Application of the scale - mixture of multivariate normal distributions in multilevel models using Markov chain Monte Carlo simulation

Application of the scale - mixture of multivariate normal distributions in multilevel models using Markov chain Monte Carlo simulation

This paper extends fitting multilevel models using scale mixtures of multivariate normal (SMMN) distributions in a Bayesian perspective. This class of models covers the analysis of several heavy-tailed correlated data asing flexible distributions, such as the multivariate t, multivariate Laplace and multivariate slash, for the error terms and the random effects. The corresponding multilevel models are shown to follow hierarchical representations that enable researchers to implement the Markov chain Monte Carlo (MCMC) methods and to make simple simulating samples from the joint ung posterior distributions. Finally, in order to highlight the theoretical concepts of these models, we conduct a simulation study