Bayesian analysis for multivariate skew-normal reproductive dispersion random effects models

Normality assumption of the random errors and the random effects is a routinely used technique in data analysis. However, this assumption might be unreasonable in many practical cases. In this paper the limitation is relaxed by assuming that the random error follows a reproductive dispersion model and the random effect is distributed as a skew-normal distribution, which is termed as a multivariate skew-normal reproductive dispersion random effects model. We propose a Bayesian procedure to simultaneously estimate the random effects and the unknown parameters on the basis of the Gibbs sampler and Metropolis-Hastings algorithm. In the end, the Framingham cholesterol data example is employed to demonstrate the preceding proposed Bayesian methodologies.