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

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  • Aldo M. Garay
  • Victor H. Lachos
  • Heleno Bolfarine

Abstract

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.

Suggested Citation

  • Aldo M. Garay & Victor H. Lachos & Heleno Bolfarine, 2015. "Bayesian estimation and case influence diagnostics for the zero-inflated negative binomial regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(6), pages 1148-1165, June.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:6:p:1148-1165
    DOI: 10.1080/02664763.2014.995610
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    References listed on IDEAS

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    1. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
    2. Garay, Aldo M. & Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Lachos, Víctor H., 2011. "On estimation and influence diagnostics for zero-inflated negative binomial regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1304-1318, March.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    5. Xiao-Hua Zhou & Wanzhu Tu, 2000. "Confidence Intervals for the Mean of Diagnostic Test Charge Data Containing Zeros," Biometrics, The International Biometric Society, vol. 56(4), pages 1118-1125, December.
    6. Martin Ridout & John Hinde & Clarice G. B. Demétrio, 2001. "A Score Test for Testing a Zero‐Inflated Poisson Regression Model Against Zero‐Inflated Negative Binomial Alternatives," Biometrics, The International Biometric Society, vol. 57(1), pages 219-223, March.
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    1. Benjamin Scharadin & Edward C. Jaenicke, 2020. "Time spent on childcare and the household Healthy Eating Index," Review of Economics of the Household, Springer, vol. 18(2), pages 357-386, June.

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