  This article describes a full Bayesian treatment for simultaneous
fixed-effect selection and parameter estimation in high-dimensional generalized
linear mixed models. The approach consists of using a Bayesian adaptive Lasso
penalty for signal-level adaptive shrinkage and a fast Variational Bayes scheme
for estimating the posterior mode of the coefficients. The proposed approach
offers several advantages over the existing methods, for example, the adaptive
shrinkage parameters are automatically incorporated, no Laplace approximation
step is required to integrate out the random effects. The performance of our
approach is illustrated on several simulated and real data examples. The
algorithm is implemented in the R package glmmvb and is made available online.
