Variable Selection in Nonparametric Random Effects Models

In analyzing longitudinal or clustered data with a mixed effects model (Laird and Ware, 1982), one may be concerned about violations of normality. Such violations can potentially impact subset selection for the fixed and random effects components of the model, inferences on the heterogeneity structure, and the accuracy of predictions. This article focuses on Bayesian methods for subset selection in nonparametric random effects models in which one is uncertain about the predictors to be included and the distribution of their random effects. We characterize the unknown distribution of the individual-specific regression coefficients using a weighted sum of Dirichlet process (DP)-distributed latent variables. By using carefully-chosen mixture priors for coefficients in the base distributions of the component DPs, we allow fixed and random effects to be effectively dropped out of the model. A stochastic search Gibbs sampler is developed for posterior computation, and the methods are illustrated using simulated data and real data from a multi-laboratory bioassay study