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

Autor(es)

Garay, Aldo M. ^[1] ; Bolfarine, Heleno ^[2] ; Lachos, Victor H. ^[1] ; Cabral, Celso R. B. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Stat, Campinas, SP - Brazil

^[2] Univ Sao Paulo, Dept Stat, Sao Paulo - Brazil

^[3] Univ Fed Amazonas, Dept Stat, Manaus, Amazonas - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Applied Statistics; v. 42, n. 12, p. 2694-2714, DEC 2 2015.
• Citações Web of Science: 11

Resumo

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 responses can be either left, interval or right censored. Linear (and nonlinear) regression models are routinely used to analyze these types of data and are based on normality assumptions for the errors terms. However, those analyzes might not provide robust inference when the normality assumptions are questionable. In this article, we develop a Bayesian framework for censored linear regression models by replacing the Gaussian assumptions for the random errors with scale mixtures of normal (SMN) distributions. The SMN is an attractive class of symmetric heavy-tailed densities that includes the normal, Student-t, Pearson type VII, slash and the contaminated normal distributions, as special cases. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is introduced to carry out posterior inference. A new hierarchical prior distribution is suggested for the degrees of freedom parameter in the Student-t distribution. 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 measure. The proposed Bayesian methods are implemented in the R package BayesCR. The newly developed procedures are illustrated with applications using real and simulated data. (AU)

• Processo FAPESP: 14/02938-9 - Estimação e diagnóstico em modelos de efeitos mistos para dados censurados usando misturas de escala skew-normal
• Beneficiário: Víctor Hugo Lachos Dávila
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/21468-0 - Modelos com erros nas variáveis para dados censurados usando distribuições de misturas da escala skew-normal
• Beneficiário: Aldo William Medina Garay
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado