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

Author(s)

Massuia, Monique B. ; Garay, Aldo M. ; Cabral, Celso R. B. ; Lachos, V. H.

• Document type: Journal article
• Source: STATISTICS AND ITS INTERFACE; v. 10, n. 3, p. 425-439, 2017.
• Web of Science Citations: 2

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 R package BayesCR, proposed by us. The newly developed procedures are illustrated with applications using real and simulated data. (AU)

• FAPESP's process: 14/02938-9 - Estimation and diagnostics for censored mixed effects models using scale mixtures of skew-normal distributions
• Grantee: Víctor Hugo Lachos Dávila
• Support Opportunities: Regular Research Grants
• FAPESP's process: 13/21468-0 - Measurement error-in-variables models for censored data using scale mixtures of skew-normal distributions
• Grantee: Aldo William Medina Garay
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 12/18702-9 - Linear and non-linear models for censored data using scale mixtures of skew-normal distributions.
• Grantee: Monique Bettio Massuia
• Support Opportunities: Scholarships in Brazil - Master