glmm

glmm: mixed models from an R-style formula, with NumPy as the only dependency.

glmm fits mixed models in Rust, Python and R, and in the browser through WASM. One fit covers ordinary least squares, generalized linear models, linear mixed models and generalized linear mixed models.

• Accuracy first. Gives the same or a more accurate result than lme4, glmmTMB, MixedModels.jl and GLMMadaptive, and converges on every model that has a solution.
• Multi-solver. Uses a multi-solver paradigm to get the best result more robustly: closed form for least squares, IRLS for GLMs, and BFGS or BOBYQA for mixed models, all written from scratch in Rust.
• Fast. Faster than every other engine on every model, usually 10 to 100 times, without RAM blowup.

On all tested models: a 923-model validation grid, checked for every release.

Install

pip install glmm

Requires Python 3.10+. The only runtime dependency is NumPy.

Quick examples

df is any data table: a dict of columns, or a pandas / polars DataFrame.

import glmm

# OLS: fixed effects only
fit = glmm.fit(df, "y ~ x1 * x2")

# LMM: correlated random intercept and slope (REML)
fit = glmm.fit(df, "y ~ x1 + (1 + x1 | subject)")

# The same LMM by maximum likelihood, as lme4's REML = FALSE
fit_ml = glmm.fit(df, "y ~ x1 + (1 + x1 | subject)", reml=False)

# GLMM: binomial with a probit link, 7-node adaptive quadrature
fit = glmm.fit(df, "passed ~ x1 + (1 | school)", "binomial", link="probit", nagq=7)

fit.summary()                     # coefficient table + variance components
fit.beta, fit.se                  # estimates and standard errors
fit.coef_df, fit.confint()        # t-test df (Satterthwaite on an LMM), intervals
fit.converged, fit.singular       # result flags
glmm.anova(fit)                   # tests of the fixed terms (Type III)
glmm.compare(df, "y ~ x1", "y ~ x1 + (1 | subject)")  # two nested models, fitted and compared

Documentation

Full walkthrough — every knob, the Fit object, and warm starts: tutorial-python.md.

The algorithm map (dispatch graph, solver paths, tuning knobs) is traced to code in documentation/algorithms.md.

What the formula accepts: formula.md. Tests of fixed terms and model comparisons: hypothesis-tests.md. Fixes for common errors: troubleshooting.md.

Citation

If you use glmm in research, please cite:

Lenartowicz, P. (2026). glmm: Mixed-model fitting in Rust, Python and R [Computer software]. https://github.com/pawlenartowicz/glmm

@software{glmm2026,
  author = {Lenartowicz, Pawe{\l}},
  title  = {{glmm}: Mixed-Model Fitting in Rust, Python and R},
  year   = {2026},
  url    = {https://github.com/pawlenartowicz/glmm}
}

License

LGPL-3.0-or-later.

Paweł Lenartowicz — Freestyler Scientist · GitHub · ORCID