Bayesian Analysis of Censored Linear Regression Models with Scale Mixtures of Skew-Normal Distributions

Monique B. Massuia
Aldo M. Garay
Víctor H. Lachos
Celso R. B. Cabral

As is the case of many studies, the data collected are limited and an exact value is recorded only if it falls within an interval range. Hence, the resp onses can b e either left, interval or right censored. Linear (and nonlinear) regression mo dels are routinely used to analyze these typ es of data and are based on the normality assumption for the errors terms. However, those analyses might not provide robust inference when the normality assumption (or symmetry) is questionable. In this article, we develop a Bayesian framework for censored linear regression mo dels by replacing the Gaussian assumption for the randomerrors with the asymmetric class of scale mixtures of skew-normal (SMSN) distributions. The SMSN is an attractive class of asymmetrical heavy-tailed densities that includes the skew-normal, skew-t, skew-slash, the skew-contaminated normal and the entire family of scale mixtures of normal distributions as sp ecial cases. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is intro duced to carry out p osterior inference. The likeliho o d function is utilized to compute not only some Bayesian mo del selection measures but also to develop Bayesian case-deletion influence diagnostics based on the q-divergence measures. The prop osed Bayesian metho ds are implemented in the R package BayesCR, prop osed by the authors. The newly develop ed pro cedures are illustrated with applications using real and simulated data.

Bayesian modeling
Censored regression models
Scale mixtures of skew-normal distributions