Bayesian quantile regression for skew-normal linear mixed models

ABSTRACT

Linear mixed models have been widely used to analyze repeated measures data which arise in many studies. In most applications, it is assumed that both the random effects and the within-subjects errors are normally distributed. This can be extremely restrictive, obscuring important features of within-and among-subject variations. Here, quantile regression in the Bayesian framework for the linear mixed models is described to carry out the robust inferences. We also relax the normality assumption for the random effects by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in the linear mixed models. For posterior inference, we propose a Gibbs sampling algorithm based on a mixture representation of the asymmetric Laplace distribution and multivariate skew-normal distribution. The procedures are demonstrated by both simulated and real data examples.

KEYWORDS:

• Asymmetric laplace distribution
• Bayesian quantile regression
• linear mixed models
• MCMC
• skew-normal distribution.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62J05
• 62G05