  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.
