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Bayesian zero-inflated generalized Poisson regression model: estimation and case influence diagnostics

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  • Feng-Chang Xie
  • Jin-Guan Lin
  • Bo-Cheng Wei

Abstract

Count data with excess zeros arises in many contexts. Here our concern is to develop a Bayesian analysis for the zero-inflated generalized Poisson (ZIGP) regression model to address this problem. This model provides a useful generalization of zero-inflated Poisson model since the generalized Poisson distribution is overdispersed/underdispersed relative to Poisson. Due to the complexity of the ZIGP model, Markov chain Monte Carlo methods are used to develop a Bayesian procedure for the considered model. Additionally, some discussions on the model selection criteria are presented and a Bayesian case deletion influence diagnostics is investigated for the joint posterior distribution based on the Kullback-Leibler divergence. Finally, a simulation study and a psychological example are given to illustrate our methodology.

Suggested Citation

  • Feng-Chang Xie & Jin-Guan Lin & Bo-Cheng Wei, 2014. "Bayesian zero-inflated generalized Poisson regression model: estimation and case influence diagnostics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1383-1392, June.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:6:p:1383-1392
    DOI: 10.1080/02664763.2013.871508
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    Cited by:

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    2. Soutik Ghosal & Timothy S. Lau & Jeremy Gaskins & Maiying Kong, 2020. "A hierarchical mixed effect hurdle model for spatiotemporal count data and its application to identifying factors impacting health professional shortages," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1121-1144, November.
    3. Wenchen Liu & Yincai Tang & Ancha Xu, 2021. "Zero-and-one-inflated Poisson regression model," Statistical Papers, Springer, vol. 62(2), pages 915-934, April.
    4. Antonio J. Sáez-Castillo & Antonio Conde-Sánchez, 2017. "Detecting over- and under-dispersion in zero inflated data with the hyper-Poisson regression model," Statistical Papers, Springer, vol. 58(1), pages 19-33, March.
    5. José Rodríguez-Avi & María José Olmo-Jiménez, 2017. "A regression model for overdispersed data without too many zeros," Statistical Papers, Springer, vol. 58(3), pages 749-773, September.

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