66.3902951788342,
        62.29566177123411,
        85.69495922921702,
        60.84682293383734,
        67.4658960490455,
        67.92398086700388,
        64.01857338006366,
        70.51911074184738,
        84.87982365676518,
        68.12500912159834,
        77.50222254193807,
        58.0990181558072,
        84.66605474894453,
        62.89610824860593,
        61.0252123037632,
        70.5370901428265,
        68.17333500909724,
        82.82641252642928,
        79.75276771058228,
        81.46901418018638,
        72.14802440383266,
        80.52471977082497,
        64.42810589182261,
        67.17004862310087,
        74.81862620496753,
        59.48118331762109,
        70.68249473982097,
        57.973123494598504,
        80.95468758620969,
        77.8928554654586,
        78.62061781493101,
        73.36896355277457,
        56.67352233279919,
        78.4711485400524,
        68.81446868067098,
        70.82047152047699,
        68.00132581230348,
        69.57877945732633,
        78.3821458195129,
        79.24290008449788,
        85.09803081015552,
        68.18600416347894,
        60.1236667012422,
        69.48528512440495,
        84.80625583296602,
        83.01373952517764,
        77.69448103901767,
        78.79612693800281,
        73.75018113645297,
        76.01865233926408,
        69.72650991073007,
        80.3470904877218,
        68.44754456835373,
        67.10033200993695,
        74.04551976789404,
        83.74929548780305,
        82.46610536710594,
        79.20481335163728,
        77.55428513557683,
        71.76958033338389,
        71.59156194085323,
        65.1536998950321,
        63.58285543213215,
        59.323216299869344,
        77.49025492698618,
        76.85436777403633,
        75.35649632913021,
        66.64924807381931,
        78.42170194949693,
        85.30686562935463,
        66.4325481426227,
        80.36036739936051,
        80.28474573379381,
        65.27981838465098,
        79.81121824822411,
        77.94313623197158,
        73.32909758307854,
        80.99071270643178,
        71.01587191789106,
        63.07298780604774,
        67.89493331600956,
        72.16996692965213,
        81.38699420945531,
        61.057871695240614,
        63.77197979974826,
        67.64665946161216,
        67.32379604311248,
        66.38342434323086,
        79.64079554333955,
        81.3893760229671,
        75.94519383937966,
        74.9668343693909,
        75.85343055706217,
        71.87033979191675,
        82.65787838229494,
        81.22805622792235,
        77.10817570344133,
        76.17690173281886,
        67.12563508392043,
        78.90805609959465,
        78.2681172202123,
        65.96330398276665,
        78.08810094301667,
        86.57710681015732,
        86.84504292990617,
        55.85014808066434,
        78.65111145043583,
        79.43211823428678,
        78.38362298750734,
        79.19213642638461,
        78.6090289482453,
        67.92636009022534,
        77.98631197330972,
        80.17579578180947,
        66.92080380492224,
        77.63575589644378,
        70.10447108957857,
        82.58604160909962,
        72.11660281019753,
        66.1560427811562,
        75.10600335194798,
        61.541742478782744,
        63.11611536115433,
        64.10968330918291,
        74.64185597144049,
        61.24844732794788,
        77.29484675870111,
        64.67517977344797,
        82.50896090757078,
        66.98993338315178,
        79.4960950760652,
        73.22225483967394,
        78.55522753313167,
        58.59383481399813,
        71.73750279626019,
        60.17778831722914,
        62.93685399020071,
        65.21567626185524,
        65.10769986394244,
        60.42075192502912,
        76.80042180022802,
        73.1839116339136,
        75.99704555605987,
        77.22361774276284,
        67.73177055615584,
        58.7195108273773,
        69.19231276473373,
        71.76908708062228,
        84.8077174592185,
        63.87154705638006,
        65.36275854264139,
        73.13407852422097,
        68.01319964508258,
        55.94685063218405,
        79.28975916516364,
        76.89141981514217,
        75.73305960969975,
        82.04383220212077,
        75.34285362067696,
        74.05137663406525,
        77.2038943397282,
        73.71545236146606,
        72.08318333189744,
        64.46548590467273,
        58.38315702999003,
        79.80319562608028,
        66.36477604731152,
        67.78329430109177,
        75.63694668340474,
        81.58916129913861,
        56.938209818589115,
        80.5851785542931,
        64.51712156381376,
        81.56115880106037,
