Statistics and Its Interface

Volume 10 (2017)

Number 3

Bayesian analysis of censored linear regression models with scale mixtures of skew-normal distributions

Pages: 425 – 439

DOI: https://dx.doi.org/10.4310/SII.2017.v10.n3.a7

Authors

Monique B. Massuia (Department of Statistics, Campinas State University, Campinas, São Paulo, Brazil)

Aldo M. Garay (Department of Statistics, Campinas State University, Campinas, São Paulo, Brazil; and Department of Statistics, Federal University of Pernambuco, Recife, Brazil)

Celso R. B. Cabral (Department of Statistics, Federal University of Amazonas, Manaus, Brazil)

V. H. Lachos (Department of Statistics, Campinas State University, Campinas, São Paulo, Brazil)

Abstract

In many studies, limited or censored data are collected. This occurs, in several practical situations, for reasons such as limitations of measuring equipment or from experimental design. Hence, the exact true value is recorded only if it falls within an interval range, so, the responses can be either left, interval or right censored. Linear (and nonlinear) regression models are routinely used to analyze these types of data. Most of these models are based on the normality assumption for the error terms. However, such 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 models by replacing the Gaussian assumption for the random errors 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 special cases. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced to carry out posterior inference. The likelihood function is utilized to compute not only some Bayesian model selection measures, but also to develop Bayesian case-deletion influence diagnostics based on the $q$-divergence measures. The proposed Bayesian methods are implemented in the $\mathrm{R}$ package $\texttt{BayesCR}$, proposed by us. The newly developed procedures are illustrated with applications using real and simulated data.

Keywords

Bayesian modeling,censored regression models, MCMC, scale mixtures of skew-normal distributions

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Published 31 January 2017