Bayesian semiparametric variable selection with applications to periodontal data.

A normality assumption is typically adopted for the random effects in a clustered or longitudinal data analysis using a linear mixed model. However, such an assumption is not always realistic, and it may lead to potential biases of the estimates, especially when variable selection is taken into account. Furthermore, flexibility of nonparametric assumptions (e.g., Dirichlet process) on these random effects may potentially cause centering problems, leading to difficulty of interpretation of fixed effects and variable selection. Motivated by these problems, we proposed a Bayesian method for fixed and random effects selection in nonparametric random effects models. We modeled the regression coefficients via centered latent variables which are distributed as probit stick-breaking scale mixtures. By using the mixture priors for centered latent variables along with covariance decomposition, we could avoid the aforementioned problems and allow efficient selection of fixed and random effects from the model. We demonstrated the advantages of our proposed approach over other competing alternatives through a simulated example and also via an illustrative application to a data set from a periodontal disease study.