Fit a mixed model to a Polars table and chart it · phit

Read a CSV file with Polars, fit reaction time with a random intercept for each subject, and chart each subject’s fitted line with phiz.

The example needs the phpolars extension (phpolars installation) and phiz (composer require phpstats/phiz). phit can be the extension or the plain-PHP polyfill (Extension or polyfill). Runnable script

The data are sleepstudy: average reaction time in milliseconds per day for 18 subjects in a sleep-deprivation study, days 0 to 9. Polars reads the file by URL.

Code

use Phiz\Plot;use function Phit\{fit_mixed_gaussian, summary};use function Phpolars\scan_csv;$data = scan_csv(    'https://raw.githubusercontent.com/phpstats/datasets/main/csv/sleepstudy.csv',)    ->select(['Reaction', 'Days', 'Subject'])    ->collect()    ->toColumns();// A random intercept per subject, fitted by REML.$fit = fit_mixed_gaussian(    'Reaction ~ Days + (1 | Subject)',    $data,);$data['fitted'] = $fit['fitted'];echo summary($fit);// Each subject's days as points, and one fitted line per subject.$chart = Plot::of($data)    ->aes(x: 'Days', y: 'Reaction')    ->point(alpha: 0.4)    ->line(        aes: ['y' => 'fitted', 'group' => 'Subject'],        alpha: 0.6,    )    ->labs(x: 'Days of sleep deprivation', y: 'Reaction time (ms)')    ->theme(baseSize: 15)    ->size('container', 380);file_put_contents(    'sleepstudy.html',    $chart->html('Reaction time by subject'),);

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

Interpretation

toColumns() converts the Polars result to PHP arrays once for use by phit and phiz.
The Days coefficient is the average change in reaction time per additional day of sleep deprivation.
fitted holds conditional fitted values, which include each subject’s predicted intercept. fixed_fitted leaves them out.
The model gives every subject the same slope, so the fitted lines are parallel. The points show that the slopes differ between subjects; (Days | Subject) fits a random slope as well.

See also: Fit a mixed model for reading the variance components and subject effects · Mixed models for the supported structures · phpolars’ Getting started · phiz’s Get started