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On the Bayesian estimation and influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes

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  • Bao Yiqi
  • Vicente G. Cancho
  • Francisco Louzada

Abstract

The purpose of this paper is to develop a Bayesian approach for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes and presence of randomized activation mechanisms. We assume the number of competing causes of the event of interest follows a Negative Binomial (NB) distribution while the latent lifetimes are assumed to follow a Weibull distribution. Markov chain Monte Carlos (MCMC) methods are used to develop the Bayesian procedure. Model selection to compare the fitted models is discussed. Moreover, we develop case deletion influence diagnostics for the joint posterior distribution based on the ψ-divergence, which has several divergence measures as particular cases. The developed procedures are illustrated with a real data set.

Suggested Citation

  • Bao Yiqi & Vicente G. Cancho & Francisco Louzada, 2017. "On the Bayesian estimation and influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1462-1489, February.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:3:p:1462-1489
    DOI: 10.1080/03610926.2015.1019150
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    Cited by:

    1. Alex Mota & Eder A. Milani & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Oilson G. Junior & Vera L. D. Tomazella & Francisco Louzada, 2023. "A new cure rate frailty regression model based on a weighted Lindley distribution applied to stomach cancer data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 883-909, September.

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