Bayesian variable selection for mixed effects model with shrinkage prior

Recently, many shrinkage priors have been proposed and studied in linear models to address massive regression problems. However, shrinkage priors are rarely used in mixed effects models. In this article, we address the problem of joint selection of both fixed effects and random effects with the use of several shrinkage priors in linear mixed models. The idea is to shrink small coefficients to zero while minimally shrink large coefficients due to the heavy tails. The shrinkage priors can be obtained via a scale mixture of normal distributions to facilitate computation. We use a stochastic search Gibbs sampler to implement a fully Bayesian approach for variable selection. The approach is illustrated using simulated data and a real example.