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

The expectation-maximization (EM) algorithm is a popular tool for maximum likelihood estimation, but its use in high-dimensional regularization problems in linear mixed-effects models has been limited. In this article, we introduce the EMLMLasso algorithm, which combines the EM algorithm with the popular and efficient R package glmnet for Lasso variable selection of fixed effects in linear mixed-effects models and allows for automatic selection of the tuning parameter. A comprehensive performance evaluation is conducted, comparing the proposed EMLMLasso algorithm against two existing algorithms implemented in the R packages glmmLasso and splmm . In both simulated and real-world applications analyzed, our algorithm showed robustness and effectiveness in variable selection, including cases where the number of predictors ( p ) is greater than the number of independent observations ( n ) . In most evaluated scenarios, the EMLMLasso algorithm consistently outperformed both glmmLasso and splmm . The proposed method is quite general and simple to implement, allowing for extensions based on ridge and elastic net penalties in linear mixed-effects models.