  We propose an L1-penalized algorithm for fitting high-dimensional generalized
linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as
an extension of generalized linear models for clustered observations. This
Lasso-type approach for GLMMs should be mainly used as variable screening
method to reduce the number of variables below the sample size. We then suggest
a refitting by maximum likelihood based on the selected variables only. This is
an effective correction to overcome problems stemming from the variable
screening procedure which are more severe with GLMMs. We illustrate the
performance of our algorithm on simulated as well as on real data examples.
Supplemental materials are available online and the algorithm is implemented in
the R package glmmixedlasso.
