  We consider linear mixed models in which the observations are grouped. A
L1-penalization on the fixed effects coefficients of the log-likelihood
obtained by considering the random effects as missing values is proposed. A
multicycle ECM algorithm is used to solve the optimization problem; it can be
combined with any variable selection method developed for linear models. The
algorithm allows the number of parameters p to be larger than the total number
of observations n; it is faster than the lmmLasso (Schelldorfer,2011) since no
n*n matrix has to be inverted. We show that the theoretical results of
Schelldorfer (2011) apply for our method when the variances of both the random
effects and the residuals are known. The combination of the algorithm with a
variable selection method (Rohart 2011) shows good results in estimating the
set of relevant fixed effects coefficients as well as estimating the variances;
it outperforms the lmmLasso both in the common case (p< n) and in the
high-dimensional case (p > n).
