The use of the EM algorithm for regularization problems in high-dimensional linear mixed-effects models

TL;DR

This paper introduces EMLMLasso, an EM algorithm-based method for regularization in high-dimensional linear mixed-effects models, demonstrating superior performance over existing methods in simulations and real data.

Contribution

The paper presents a novel EM algorithm combined with glmnet for variable selection in high-dimensional linear mixed-effects models, outperforming existing methods.

Findings

EMLMLasso outperforms glmmLasso in simulations and real data

The method shows good properties like consistency and effectiveness

Applicable for both p < n and p > n scenarios

Abstract

The EM algorithm is a popular tool for maximum likelihood estimation but has not been used much for high-dimensional regularization problems in linear mixed-effects models. In this paper, we introduce the EMLMLasso algorithm, which combines the EM algorithm and the popular and efficient R package glmnet for Lasso variable selection of fixed effects in linear mixed-effects models. We compare the performance of our proposed EMLMLasso algorithm with the one implemented in the well-known R package glmmLasso through the analyses of both simulated and real-world applications. The simulations and applications demonstrated good properties, such as consistency, and the effectiveness of the proposed variable selection procedure, for both $p < n$ and $p > n$. Moreover, in all evaluated scenarios, the EMLMLasso algorithm outperformed glmmLasso. The proposed method is quite general and can be easily extended for ridge and elastic net penalties in linear mixed-effects models.