# Moment-Based Selection of Multiresponse Linear Mixed-Effects Models

arXiv: https://arxiv.org/abs/2607.01971 · HTML: https://mlsanity.com/paper/2607.01971/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 49 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Builds on (most cited first, 2 of 2)

- [Scalable Subset Selection in Linear Mixed Models](https://mlsanity.com/paper/2506.20425/) (2025)
- [Sparse Positive-Definite Estimation for Covariance Matrices with Repeated Measurements](https://mlsanity.com/paper/2304.08020/) (2023)

## Abstract (arXiv)

We propose MOMENT (MOment-Based Mixed-Effects SelectioN and EsTimation), 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.