Multivariate mixed models with model-free random effects

Angela Andreella; Livio Finos

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arXiv · 2604.27907

Multivariate mixed models with model-free random effects

Angela Andreella·Livio Finos

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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.

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Angela Andreella, Livio Finos. 2026-04-30. Multivariate mixed models with model-free random effects. https://arxiv.org/abs/2604.27907

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