Feature comparison¶

This page compares interlace with statsmodels.MixedLM (Python), linearmodels.RandomEffects (Python), and lme4::lmer() (R) across the features that most often determine library choice.

At a glance¶

Feature	interlace	statsmodels MixedLM	linearmodels RE	lme4 (R)
Random effect structures
Single random intercept	✓	✓	One-way entity⁴	✓
Crossed random intercepts	✓	Workaround¹	✗	✓
Nested random effects	✓ (v0.2.4+)	✓	✗	✓
Random slopes	✓ (v0.2.1+)	✓	✗	✓
Correlated random effects	✓ (v0.2.1+)	✓	✗	✓
Generalised LMM (10+ families)	✓ (`glmer`)	✗²	✗	✓ (`glmer`)
Ordinal mixed models (CLMM)	✓ (`clmm`)	✗	✗	Via `ordinal`
Cox frailty (survival)	✓ (`coxme`)	✗	✗	Via `coxme`
Residual correlation (AR1, CS)	✓ (v0.3.0+)	✗	✗	Via `nlme`
Estimation
REML (default)	✓	✓	✗ (Swamy-Arora⁵)	✓
ML (for LRT / model comparison)	✓	✓	✗	✓
Profiled REML	✓	✗	✗	✓
IV / 2SLS fixed-effects estimator	✗	✗	✓	✗
Cluster-robust / HAC standard errors	✗	✗	✓ (4 types)	✗
Optimizers
Default optimizer	L-BFGS-B	L-BFGS-B	Closed form	BOBYQA
BOBYQA (gradient-free)	✓ (optional extra)	✗	—	✓
Sparse Cholesky	✓ (optional extra)	✗	—	✓ (always)
Formula syntax
Wilkinson formula for fixed effects	✓	✓	✓ (formulaic)	✓
Grouping via `groups=` argument	✓	✓	Multi-index DF	—
lme4 `(1\|g)` notation	✓ (`random=`)	✗	✗	✓
Diagnostics
Residuals (marginal + conditional)	✓	Marginal only	Residuals only	Via HLMdiag
Leverage decomposition (H1/H2)	✓	✗	✗	Via HLMdiag
Cook’s distance	✓	✗	✗	Via HLMdiag
MDFFITS	✓	✗	✗	Via HLMdiag
COVTRACE / COVRATIO	✓	✗	✗	Via HLMdiag
Relative variance change (RVC)	✓	✗	✗	Via HLMdiag
Augmented data frame	✓ (`hlm_augment`)	✗	✗	Via HLMdiag
Cluster-bootstrap SE	✓	✗	✗	Via `bootMer`
Output
Fixed-effect coefficients	✓	✓	✓	✓
Variance components	✓	✓	✗ (θ only)	✓
BLUPs / conditional modes	✓	✓	✗	✓
Estimated marginal means (`emmeans`)	✓ (v0.2.8+)	✗	✗	Via `emmeans`
Satterthwaite DFs	✓	✗	✗	Via `lmerTest`
Kenward-Roger DFs	✓ (v0.3.0+)	✗	✗	Via `lmerTest`/`pbkrtest`
AIC / BIC	✓	✓	✓	✓
Numerical parity with lme4	✓³	✗	✗	—
Language	Python	Python	Python	R

¹ See statsmodels workaround below. ² statsmodels has separate GLM support; mixed GLMs require a different approach. ³ Fixed effects within 1e-4 (absolute); variance components within 5% (relative) on standard benchmarks. ⁴ One-way entity-level random intercept only, using the Swamy-Arora estimator. Requires a multi-index (entity, time) DataFrame. ⁵ Uses a method-of-moments estimator, not ML or REML. Variance component is not directly comparable to lme4/interlace output.

Notes on key rows¶

Crossed random effects — statsmodels workaround¶

statsmodels.MixedLM accepts only a single grouping column. To approximate crossed random effects you must pass the whole dataset as one group and add variance components via vc_formula. This is documented in the statsmodels manual but produces estimates that are not numerically equivalent to lme4 REML — particularly in unbalanced designs. See For Python / statsmodels users for a worked example.

