IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v42y2015i6p1148-1165.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2014.995610
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2014.995610?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    4. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Jussiane Nader Gonçalves & Wagner Barreto-Souza, 2020. "Flexible regression models for counts with high-inflation of zeros," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 71-95, April.
    3. 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.
    4. Tousifur Rahman & Partha Jyoti Hazarika & M. Masoom Ali & Manash Pratim Barman, 2022. "Three-Inflated Poisson Distribution and its Application in Suicide Cases of India During Covid-19 Pandemic," Annals of Data Science, Springer, vol. 9(5), pages 1103-1127, October.
    5. Derek S. Young & Andrew M. Raim & Nancy R. Johnson, 2017. "Zero-inflated modelling for characterizing coverage errors of extracts from the US Census Bureau's Master Address File," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 73-97, January.
    6. Maria Goranova & Rahi Abouk & Paul C. Nystrom & Ehsan S. Soofi, 2017. "Corporate governance antecedents to shareholder activism: A zero-inflated process," Strategic Management Journal, Wiley Blackwell, vol. 38(2), pages 415-435, February.
    7. Abbas Moghimbeigi & Mohammed Reza Eshraghian & Kazem Mohammad & Brian Mcardle, 2008. "Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zeros," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1193-1202.
    8. Moghimbeigi, Abbas & Eshraghian, Mohammad Reza & Mohammad, Kazem & McArdle, Brian, 2009. "A score test for zero-inflation in multilevel count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1239-1248, February.
    9. Yanlin Tang & Liya Xiang & Zhongyi Zhu, 2014. "Risk Factor Selection in Rate Making: EM Adaptive LASSO for Zero‐Inflated Poisson Regression Models," Risk Analysis, John Wiley & Sons, vol. 34(6), pages 1112-1127, June.
    10. Damgaard, Christian, 2008. "Modelling pin-point plant cover data along an environmental gradient," Ecological Modelling, Elsevier, vol. 214(2), pages 404-410.
    11. 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.
    12. Liu, Juxin & Ma, Yanyuan & Johnstone, Jill, 2020. "A goodness-of-fit test for zero-inflated Poisson mixed effects models in tree abundance studies," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    13. Kathryn M. Irvine & T. J. Rodhouse & Ilai N. Keren, 2016. "Extending Ordinal Regression with a Latent Zero-Augmented Beta Distribution," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 619-640, December.
    14. Feng, Jiarui & Zhu, Zhongyi, 2011. "Semiparametric analysis of longitudinal zero-inflated count data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 61-72, January.
    15. Lim, Hwa Kyung & Song, Juwon & Jung, Byoung Cheol, 2013. "Score tests for zero-inflation and overdispersion in two-level count data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 67-82.
    16. Wei-Wen Hsu & David Todem & Kyungmann Kim, 2015. "Adjusted Supremum Score-Type Statistics for Evaluating Non-Standard Hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 746-759, September.
    17. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    18. Loni Philip Tabb & Eric J. Tchetgen Tchetgen & Greg A. Wellenius & Brent A. Coull, 2016. "Marginalized Zero-Altered Models for Longitudinal Count Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(2), pages 181-203, October.
    19. Wenchen Liu & Yincai Tang & Ancha Xu, 2021. "Zero-and-one-inflated Poisson regression model," Statistical Papers, Springer, vol. 62(2), pages 915-934, April.
    20. Zhao-Hua Lu & Sy-Miin Chow & Nilam Ram & Pamela M. Cole, 2019. "Zero-Inflated Regime-Switching Stochastic Differential Equation Models for Highly Unbalanced Multivariate, Multi-Subject Time-Series Data," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 611-645, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:42:y:2015:i:6:p:1148-1165. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.