Multivariate mixed models with model-free random effects

TL;DR

This paper introduces a robust testing method for fixed effects in multivariate linear mixed models that does not rely on correct random-effects distribution or Fisher information estimation, improving reliability under model misspecification.

Contribution

It proposes a novel, model-free testing procedure combining score statistics with sign-flipping, accommodating dependence structures and ensuring valid inference with weak assumptions.

Findings

Method avoids Fisher information estimation and distributional assumptions.

Provides asymptotically valid inference under model misspecification.

Handles both within-cluster and between-response dependence effectively.

Abstract

Linear mixed models are widely used to analyze non-independent data, but inference for fixed effects can be unreliable under misspecification of the random-effects distribution, inaccurate Fisher information estimation, or convergence failures, leading to a lack of control over false positives. These difficulties are amplified in multivariate settings, where within-cluster and between-response dependence must be modeled jointly. We propose a testing procedure for fixed effects in multivariate linear mixed models that avoids Fisher information estimation and does not require correct specification of the random-effects distribution by combining score statistics with clusterwise sign-flipping transformations. Our method accommodates both forms of dependence and yields asymptotically valid inference under weak distributional assumptions on the data-generating process.