interlace

Documentation

Pure-Python mixed-effects modelling library — linear (LMM), generalised (GLMM), ordinal (CLMM), and survival (Cox frailty) — validated against R's lme4, glmer, ordinal, and coxme.

Designed as a drop-in replacement for statsmodels.MixedLM in diagnostics pipelines that require crossed grouping factors (e.g. (1|worker) + (1|company)), which statsmodels does not support.

Installation

pip install interlace-lme

Requires Python ≥ 3.13.

Quick start

import pandas as pd
from interlace import fit

result = fit(
    formula="score ~ hours_studied + prior_gpa",
    data=df,
    groups=["student_id", "school_id"],   # crossed random intercepts
)

print(result.fe_params)          # fixed-effect coefficients
print(result.variance_components) # per-factor variance components
print(result.scale)              # residual variance σ²

groups accepts a single string (one random intercept) or a list (crossed intercepts). The first entry is the primary grouping factor.

Model types

Linear mixed models (LMM)

from interlace import fit

result = fit(
    formula="score ~ hours_studied + prior_gpa",
    data=df,
    groups=["student_id", "school_id"],
    method="REML",           # or "ML" for likelihood-ratio tests
    df_method="satterthwaite", # or "kenward-roger"
)

Supports crossed and nested random intercepts, random slopes ((1 + x | g)), observation-level weights, AR(1) and compound-symmetry residual correlation structures, and Satterthwaite or Kenward-Roger denominator degrees of freedom.

Generalised linear mixed models (GLMM)

from interlace import glmer

result = glmer(
    formula="incidence / size ~ period",
    data=df,
    family="binomial",       # or "poisson", "gaussian", "negativebinomial"
    groups="herd",
    weights=df["size"].values,
)

Families: binomial, Poisson, Gaussian, NB1, NB2, Beta, Gamma, zero-inflated Poisson/NB2, hurdle Poisson, zero-one-inflated Beta. Supports Laplace approximation and adaptive Gauss-Hermite quadrature.

Cumulative link mixed models (CLMM)

from interlace import clmm

result = clmm(
    formula="rating ~ condition",
    data=df,
    groups="subject",
)

Ordinal regression with random effects, matching R's ordinal::clmm().

Cox frailty models

from interlace import coxme

result = coxme(
    formula="Surv(time, event) ~ treatment + age",
    data=df,
    groups="centre",
)

Cox proportional hazards with Gaussian frailty, matching R's coxme::coxme().

Diagnostics

from interlace import hlm_resid, leverage, hlm_influence, hlm_augment

resid_df = hlm_resid(result, type="conditional")  # or "marginal"
lev = leverage(result)                              # hat-matrix diagonal
infl = hlm_influence(result, level=1)               # Cook's D, MDFFITS, etc.
aug = hlm_augment(result)                           # data + residuals + influence

# Plotting (all return plotnine.ggplot objects)
from interlace import plot_resid, plot_influence, dotplot_diag

plot_resid(resid_df, type="resid_vs_fitted")
plot_influence(infl, measure="cooks_d")
dotplot_diag(infl, variable="cooks_d", cutoff="internal")

statsmodels compatibility

CrossedLMEResult exposes the same interface as statsmodels.MixedLMResults so it can be used as a drop-in in downstream code that accesses fe_params, resid, scale, fittedvalues, random_effects, predict(), and model.exog / model.groups / model.data.frame.

hlm_resid, hlm_influence, and hlm_augment all accept either a CrossedLMEResult or a statsmodels MixedLMResults object.

Parity with R

Results are validated against R reference implementations to the following tolerances:

Model type	R reference	Fixed effects	Variance components
LMM	lme4::lmer()	abs diff < 1e-4	rel diff < 5%
GLMM	lme4::glmer()	abs diff < 1e-3	rel diff < 5%
CLMM	ordinal::clmm()	abs diff < 1e-3	rel diff < 5%
Cox frailty	coxme::coxme()	abs diff < 1e-3	rel diff < 10%
AR(1) / CS	nlme::lme()	abs diff < 1e-3	rel diff < 5%

Contributing

Bug reports, documentation fixes, and new features are welcome — see CONTRIBUTING.md for how to get started. To open an issue or ask a question, use the GitHub issue tracker.

Attribution

• lme4 — the reference implementation for mixed-effects models in R; interlace targets parity with lme4::lmer() and lme4::glmer().
• ordinal — R package for cumulative link models; interlace's clmm() targets parity with ordinal::clmm().
• coxme — R package for Cox models with random effects; interlace's coxme() targets parity with coxme::coxme().
• nlme — R package for linear mixed models with correlation structures; AR(1) and CS validation benchmarks.
• HLMdiag — the R package whose diagnostics API (hlm_resid, hlm_influence, hlm_augment, dotplot_diag) interlace replicates in Python.