Variable selection in linear mixed effects models

TL;DR

This paper introduces nonconcave penalized profile likelihood methods for fixed and random effects selection in linear mixed effects models, achieving model selection consistency even with exponentially growing parameters.

Contribution

It proposes a novel proxy matrix approach for selecting fixed and random effects, ensuring consistency and asymptotic identification in high-dimensional settings.

Findings

Method achieves model selection consistency.

Effective in high-dimensional scenarios with exponential growth.

Validated through simulations and real data.

Abstract

This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed effects. To overcome the difficulty of unknown covariance matrix of random effects, we propose to use a proxy matrix in the penalized profile likelihood. We establish conditions on the choice of the proxy matrix and show that the proposed procedure enjoys the model selection consistency where the number of fixed effects is allowed to grow exponentially with the sample size. We further propose a group variable selection strategy to simultaneously select and estimate important random effects, where the unknown covariance matrix of random effects is replaced with a proxy matrix. We prove that, with the proxy matrix appropriately chosen, the proposed procedure can identify all true random effects with asymptotic probability one, where the dimension of random effects vector is allowed to increase exponentially with the sample size. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. We further illustrate the proposed procedures via a real data example.