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The EM algorithm is a popular tool for maximum likelihood estimation but hasnot been used much for high-dimensional regularization problems in linearmixed-effects models. In this paper, we introduce the EMLMLasso algorithm,which combines the EM algorithm and the popular and efficient R package glmnetfor Lasso variable selection of fixed effects in linear mixed-effects models.We compare the performance of our proposed EMLMLasso algorithm with the oneimplemented in the well-known R package glmmLasso through the analyses of bothsimulated and real-world applications. The simulations and applicationsdemonstrated good properties, such as consistency, and the effectiveness of theproposed variable selection procedure, for both $p < n$ and $p > n$. Moreover,in all evaluated scenarios, the EMLMLasso algorithm outperformed glmmLasso. Theproposed method is quite general and can be easily extended for ridge andelastic net penalties in linear mixed-effects models.

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