Bayesian inference for scale mixtures of skew-normal linear models under the centered parameterization

TL;DR

This paper introduces a Bayesian approach for scale mixtures of skew-normal linear models using centered parameterization, addressing inferential issues and providing tools for residual and influence analysis.

Contribution

It develops a new class of models with centered parameterization, along with a hierarchical representation, MCMC estimation scheme, and diagnostic tools.

Findings

MCMC algorithm performs well in simulations

Residuals and influence measures are effective

Method applied successfully to real data

Abstract

In many situations we are interested in modeling real data where the response distribution, even conditionally on the covariates, presents asymmetry and/or heavy/light tails. In these situations, it is more suitable to consider models based on the skewed and/or heavy/light tailed distributions, such as the class of scale mixtures of skew-normal distributions. The classical parameterization of this distributions may not be good due to the some inferential issues when the skewness parameter is in a neighborhood of 0, then, the centered parameterization becomes more appropriate. In this paper, we developed a class of scale mixtures of skew-normal distributions under the centered parameterization, also a linear regression model based on them was proposed. We explore a hierarchical representation and set up a MCMC scheme for parameter estimation. Furthermore, we developed residuals and influence analysis tools. A Monte Carlo experiment is conducted to evaluate the performance of the MCMC algorithm and the behavior of the residual distribution. The methodology is illustrated with the analysis of a real data set.