Bayesian estimation and case influence diagnostics for the zero-inflated negative binomial regression model

Autor(es)

Garay, Aldo M. ^[1] ; Lachos, Victor H. ^[1] ; Bolfarine, Heleno ^[2]

Afiliação do(s) autor(es)

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

^[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Applied Statistics; v. 42, n. 6, p. 1148-1165, JUN 3 2015.
• Citações Web of Science: 2

Resumo

In recent years, there has been considerable interest in regression models based on zero-inflated distributions. These models are commonly encountered in many disciplines, such as medicine, public health, and environmental sciences, among others. The zero-inflated Poisson (ZIP) model has been typically considered for these types of problems. However, the ZIP model can fail if the non-zero counts are overdispersed in relation to the Poisson distribution, hence the zero-inflated negative binomial (ZINB) model may be more appropriate. In this paper, we present a Bayesian approach for fitting the ZINB regression model. This model considers that an observed zero may come from a point mass distribution at zero or from the negative binomial model. 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 q-divergence measures. The approach can be easily implemented using standard Bayesian software, such as WinBUGS. The performance of the proposed method is evaluated with a simulation study. Further, a real data set is analyzed, where we show that ZINB regression models seems to fit the data better than the Poisson counterpart. (AU)

• 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
• Processo FAPESP: 14/13994-7 - Regressão e séries temporais em modelamento de dados incompletos
• Beneficiário: Aldo William Medina Garay
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado