Moment-Based Selection of Multiresponse Linear Mixed-Effects Models

2026-07-02

AI Summary

This work addresses the joint selection and estimation of random-effect covariance matrices and fixed-effect coefficients in multivariate linear mixed-effects models by proposing the MOMENT framework. Leveraging second-order cross-moment identities, MOMENT identifies and estimates random and fixed effects in stages, imposing diagonal-induced sparsity on the covariance matrix under a positive semidefinite constraint, thereby casting the problem as a smooth constrained convex optimization. As the first moment-based approach enabling joint variable selection in multivariate mixed models, MOMENT establishes finite-sample selection consistency under joint sub-Weibull errors. Empirical results demonstrate its superior performance over univariate analyses in settings with correlated responses, and its application to hemodialysis data highlights strong interpretability and flexibility.

Abstract

We propose MOMENT (\textbf{MO}ment-Based \textbf{M}ixed-\textbf{E}ffects Selectio\textbf{N} and Es\textbf{T}imation), a stage-wise moment-based framework that exploits second-order cross-moment identities to select and estimate the random-effects covariance matrix and fixed-effects coefficients. By inducing sparsity through its diagonal under a positive semidefinite constraint, the random-effects selection problem reduces to a smooth constrained convex optimization problem that can be solved efficiently by projected gradient descent. We further establish finite-sample theoretical guarantees for the proposed procedure, including random-effects selection consistency and fixed-effects selection consistency under joint sub-Weibull errors. Simulation studies show that MOMENT performs competitively overall and can substantially outperform separate univariate analyses when responses are correlated. An application to the hemodialysis dataset demonstrates that the proposed method yields an interpretable and flexible approach for multivariate longitudinal data.

Problem

• multiresponse
• linear mixed-effects models
• random-effects selection
• fixed-effects selection
• covariance matrix

Innovation

• moment-based selection
• mixed-effects models
• convex optimization
• selection consistency
• multivariate longitudinal data