mixedlm

A Python implementation of mixed-effects models inspired by R's lme4 package. Features a Rust backend for performance-critical operations and native support for both pandas and polars DataFrames.

Documentation | PyPI | Changelog

Features

• Linear Mixed Models (LMM) via lmer() - REML and ML estimation
• Generalized Linear Mixed Models (GLMM) via glmer() - Laplace approximation and adaptive Gauss-Hermite quadrature
• Nonlinear Mixed Models (NLMM) via nlmer() - Self-starting models (SSasymp, SSlogis, SSmicmen, and more) and custom nonlinear functions
• Formula interface - lme4-style formulas with random effects syntax
• Tidy reporting - Analysis-ready coefficient, random-effect, and model-fit tables
• Inference tools - Linear hypotheses, profile likelihood, bootstrap, confidence intervals, Satterthwaite/Kenward-Roger degrees of freedom
• Model comparison - ANOVA (including Type III), drop1, allFit
• Model selection - AIC/AICc/BIC rankings, normalized weights, and evidence sets
• Model validation - Case-level, whole-group, and custom-partition cross-validation with weighted scoring and leakage checks
• Prediction uncertainty - Conditional LMM and GLMM mean intervals with joint fixed/random-effect covariance and prior variance for new groups
• Power analysis - powerSim, powerCurve for sample size planning
• Diagnostics - Dispersion and zero-inflation checks, influence measures, Cook's distance, leverage, VIF/GVIF, condition indices
• Fit metrics - Nakagawa marginal/conditional R² and adjusted/unadjusted ICC
• Fast startup - Public objects are loaded on demand, so lightweight imports avoid the modeling stack

Installation

pip install mixedlm

mixedlm requires Python >= 3.10, NumPy >= 1.23.5, SciPy >= 1.14, and pandas >= 1.4. Optional extras add polars input (mixedlm[polars]), plotting with matplotlib (mixedlm[plots]), and nlopt optimizers (mixedlm[optimizers]). Building from source requires a Rust toolchain; see the installation guide.

Quick Start

import mixedlm as mlm

# Random intercept and slope for each subject
data = mlm.load_sleepstudy()
result = mlm.lmer("Reaction ~ Days + (Days | Subject)", data)
print(result.summary())  # Includes p-values via Satterthwaite DF

result.fixef()               # Fixed effects
result.ranef()               # Random effects (BLUPs)
result.VarCorr()             # Variance components
result.tidy(conf_int=True)   # Analysis-ready pandas table

# Binomial GLMM with successes / trials responses
cbpp = mlm.load_cbpp()
gm = mlm.glmer(
    "incidence / size ~ period + (1 | herd)", cbpp, family=mlm.families.Binomial()
)
print(gm.summary())

Documentation

• Quickstart and Coming from R
• Tutorials for LMMs, GLMMs, NLMMs, inference, and power analysis
• API reference
• Contributing, including development setup and CI
• Changelog

License

The mixedlm code uses the MIT License; see LICENSE. The bundled lme4 datasets retain their upstream GPL (>= 2) license, with attribution and license text in datasets/data.

Acknowledgments

This package is inspired by and aims to be compatible with R's lme4 package by Douglas Bates, Martin Maechler, Ben Bolker, and Steve Walker.