Multivariate mixed models with model-free random effects

2026-04-30

AI Summary

This study addresses the unreliability of fixed-effect inference in multivariate linear mixed models, which often arises from misspecification of the random-effects distribution, bias in Fisher information estimation, or algorithmic non-convergence—issues exacerbated by simultaneous within-cluster and between-response dependencies. To overcome these limitations, this work proposes a robust testing procedure that neither requires specifying the random-effects distribution nor relies on Fisher information estimation. By integrating score statistics with cluster-level sign-flipping transformations, the method achieves asymptotically valid and efficient inference under weak distributional assumptions. Notably, it is the first approach to enable asymptotically efficient, distribution-free inference for fixed effects in multivariate mixed models, substantially improving control of type I error rates and overall inferential reliability.

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.

Problem

• multivariate linear mixed models
• fixed effects inference
• random-effects distribution misspecification
• false positive control
• within-cluster dependence

Innovation

• multivariate linear mixed models
• model-free random effects
• score statistics
• sign-flipping
• asymptotically valid inference