Mixed-model functions · phit

Gaussian and binomial mixed models. See Mixed models for the supported structures and Model contracts for result keys and algorithms.

Formula models

`fit_mixed_gaussian()`

Fits a Gaussian mixed model from an lme4 formula, like lme4::lmer().

Fixed terms are as in fit_ols(). Random terms can be (x | g), (x || g), (1 | g1) + (1 | g2), (1 | g1:g2), and (1 | g1/g2).
Fits by REML unless reml is false.
Groups and effects follow first appearance after missing rows are dropped, not lme4’s sorted levels; terms keep formula order.
Each random term’s effects_cond_var holds one k × k conditional covariance per group, as ranef(condVar = TRUE).
Rows with null or NAN in a variable the formula uses are dropped with one warning; missing: 'raise' rejects them instead. retained_rows and dropped_rows give the original row positions.

Phit\fit_mixed_gaussian(    string $formula,    array|object $data,    bool $reml = true,    string $missing = 'drop',    array|string|null $weights = NULL,    ?array $start = NULL,    int $maxEvaluations = 20000,    float $tolerance = 1.0E-7,    string $optimizer = 'bobyqa',    float $objectiveTolerance = 1.0E-12,): MixedGaussianFit

Parameter	Type	Default	Description
`$formula`	`string`	required	R formula, such as `'y ~ log(x) + f * z + offset(log(t))'`
`$data`	`array\\|object`	required	Named columns or factor descriptors; objects use `toModelData()`, else `toColumns()`
`$reml`	`bool`	`true`	`true` for REML, `false` for ML
`$missing`	`string`	`'drop'`	`'drop'` removes rows with `null` or `NAN` in any variable the model uses and warns once; `'raise'` rejects them
`$weights`	`array\\|string\\|null`	`NULL`	Positive prior weights aligned with the original rows, or a column name
`$start`	`?array`	`NULL`	Starting relative covariance factors, in the units of the random columns; `null` starts diagonal factors at one and off-diagonals at zero
`$maxEvaluations`	`int`	`20000`	Largest number of optimizer evaluations
`$tolerance`	`float`	`1.0E-7`	BOBYQA final trust-region radius, in (0, 0.1]
`$optimizer`	`string`	`'bobyqa'`	`'bobyqa'` or `'nelder_mead'`
`$objectiveTolerance`	`float`	`1.0E-12`	Nelder–Mead stopping tolerance: the standard deviation of the simplex objective values

Returns

MixedGaussianFit A fit object, read like this array:array{  model: 'linear'|'generalized_linear'|'mixed_gaussian'|'mixed_logistic',  coefficients: list<float>,  covariance: list<list<float>>,  std_errors: list<float>,  p_values: list<float>,  conf_int: list<array{float,float}>,  fitted: list<float>,  residuals: list<float>,  log_likelihood: float,  df_residual: int,  diagnostics: array{converged:bool,solver:string,warnings:list<string>,iterations?:int,evaluations?:int,gradient_max?:float,boundary?:bool,singular?:bool},  n_input: int,  n_observations: int,  n_dropped: int,  retained_rows: list<int>,  dropped_rows: list<int>,  z_statistics: list<float>,  fixed_fitted: list<float>,  marginal_residuals: list<float>,  aic: float,  residual_variance: float,  sigma: float,  method: string,  converged: bool,  n_parameters: int,  bic: float,  theta: list<float>,  singular: bool,  optimizer: string,  optimizer_implementation: string,  evaluations: int,  random: list<array{covariance:list<list<float>>,effects:list<list<float>>,effects_cond_var:list<list<list<float>>>,group_labels:list<int|string>,group_sizes:list<int>,label:string,group:string,columns:list<string>,correlated:bool}>,  formula: string,  response: string,  columns: list<string>,  terms: list<string>,  assign: list<int>,  intercept: bool,  named: array<string,float>,  predvars: array{levels:array<string,list<string>>,poly:array<string,array{alpha:list<float>,norm2:list<float>}>},}

Errors Exception: a code from 1001 to 1008 for an input or statistical error; 1007 for an unsupported function, family, or random term.

See also Details · Example

`fit_mixed_logistic()`

Fits a binomial logit model with one random intercept from a formula, like lme4::glmer(family = binomial).

