Bayesian Analysis for Multivariate Skew-Normal Simplex Mixed-Effects Models with Heterogeneous Dispersion

Abstract

Continuous proportional data frequently appears in many areas of research, where proportional outcome are in the open interval (0, 1). Simplex mixed-effects model is a powerful tool for modeling longitudinal continuous proportional data; however, the normality assumption of random effects in classic simplex mixed-effects model may be questionable in the analysis of skewed data. In this paper, we relax the normality assumption of random effects by specifying the random-effect distribution with the multivariate skew-normal distribution in mixed-effect model and simultaneously model the dispersion parameter (heterogeneity) in mixed-effect model. An efficient Markov chain Monte Carlo algorithm that combines the block Gibbs sampler, the Metropolis-Hastings algorithm and the data-augmentation technique is proposed for producing the joint Bayesian estimates of unknown parameters and random effects. The Deviance Information Criterion (DIC), as a popular model comparison criterion, is employed to select better model. The proposed methodology is illustrated by several simulation studies and a real example.