        70.14131743430653,
        67.95116732115689,
        74.0160022767511,
        65.34487551412539,
        67.25851508522788,
        67.53025163909011,
        73.92092663250116,
        59.543957596337144,
        75.97228392106956,
        64.55671551886806,
        85.76034433043573,
        68.26364184574291,
        65.44119672708861,
        73.2951796714362,
        81.46461375968698,
        82.44606694377865,
        84.6170350928868,
        71.66762608265962,
        56.55948855291795,
        72.40437942776677,
        76.56128868074067,
        57.683410130047506,
        62.63386112372067,
        61.08008364541149,
        65.52305659738303,
        72.54277796233985,
        81.14982114956268,
        67.19475689127897,
        64.68847222682864,
        81.36992204428387,
        62.538678745846305,
        76.77425449608776,
        73.21403170173289,
        68.1620026153113,
        84.58209544094134,
        67.51773999485474,
        63.48463788754775,
        81.55579000707009,
        75.10822765531346,
        82.20710428588927,
        72.54895502938439,
        69.82061200090845,
        80.77646608759147,
        76.1517639398527,
        60.83473563380937,
        63.50332659882764,
        66.13509194144058,
        64.79079745494809,
        81.12008242029988,
        58.84963285719711,
        62.156596932011134,
        74.44884256811886,
        69.96384048076902,
        58.334836323071784,
        62.87059688795424,
        73.10400923292356,
        59.89327587536079,
        71.82228073847892
      ],
      "marginal_residuals": [
        -6.0902508277483065,
        6.039342871833583,
        4.744667990126118,
        -0.8983478183231881,
        -2.550429806275261,
        -1.1707923196073295,
        -3.0233235839109227,
        -3.7685426533884794,
        2.3743032173749086,
        -5.76689808346643,
        4.46283864489105,
        7.712690052728533,
        -0.10604680959808377,
        0.6809896277157179,
        3.6803552864028575,
        2.783704821165813,
        -3.2446617712341066,
        6.388040770782979,
        3.570177066162664,
        -0.4008960490454996,
        12.87901913299612,
        4.222426619936343,
        -4.891110741847385,
        1.3561763432348215,
        2.5599908784016634,
        1.9397774580619256,
        -0.019018155807202675,
        4.058945251055462,
        1.9718917513940681,
        -3.388212303763197,
        4.986909857173501,
        -4.933335009097242,
        1.3135874735707205,
        3.0402322894177303,
        0.245985819813626,
        -6.6520244038326695,
        -1.8067197708249694,
        5.5198941081773825,
        8.826951376899132,
        -1.941626204967534,
        -3.6521833176210876,
        -8.06549473982097,
        -5.337123494598501,
        2.160312413790308,
        -11.9088554654586,
        5.356382185068995,
        -7.725963552774573,
        -8.374522332799188,
        1.562851459947609,
        3.498531319329018,
        1.8755284795230125,
        -1.4663258123034808,
        5.987220542673668,
        -1.6791458195128968,
        -15.496900084497874,
        -1.1570308101555185,
        -15.384004163478942,
        -8.264666701242199,
        -12.34028512440495,
        -1.7312558329660135,
        -10.056739525177647,
        -1.120481039017676,
        -10.499126938002817,
        -1.837181136452969,
        0.169347660735923,
        3.47649008926993,
        0.04090951227820483,
        -12.697544568353734,
        -9.63933200993695,
        -0.6275197678940287,
        -6.786295487803059,
        -5.056105367105943,
        -8.527813351637278,
        -5.533285135576833,
        -4.76258033338388,
        -2.96256194085322,
        3.147300104967897,
        3.9801445678678533,
        1.1447837001306596,
        4.138745073013823,
        -1.7003677740363372,
        0.05850367086979702,
        8.813751926180686,
        -0.627701949496938,
        -0.31086562935463746,
        2.8034518573773113,
        -4.426367399360515,
        -5.038745733793817,
        3.4101816153490176,
        -0.0662182482241036,
        2.124863768028419,
        -8.100097583078536,
        6.018287293568221,
        -7.707871917891062,
        1.1060121939522602,
        -3.8709333160095554,
        9.325033070347871,
        8.001005790544696,
        -0.3478716952406131,
        -1.2939797997482572,
        0.9283405383878431,
        7.123203956887522,
        -6.876424343230859,
        -5.919795543339546,
        -2.084376022967092,
        11.621806160620338,
        -1.1188343693908962,
        -4.079430557062167,
        -7.873339791916749,
        0.6871216177050599,
