IDEAS home Printed from https://ideas.repec.org/a/spr/jstada/v8y2021i1d10.1186_s40488-021-00117-0.html
   My bibliography  Save this article

Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models

Author

Listed:
  • Yixuan Zou

    (Genentech)

  • Jan Hannig

    (Department of Statistics and Operations Research, University of North Carolina at Chapel Hill)

  • Derek S. Young

    (Dr. Bing Zhang Department of Statistics, University of Kentucky)

Abstract

Zero-inflated and hurdle models are widely applied to count data possessing excess zeros, where they can simultaneously model the process from how the zeros were generated and potentially help mitigate the effects of overdispersion relative to the assumed count distribution. Which model to use depends on how the zeros are generated: zero-inflated models add an additional probability mass on zero, while hurdle models are two-part models comprised of a degenerate distribution for the zeros and a zero-truncated distribution. Developing confidence intervals for such models is challenging since no closed-form function is available to calculate the mean. In this study, generalized fiducial inference is used to construct confidence intervals for the means of zero-inflated Poisson and Poisson hurdle models. The proposed methods are assessed by an intensive simulation study. An illustrative example demonstrates the inference methods.

Suggested Citation

  • Yixuan Zou & Jan Hannig & Derek S. Young, 2021. "Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-15, December.
    • Handle: RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00117-0
    DOI: 10.1186/s40488-021-00117-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40488-021-00117-0
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40488-021-00117-0?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
    ---><---

    References listed on IDEAS

    as
    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
    2. Lidong, E. & Hannig, Jan & Iyer, Hari, 2008. "Fiducial Intervals for Variance Components in an Unbalanced Two-Component Normal Mixed Linear Model," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 854-865, June.
    3. Jan Hannig & Hari Iyer & Randy C. S. Lai & Thomas C. M. Lee, 2016. "Generalized Fiducial Inference: A Review and New Results," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1346-1361, July.
    4. David Todem & Wei‐Wen Hsu & Jason P. Fine, 2018. "A Quasi‐Score Statistic for Homogeneity Testing against Covariate‐Varying Heterogeneity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 465-481, September.
    5. Jansakul, N. & Hinde, J. P., 2002. "Score Tests for Zero-Inflated Poisson Models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 75-96, July.
    6. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    7. Mathew, Thomas & Young, Derek S., 2013. "Fiducial-based tolerance intervals for some discrete distributions," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 38-49.
    8. Jan Hannig & Thomas C. M. Lee, 2009. "Generalized fiducial inference for wavelet regression," Biometrika, Biometrika Trust, vol. 96(4), pages 847-860.
    9. SPRINGAEL, Johan & VAN NIEUWENHUYSE, Inneke, 2006. "On the sum of independent zero-truncated Poisson random variables," Working Papers 2006011, University of Antwerp, Faculty of Business and Economics.
    10. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    11. Cameron, A. Colin & Trivedi, Pravin K., 1990. "Regression-based tests for overdispersion in the Poisson model," Journal of Econometrics, Elsevier, vol. 46(3), pages 347-364, December.
    12. 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.
    13. David Todem & KyungMann Kim & Wei-Wen Hsu, 2016. "Marginal mean models for zero-inflated count data," Biometrics, The International Biometric Society, vol. 72(3), pages 986-994, September.
    Full references (including those not matched with items on IDEAS)

    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. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    2. 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.
    3. Jiang, Yuan & House, Lisa A., 2017. "Comparison of the Performance of Count Data Models under Different Zero-Inflation Scenarios Using Simulation Studies," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258342, Agricultural and Applied Economics Association.
    4. Hannig, Jan & Lai, Randy C.S. & Lee, Thomas C.M., 2014. "Computational issues of generalized fiducial inference," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 849-858.
    5. Hsin-I Lee & Hungyen Chen & Hirohisa Kishino & Chen-Tuo Liao, 2016. "A Reference Population-Based Conformance Proportion," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 684-697, December.
    6. Candelon, Bertrand & Joëts, Marc & Mignon, Valérie, 2024. "What makes econometric ideas popular: The role of connectivity," Research Policy, Elsevier, vol. 53(7).
    7. 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.
    8. Shen-Ming Lee & T. Martin Lukusa & Chin-Shang Li, 2020. "Estimation of a zero-inflated Poisson regression model with missing covariates via nonparametric multiple imputation methods," Computational Statistics, Springer, vol. 35(2), pages 725-754, June.
    9. Shin-Fu Tsai, 2019. "Comparing Coefficients Across Subpopulations in Gaussian Mixture Regression Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 610-633, December.
    10. 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.
    11. Habtamu K. Benecha & Brian Neelon & Kimon Divaris & John S. Preisser, 2017. "Marginalized mixture models for count data from multiple source populations," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    12. Luiz Paulo Fávero & Joseph F. Hair & Rafael de Freitas Souza & Matheus Albergaria & Talles V. Brugni, 2021. "Zero-Inflated Generalized Linear Mixed Models: A Better Way to Understand Data Relationships," Mathematics, MDPI, vol. 9(10), pages 1-28, May.
    13. Boncinelli, Fabio & Bartolini, Fabio & Casini, Leonardo, 2018. "Structural factors of labour allocation for farm diversification activities," Land Use Policy, Elsevier, vol. 71(C), pages 204-212.
    14. Greene, William, 2007. "Functional Form and Heterogeneity in Models for Count Data," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(2), pages 113-218, August.
    15. Christopher J. W. Zorn, 1998. "An Analytic and Empirical Examination of Zero-Inflated and Hurdle Poisson Specifications," Sociological Methods & Research, , vol. 26(3), pages 368-400, February.
    16. J. M. C. Santos Silva & Silvana Tenreyro, 2022. "The Log of Gravity at 15," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 423-437, September.
    17. Ulf‐ G. Gerdtham, 1997. "Equity in Health Care Utilization: Further Tests Based on Hurdle Models and Swedish Micro Data," Health Economics, John Wiley & Sons, Ltd., vol. 6(3), pages 303-319, May.
    18. Chiara Bocci & Laura Grassini & Emilia Rocco, 2021. "A multiple inflated negative binomial hurdle regression model: analysis of the Italians’ tourism behaviour during the Great Recession," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1109-1133, October.
    19. Xie, Feng-Chang & Wei, Bo-Cheng & Lin, Jin-Guan, 2009. "Score tests for zero-inflated generalized Poisson mixed regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3478-3489, July.
    20. 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.

    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:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00117-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.