Moment-Based Selection of Multiresponse Linear Mixed-Effects Models

We propose MOMENT ($\mathbf{\text{MO}}$ment-Based $\mathbf{\text{M}}$ixed-$\mathbf{\text{E}}$ffects Selectio$\mathbf{\text{N}}$ and Es$\mathbf{\text{T}}$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.