The formula has exactly one (1 | g) term. The model is binomial with the logit link only, so the function takes no family or link.
Uses the Laplace approximation by default, and adaptive quadrature when quadraturePoints is above 1.
Responses are as in fit_generalized_linear().
random_effects_cond_var holds the variance of each conditional mode, as ranef(condVar = TRUE).
Rows with null or NAN in a variable the formula uses are dropped with one warning; missing: 'raise' rejects them instead. retained_rows and dropped_rows give the original row positions.

Phit\fit_mixed_logistic(    string $formula,    array|object $data,    string $missing = 'drop',    array|string|null $weights = NULL,    int $quadraturePoints = 1,    int $maxEvaluations = 20000,    float $tolerance = 1.0E-7,): MixedLogisticFit

Parameter	Type	Default	Description
`$formula`	`string`	required	R formula, such as `'y ~ log(x) + f * z + offset(log(t))'`
`$data`	`array\\|object`	required	Named columns or factor descriptors; objects use `toModelData()`, else `toColumns()`
`$missing`	`string`	`'drop'`	`'drop'` removes rows with `null` or `NAN` in any variable the model uses and warns once; `'raise'` rejects them
`$weights`	`array\\|string\\|null`	`NULL`	Positive prior weights aligned with the original rows, or a column name
`$quadraturePoints`	`int`	`1`	1 for the Laplace approximation, or 2 to 61 for adaptive Gauss–Hermite quadrature
`$maxEvaluations`	`int`	`20000`	Largest number of optimizer evaluations
`$tolerance`	`float`	`1.0E-7`	BOBYQA final trust-region radius, in (0, 0.1]

Returns

MixedLogisticFit A fit object, read like this array:array{  model: 'linear'|'generalized_linear'|'mixed_gaussian'|'mixed_logistic',  coefficients: list<float>,  covariance: list<list<float>>,  std_errors: list<float>,  p_values: list<float>,  conf_int: list<array{float,float}>,  fitted: list<float>,  residuals: list<float>,  log_likelihood: float,  df_residual: int,  diagnostics: array{converged:bool,solver:string,warnings:list<string>,iterations?:int,evaluations?:int,gradient_max?:float,boundary?:bool,singular?:bool},  n_input: int,  n_observations: int,  n_dropped: int,  retained_rows: list<int>,  dropped_rows: list<int>,  z_statistics: list<float>,  fixed_fitted: list<float>,  linear_predictor: list<float>,  aic: float,  bic: float,  n_parameters: int,  group_labels: list<int|string>,  group_sizes: list<int>,  random_effects: list<float>,  random_effects_cond_var: list<float>,  n_groups: int,  random_intercept_sd: float,  random_intercept_variance: float,  neg2_log_likelihood: float,  quadrature_points: int,  integration: string,  method: string,  family: string,  link: string,  optimizer: string,  converged: bool,  evaluations: int,  gradient_max: float,  boundary: bool,  singular: bool,  random: list<array{label:string,group:string,columns:list<string>}>,  formula: string,  response: string,  columns: list<string>,  terms: list<string>,  assign: list<int>,  intercept: bool,  named: array<string,float>,  predvars: array{levels:array<string,list<string>>,poly:array<string,array{alpha:list<float>,norm2:list<float>}>},}

Errors Exception: a code from 1001 to 1008 for an input or statistical error; 1007 for an unsupported function, family, or random term.

See also Details

Matrix models

`fit_mixed_gaussian_matrix()`

Fits a Gaussian mixed model on a numeric design with explicit random terms, like lme4::lmer().

Fits by ML unless reml is true.
An intercept column is prepended unless intercept is false, in which case x is used exactly.
Rows with null or NAN in x, y, or another aligned input are dropped with one warning; missing: 'raise' rejects them instead. retained_rows and dropped_rows give the original row positions.

