Fit a mixed model · phit

Fit reaction time on days of sleep deprivation with a random intercept for each subject, then read the fixed effects, the variance components, and each subject’s estimated effect.

The data are sleepstudy: average reaction time per day for 18 subjects in a sleep-deprivation study, days 0 to 9. Reaction is in milliseconds. The example reads the file by URL with phibble (composer require phpstats/phibble) and runs with the phit extension or the plain-PHP polyfill (Extension or polyfill).

Code

use Phibble\DataFrame;use function Phit\fit_mixed_gaussian;$sleep = DataFrame::fromCsv(    'https://raw.githubusercontent.com/phpstats/datasets/main/csv/sleepstudy.csv',);$fit = fit_mixed_gaussian(    'Reaction ~ Days + (1 | Subject)',    $sleep,);echo $fit, "\n";echo $fit->tidy(effects: 'ran_vals'), "\n";

Output

Linear mixed model fit by REML
Formula: Reaction ~ Days + (1 | Subject)

REML criterion at convergence: 1786.5

Random effects:
Groups   Name        Variance Std.Dev.
Subject  (Intercept)   1378.2    37.12
Residual                960.5    30.99
Number of obs: 180, groups: Subject, 18

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)
(Intercept) 251.4051     9.7467   25.79   <2e-16
Days         10.4673     0.8042   13.02   <2e-16

     group level        term   estimate std_error
1  Subject   308 (Intercept)  40.783709  9.475668
2  Subject   309 (Intercept) -77.849553  9.475668
3  Subject   310 (Intercept) -63.108567  9.475668
4  Subject   330 (Intercept)   4.406442  9.475668
5  Subject   331 (Intercept)  10.216189  9.475668
6  Subject   332 (Intercept)   8.221238  9.475668
7  Subject   333 (Intercept)  16.500494  9.475668
8  Subject   334 (Intercept)  -2.996981  9.475668
9  Subject   335 (Intercept) -45.282127  9.475668
10 Subject   337 (Intercept)  72.182685  9.475668
11 Subject   349 (Intercept) -21.196249  9.475668
12 Subject   350 (Intercept)  14.111363  9.475668
13 Subject   351 (Intercept)  -7.862221  9.475668
14 Subject   352 (Intercept)  36.378425  9.475668
15 Subject   369 (Intercept)   7.036381  9.475668
16 Subject   370 (Intercept)  -6.362703  9.475668
17 Subject   371 (Intercept)  -3.294273  9.475668
18 Subject   372 (Intercept)  18.115747  9.475668

Interpretation

(1 | Subject) gives each subject an intercept of its own, assumed to come from a normal distribution. The fit uses REML, as lme4::lmer() does by default.
The Days coefficient is the average change in reaction time per additional day of sleep deprivation. The model gives every subject the same slope.
The Subject standard deviation (37.12) describes how baseline reaction times vary between subjects. The residual standard deviation (30.99) describes how each subject’s days vary around their own line.
$fit->tidy(effects: 'ran_vals') gives each subject’s predicted intercept relative to the average and its conditional standard error, as R’s ranef(condVar = TRUE) and broom.mixed report them. They are shrunk toward zero, more so for subjects with fewer observations. Every subject here has ten days, so their conditional standard errors are equal.
In these data the slopes also differ between subjects; (Days | Subject) fits a random slope as well. See Mixed models.

See also: Mixed models for the supported structures, the full result, singular fits, and fit_mixed_logistic()