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This article describes a full Bayesian treatment for simultaneousfixed-effect selection and parameter estimation in high-dimensional generalizedlinear mixed models. The approach consists of using a Bayesian adaptive Lassopenalty for signal-level adaptive shrinkage and a fast Variational Bayes schemefor estimating the posterior mode of the coefficients. The proposed approachoffers several advantages over the existing methods, for example, the adaptiveshrinkage parameters are automatically incorporated, no Laplace approximationstep is required to integrate out the random effects. The performance of ourapproach is illustrated on several simulated and real data examples. Thealgorithm is implemented in the R package glmmvb and is made available online.

Bayesian Adaptive Lasso with Variational Bayes for Variable Selection in High-dimensional Generalized Linear Mixed Models