Phit\fit_mixed_gaussian_matrix(    array $x,    array $y,    array $random,    string $missing = 'drop',    bool $reml = false,    ?array $weights = NULL,    ?array $offset = NULL,    ?array $start = NULL,    int $maxEvaluations = 20000,    float $tolerance = 1.0E-7,    string $optimizer = 'bobyqa',    float $objectiveTolerance = 1.0E-12,    bool $intercept = true,): MixedGaussianFit

Parameter	Type	Default	Description
`$x`	`array`	required	Predictor matrix: one row per observation and one numeric column per predictor; `null` or `NAN` is missing
`$y`	`array`	required	Numeric response, one value per row; `null` or `NAN` is missing
`$random`	`array`	required	Random terms, each an array with `'z'` (n × k design), `'groups'` (one label per row), and optional `'correlated'` (default `true`; `false` is (x \|\| g))
`$missing`	`string`	`'drop'`	`'drop'` removes rows with `null` or `NAN` in any variable the model uses and warns once; `'raise'` rejects them
`$reml`	`bool`	`false`	`true` for REML, `false` for ML
`$weights`	`?array`	`NULL`	Positive prior weights aligned with the rows
`$offset`	`?array`	`NULL`	Known part of the linear predictor, aligned with the rows; `null` is zero
`$start`	`?array`	`NULL`	Starting relative covariance factors, in the units of the random columns; `null` starts diagonal factors at one and off-diagonals at zero
`$maxEvaluations`	`int`	`20000`	Largest number of optimizer evaluations
`$tolerance`	`float`	`1.0E-7`	BOBYQA final trust-region radius, in (0, 0.1]
`$optimizer`	`string`	`'bobyqa'`	`'bobyqa'` or `'nelder_mead'`
`$objectiveTolerance`	`float`	`1.0E-12`	Nelder–Mead stopping tolerance: the standard deviation of the simplex objective values
`$intercept`	`bool`	`true`	False uses x exactly (including any caller-supplied ones).

Returns

MixedGaussianFit A fit object, read like this array:array{  model: 'linear'|'generalized_linear'|'mixed_gaussian'|'mixed_logistic',  coefficients: list<float>,  covariance: list<list<float>>,  std_errors: list<float>,  p_values: list<float>,  conf_int: list<array{float,float}>,  fitted: list<float>,  residuals: list<float>,  log_likelihood: float,  df_residual: int,  diagnostics: array{converged:bool,solver:string,warnings:list<string>,iterations?:int,evaluations?:int,gradient_max?:float,boundary?:bool,singular?:bool},  n_input: int,  n_observations: int,  n_dropped: int,  retained_rows: list<int>,  dropped_rows: list<int>,  z_statistics: list<float>,  fixed_fitted: list<float>,  marginal_residuals: list<float>,  aic: float,  residual_variance: float,  sigma: float,  method: string,  converged: bool,  n_parameters: int,  bic: float,  theta: list<float>,  singular: bool,  optimizer: string,  optimizer_implementation: string,  evaluations: int,  random: list<array{covariance:list<list<float>>,effects:list<list<float>>,effects_cond_var:list<list<list<float>>>,group_labels:list<int|string>,group_sizes:list<int>}>,}

Errors Exception: a code from 1001 to 1008 for an input or statistical error.

See also Details

`fit_mixed_gaussian_intercept_matrix()`

Fits a Gaussian model with one random intercept by ML on a numeric design.

Has no random slopes, additional grouping terms, offsets, weights, or REML; use fit_mixed_gaussian_matrix() for those.
An intercept column is prepended unless intercept is false, in which case x is used exactly.
Rows with null or NAN in x, y, or another aligned input are dropped with one warning; missing: 'raise' rejects them instead. retained_rows and dropped_rows give the original row positions.

Phit\fit_mixed_gaussian_intercept_matrix(    array $x,    array $y,    array $groups,    string $missing = 'drop',    bool $intercept = true,): MixedGaussianFit

Parameter	Type	Default	Description
`$x`	`array`	required	Predictor matrix: one row per observation and one numeric column per predictor; `null` or `NAN` is missing
`$y`	`array`	required	Numeric response, one value per row; `null` or `NAN` is missing
`$groups`	`array`	required	Group label per row, an integer or a string; integer 1 and string “1” are different groups
`$missing`	`string`	`'drop'`	`'drop'` removes rows with `null` or `NAN` in any variable the model uses and warns once; `'raise'` rejects them
`$intercept`	`bool`	`true`	False uses x exactly (including any caller-supplied ones).