        8.570943772077655,
        -3.705175703441327,
        8.14809826718114,
        -3.2106350839204296,
        -5.956056099594647,
        -1.7361172202123072,
        6.837696017233355,
        6.710899056983337,
        10.021893189842686,
        -0.798042929906174,
        8.213851919335653,
        5.765888549564167,
        16.573881765713224,
        6.579377012492657,
        11.602863573615394,
        17.585971051754697,
        3.3436399097746516,
        10.27068802669028,
        8.69620421819053,
        9.94019619507776,
        16.35924410355622,
        6.3025289104214295,
        10.389958390900375,
        15.181397189802468,
        13.201957218843802,
        17.07099664805203,
        21.309257521217255,
        5.658884638845677,
        11.508316690817082,
        11.895144028559514,
        8.799552672052123,
        4.559153241298887,
        -5.986179773447965,
        -7.110960907570785,
        -6.222933383151776,
        -8.644095076065199,
        -10.121254839673938,
        0.058772466868333595,
        -5.981834813998127,
        -8.430502796260186,
        -1.1477883172291357,
        0.4571460097992883,
        -8.816676261855235,
        0.4843001360575556,
        -0.4917519250291207,
        -18.506421800228026,
        -9.364911633913593,
        -2.2300455560598778,
        -8.813617742762844,
        -4.019770556155834,
        -5.163510827377301,
        -1.5483127647337227,
        -3.292087080622281,
        4.280282540781499,
        10.821452943619938,
        8.014241457358608,
        4.2199214757790315,
        -11.844199645082583,
        2.667149367815945,
        -8.376759165163648,
        4.310580184857827,
        -6.220059609699746,
        6.212167797879232,
        10.632146379323032,
        6.572623365934746,
        -0.9688943397281946,
        6.1805476385339375,
        0.9138166681025552,
        -1.1714859046727355,
        -1.9821570299900273,
        -1.018195626080285,
        2.214223952688471,
        4.197705698908223,
        -6.221946683404738,
        0.34283870086139245,
        0.4387901814108872,
        9.535821445706901,
        4.182878436186243,
        2.9108411989396217,
        -1.490317434306533,
        -3.5151673211568806,
        -0.7170022767510886,
        -2.8668755141253897,
        6.584484914772119,
        -2.044251639090106,
        -0.13792663250116277,
        3.318042403662858,
        2.605716078930442,
        0.16528448113193406,
        -7.698344330435731,
        -1.7616418457429148,
        0.9688032729113871,
        1.7438203285637996,
        4.618386240313015,
        -0.05206694377864096,
        -0.197035092886793,
        -2.32762608265962,
        1.5055114470820499,
        8.858620572233235,
        -1.1572886807406775,
        5.266589869952497,
        -9.494861123720668,
        6.410916354588508,
        -1.9420565973830293,
        6.256222037660152,
        -10.68682114956269,
        2.7572431087210276,
        2.075527773171359,
        -2.42092204428387,
        -1.0496787458463075,
        -4.7412544960877625,
        -0.2820317017328904,
        -2.397002615311294,
        5.53790455905866,
        -2.61673999485474,
        -2.9736378875477456,
        5.074209992929909,
        -7.778227655313458,
        -3.8211042858892768,
        -19.281955029384385,
        -2.5906120009084503,
        -0.7664660875914677,
        -3.825763939852706,
        -1.990735633809372,
        -6.655326598827642,
        -3.146091941440581,
        -2.69679745494809,
        0.5079175797001199,
        -5.899632857197105,
        -2.1875969320111324,
        -6.167842568118857,
        -7.629840480769019,
        -4.879836323071785,
        -1.8525968879542418,
        -7.3970092329235655,
        -9.207275875360793,
        -7.59828073847892
      ],
      "random_effects": [
        0.3853769520519602,
        1.5876453922747338,
        -1.81150349827423,
        -5.589253891767545,
        0.2288146866301519,
        2.2368808089219767,
        10.306143890518353,
        -5.128904595781347,
        2.0828454606122846,
        0.5444425359627576,
        0.057527326374829664,
        -4.900015067523683
      ],
      "group_sizes": [
        15,
        24,
        15,
        22,
        20,
        27,
        19,
        21,
        16,
        25,
        23,
        20
      ],
      "n_groups": 12,
      "group_labels": [
        107,
        114,
        121,
        128,
        135,
        142,
        149,
        156,
        163,
        170,
        177,
        184
      ],
      "residual_variance": 25.418207567683723,
