Bayesian Variable Selection and Estimation in Semiparametric Simplex Mixed-Effects Models with Longitudinal Proportional Data

Abstract

In the development of simplex mixed-effects models, random effects in these mixed-effects models are generally distributed in normal distribution. The normality assumption may be violated in an analysis of skewed and multimodal longitudinal data. In this paper, we adopt the centered Dirichlet process mixture model (CDPMM) to specify the random effects in the simplex mixed-effects models. Combining the block Gibbs sampler and the Metropolis–Hastings algorithm, we extend a Bayesian Lasso (BLasso) to simultaneously estimate unknown parameters of interest and select important covariates with nonzero effects in semiparametric simplex mixed-effects models. Several simulation studies and a real example are employed to illustrate the proposed methodologies.

Keywords

• simplex distribution
• Gibbs sampler
• Metropolis–Hastings algorithm
• Dirichlet process prior
• Bayesian Lasso