Department of Statistics, University of Isfahan, Isfahan, Iran
Multilevel models provide suitable framework to study related data that are collected at various levels in many researches. In this paper, we propose a family of scale mixture of multivariate normal distributions for multilevel models. This family is more flexible than the normal distribution. The proposed model provides a better fit to the observed data in which their distribution has tails heavier than normal. The statistical inference of model parameters done by the marginal maximum likelihood leads to complex high-dimensional integrals and thus we implement the Markov chain Monte Carlo simulation approach for the Bayesian estimation of related parameters. In is shown that the kurtosis measure of different members in this family is different, therefore we fit multilevel models on a set of real data with imposing a variety of distributions in this family. Finally, by using the common model selection criteria we choose the best fitted model.