      "random_intercept_variance": 18.14329320136849,
      "sigma": 5.041647306950748,
      "icc": 0.41649835017296266,
      "boundary": false,
      "method": "ML",
      "converged": true,
      "n_input": 250,
      "n_observations": 247,
      "n_dropped": 3,
      "retained_rows": [
        0,
        2,
        3,
        5,
        6,
        7,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119,
        120,
        121,
        122,
        123,
        124,
        125,
        126,
        127,
        128,
        129,
        130,
        131,
        132,
        133,
        134,
        135,
        136,
        137,
        138,
        139,
        140,
        141,
        142,
        143,
        144,
        145,
        146,
        147,
        148,
        149,
        150,
        151,
        152,
        153,
        154,
        155,
        156,
        157,
        158,
        159,
        160,
        161,
        162,
        163,
        164,
        165,
        166,
        167,
        168,
        169,
        170,
        171,
        172,
        173,
        174,
        175,
        176,
        177,
        178,
        179,
        180,
        181,
        182,
        183,
        184,
        185,
        186,
        187,
        188,
        189,
        190,
        191,
        192,
        193,
        194,
        195,
        196,
        197,
        198,
        199,
        200,
        201,
        202,
        203,
        204,
        205,
        206,
        207,
        208,
        209,
        210,
        211,
        212,
        213,
        214,
        215,
        216,
        217,
        218,
        219,
        220,
        221,
        222,
        223,
        224,
        225,
        226,
        227,
        228,
        229,
        230,
        231,
        232,
        233,
        234,
        235,
        236,
        237,
        238,
        239,
        240,
        241,
        242,
        243,
        244,
        245,
        246,
        247,
        248,
        249
      ],
      "dropped_rows": [
        1,
        4,
        8
      ]
    },
    "python_diagnostics": {
      "backend": "statsmodels MixedLM (ML)",
      "warnings": [],
      "covariance_convention": "plug-in GLS, matching lme4"
    },
    "warnings": [
      {
        "severity": 2,
        "message": "stats_lmm(): stats_lmm dropped 3 of 250 observations with missing values (listwise deletion)"
      }
    ],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "Python": 6.264315288717626e-09,
        "phit": 6.26160812089438e-09
      },
      "covariance": {
        "Python": 8.481738245080805e-08,
        "phit": 8.478141211298862e-08
      },
      "std_errors": {
        "Python": 1.918982661663904e-08,
        "phit": 1.9181688237779326e-08
      },
      "z_statistics": {
        "Python": 1.8081269459457872e-07,
        "phit": 1.8073603413881756e-07
      },
      "p_values": {
        "Python": 1.6165611390639134e-16,
        "phit": 1.614549733599205e-16
      },
      "conf_int": {
        "Python": 4.387568708352774e-08,
        "phit": 4.3857028231286677e-08
      },
      "fixed_fitted": {
        "Python": 3.437314433085703e-09,
        "phit": 3.4358151879132492e-09
      },
      "fitted": {
        "Python": 4.8232308813567215e-08,
        "phit": 4.8211845182777324e-08
      },
      "residuals": {
        "Python": 4.8232308813567215e-08,
        "phit": 4.8211845182777324e-08
      },
      "marginal_residuals": {
        "Python": 3.437314433085703e-09,
        "phit": 3.4358151879132492e-09
      },
      "random_effects": {
        "Python": 4.5783529856180394e-08,
        "phit": 4.5764158684846734e-08
      },
      "residual_variance": {
        "Python": 7.50255999548699e-08,
        "phit": 7.499378540387625e-08
      },
      "random_intercept_variance": {
        "Python": 1.1262436885317584e-06,
        "phit": 1.125766054599353e-06
      },
      "sigma": {
        "Python": 7.440584148810103e-09,
        "phit": 7.437428450884909e-09
      },
      "icc": {
        "Python": 1.5803245878576178e-08,
        "phit": 1.5796543850754574e-08
      },
      "log_likelihood": {
        "Python": 3.410605131648481e-13,
        "phit": 2.2737367544323206e-13
      },
      "aic": {
        "Python": 6.821210263296962e-13,
        "phit": 4.547473508864641e-13
      },
      "df_residual": {
        "Python": 0.0,
        "phit": 0.0
      }
    },
    "tolerance": {
      "absolute": 1e-07,
      "relative": 1e-06
    },
    "extension_sha256": "2105dd47a15f21b0da6ae81a23461ef385285517e1af0519a0bb22238bc3ffc6"
  }
]