Bayesian Analysis of Multilevel Models with the Skew-Slash Distribution

Abstract

In fitting multilevel models, itis commonly assumed that the random effects and the error terms follow the normal distribution. In many empirical applications, the true distribution of data obeys non-normality and thus the main concern of most recent studies is the use of alternative distributions. In this paper, we propose a new class ofrandom-intercept models using the skew-slash distribution. The new regression model is flexible in the analysis of correlated data and simple in the implementation of Markov Chain Monte Carlo methods, such as the Gibbs sampling approach. Using the stochastic representation of the skewslash distribution we derive the full conditional posteriors distributionsin order to present the bayesian inference of model parameters. A real data analysis is illustrated to show the usefulness of the proposed model.