Returns

MixedGaussianFit A fit object, read like this array:array{  model: 'linear'|'generalized_linear'|'mixed_gaussian'|'mixed_logistic',  coefficients: list<float>,  covariance: list<list<float>>,  std_errors: list<float>,  p_values: list<float>,  conf_int: list<array{float,float}>,  fitted: list<float>,  residuals: list<float>,  log_likelihood: float,  df_residual: int,  diagnostics: array{converged:bool,solver:string,warnings:list<string>,iterations?:int,evaluations?:int,gradient_max?:float,boundary?:bool,singular?:bool},  n_input: int,  n_observations: int,  n_dropped: int,  retained_rows: list<int>,  dropped_rows: list<int>,  z_statistics: list<float>,  fixed_fitted: list<float>,  marginal_residuals: list<float>,  aic: float,  residual_variance: float,  sigma: float,  method: string,  converged: bool,  group_labels: list<int|string>,  group_sizes: list<int>,  random_effects: list<float>,  random_effects_cond_var: list<float>,  evaluations: int,  n_groups: int,  random_intercept_variance: float,  icc: float,  boundary: bool,}

Errors Exception: a code from 1001 to 1008 for an input or statistical error.

See also Details

`fit_mixed_logistic_matrix()`

Fits a binomial logit model with one random intercept on a numeric design, like lme4::glmer(family = binomial).

Uses the Laplace approximation by default, and adaptive quadrature when quadraturePoints is above 1.
An intercept column is prepended unless intercept is false, in which case x is used exactly.
Rows with null or NAN in x, y, or another aligned input are dropped with one warning; missing: 'raise' rejects them instead. retained_rows and dropped_rows give the original row positions.

Phit\fit_mixed_logistic_matrix(    array $x,    array $y,    array $groups,    string $missing = 'drop',    ?array $weights = NULL,    ?array $offset = NULL,    int $quadraturePoints = 1,    int $maxEvaluations = 20000,    float $tolerance = 1.0E-7,    bool $intercept = true,): MixedLogisticFit

Parameter	Type	Default	Description
`$x`	`array`	required	Predictor matrix: one row per observation and one numeric column per predictor; `null` or `NAN` is missing
`$y`	`array`	required	0/1 outcomes, or proportions with integer trial weights; `null` or `NAN` is missing
`$groups`	`array`	required	Group label per row, an integer or a string; integer 1 and string “1” are different groups
`$missing`	`string`	`'drop'`	`'drop'` removes rows with `null` or `NAN` in any variable the model uses and warns once; `'raise'` rejects them
`$weights`	`?array`	`NULL`	Positive integer trial counts, at most 1,000,000 per row; `null` is one trial per row
`$offset`	`?array`	`NULL`	Known part of the linear predictor, aligned with the rows; `null` is zero
`$quadraturePoints`	`int`	`1`	1 for the Laplace approximation, or 2 to 61 for adaptive Gauss–Hermite quadrature
`$maxEvaluations`	`int`	`20000`	Largest number of optimizer evaluations
`$tolerance`	`float`	`1.0E-7`	BOBYQA final trust-region radius, in (0, 0.1]
`$intercept`	`bool`	`true`	False uses x exactly (including any caller-supplied ones).

Returns

MixedLogisticFit A fit object, read like this array:array{  model: 'linear'|'generalized_linear'|'mixed_gaussian'|'mixed_logistic',  coefficients: list<float>,  covariance: list<list<float>>,  std_errors: list<float>,  p_values: list<float>,  conf_int: list<array{float,float}>,  fitted: list<float>,  residuals: list<float>,  log_likelihood: float,  df_residual: int,  diagnostics: array{converged:bool,solver:string,warnings:list<string>,iterations?:int,evaluations?:int,gradient_max?:float,boundary?:bool,singular?:bool},  n_input: int,  n_observations: int,  n_dropped: int,  retained_rows: list<int>,  dropped_rows: list<int>,  z_statistics: list<float>,  fixed_fitted: list<float>,  linear_predictor: list<float>,  aic: float,  bic: float,  n_parameters: int,  group_labels: list<int|string>,  group_sizes: list<int>,  random_effects: list<float>,  random_effects_cond_var: list<float>,  n_groups: int,  random_intercept_sd: float,  random_intercept_variance: float,  neg2_log_likelihood: float,  quadrature_points: int,  integration: string,  method: string,  family: string,  link: string,  optimizer: string,  converged: bool,  evaluations: int,  gradient_max: float,  boundary: bool,  singular: bool,}

Errors Exception: a code from 1001 to 1008 for an input or statistical error.

See also Details