interlace: Closing the Mixed-Effects Modelling Gap in Python

Helio Pais${}^a$

${}^a$The StepStone Group

Mixed-effects models are central to applied statistics, yet Python’s ecosystem for fitting them remains limited compared to R. The most widely used Python option, statsmodels’ MixedLM [3], cannot accommodate crossed random effects and offers no influence diagnostics beyond residuals. Practitioners who need these capabilities must either bridge to R via rpy2 (incurring computational overhead) or turn to Bayesian frameworks whose cost can be orders of magnitude higher. This leaves a large class of routine mixed-model analyses inaccessible from a Python workflow.

We present interlace, an open-source Python library for mixed-effects modelling. interlace implements profiled restricted maximum likelihood (REML) estimation with sparse Cholesky factorisation—the same algorithmic strategy underlying R’s lme4 [1]—and supports both crossed and nested random intercepts and slopes through a formula interface. Beyond point estimation, the library provides estimated marginal means, Type I–III ANOVA tables, profile likelihood confidence intervals, parametric bootstrap, and group-level cross-validation—none of which are available together in any existing Python package.

interlace also provides regression diagnostics for hierarchical models: leverage, Cook’s distance, MDFFITS, and COVTRACE at both the observation and group level, mirroring R’s HLMdiag package [2]. These measures allow practitioners to assess the influence of individual observations and clusters on fixed-effect estimates and variance components—functionality that has been largely absent from the Python ecosystem.

Systematic benchmarks against lme4 confirm numerical parity: fixed-effect estimates agree within ${10}^{-4}$. Computationally, interlace is competitive with or faster than lme4 on problems involving nested random effects (approximately $8\times$ faster at ${10}^6$ observations) and operates within the same order of magnitude as fixest [4] on high-dimensional fixed-effects specifications. interlace is available on PyPI and GitHub under a BSD-3 licence.

Keywords: Mixed-effects models, REML estimation, regression diagnostics.