Bayesian variable selection for logistic mixed model with nonparametric random effects

In analyzing correlated data or clustered data with linear or logistic mixed effects model, one commonly assumes that the random effects follow a normal distribution with mean zero. However, this assumption might not be appropriate in many cases. In particular, substantial violation of normality assumption might potentially impact the subset selection of variables in these models. In this article, we address the problem of joint selection of both fixed and random effects and bias control for random effects in nonparametric settings. An efficient Bayesian variable selection is implemented using a stochastic search Gibbs sampler to allow both fixed and random effects to be dropped effectively out of the model. The approach is illustrated using a simulation study and a real data example.