Profiled REML¶

In profiled REML, the fixed effects are eliminated analytically so the optimiser only searches over variance parameters. This reduces the dimension of the search space and produces tighter convergence. Both interlace and lme4 use this parameterisation. statsmodels.MixedLM optimises over all parameters jointly.

Optimizers¶

interlace defaults to scipy’s L-BFGS-B. BOBYQA (gradient-free, matches lme4’s default) is available via pip install "interlace-lme[bobyqa]". BOBYQA is more robust near variance-component boundaries and gives closer numerical parity with lme4. See FAQ: Optimizer choice.

Sparse Cholesky¶

lme4 always uses Eigen’s sparse Cholesky factorisation. interlace ships a dense path by default and a sparse path when scikit-sparse is installed (pip install "interlace-lme[cholmod]"). For small-to-medium models the dense path is fast enough; for models with thousands of group levels the sparse path can be substantially faster. See FAQ: Solver choice.

linearmodels — panel econometrics, not LMM¶

linearmodels is a panel-data and instrumental-variables econometrics library, not a general-purpose linear mixed model package. The distinction matters:

Dimension	interlace	linearmodels
Data structure	Flat DataFrame with grouping columns	Multi-index (entity, time) DataFrame
Random effect	Crossed/nested intercepts and slopes via REML	One-way entity intercept (Swamy-Arora)
Estimation	Profiled REML or ML	Closed-form moments estimator
Primary use cases	Psycholinguistics, social science, medicine	Macroeconomics, finance, policy evaluation
IV / 2SLS	✗	✓ (`IV2SLS`, `IVLIML`, `IVGMM`)
System estimators	✗	✓ (`SUR`, `IV3SLS`)
Clustered / HAC SEs	✗	✓ (4 covariance types)

Use linearmodels.RandomEffects when:

Your data has a two-dimensional panel structure (entities × time periods).
You need IV/2SLS or system estimators alongside the RE model.
You need cluster-robust or Driscoll-Kraay HAC standard errors.
The econometric one-way RE assumption (individual effect uncorrelated with regressors) is acceptable.

Use interlace (or lme4) when:

Your data has crossed random effects (e.g. subjects × stimuli).
You need REML variance components that are numerically equivalent to lme4.
You need random slopes, nested designs, or profile-likelihood CIs on variance parameters.
You need a built-in diagnostics suite (Cook’s D, leverage, MDFFITS, …).

Diagnostics¶

lme4 has no built-in diagnostics — users rely on the R package HLMdiag (Loy & Hofmann, 2014). interlace bundles an equivalent suite directly so no additional package is needed. See For R / lme4 users for the function-by-function mapping.

Random slopes and nested designs¶

interlace supports random slopes (v0.2.1+) and nested random effects (v0.2.4+) via the random= parameter using lme4-style (term | group) notation. For generalised outcomes, use interlace.glmer(). For ordinal outcomes, use interlace.clmm(). For survival data, use interlace.coxme().

When to use each¶

Situation	Recommended library
Crossed random intercepts in Python	interlace
Need lme4 numerical parity from Python	interlace
Need built-in diagnostics in Python	interlace
Random slopes or nested designs in Python	interlace (v0.2.1+ / v0.2.4+) or statsmodels MixedLM
One-way entity RE with panel (entity × time) data	linearmodels
Need IV/2SLS, SUR, or IV3SLS alongside RE	linearmodels
Need clustered or Driscoll-Kraay HAC SEs	linearmodels
GLMM (Poisson, binomial, Beta, …) in Python	interlace (`glmer()`)
Ordinal regression with random effects in Python	interlace (`clmm()`)
Survival with frailty in Python	interlace (`coxme()`)
Longitudinal data with AR(1)/CS correlation	interlace (`fit(correlation=...)`)
Full lme4 feature set	lme4 (R)