IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v58y2017i1d10.1007_s00362-015-0683-1.html
   My bibliography  Save this article

Detecting over- and under-dispersion in zero inflated data with the hyper-Poisson regression model

Author

Listed:
  • Antonio J. Sáez-Castillo

    (Universidad de Jaén)

  • Antonio Conde-Sánchez

    (Universidad de Jaén)

Abstract

The zero inflated hyper-Poisson regression model permits count data to be analysed with covariates that determine different levels of dispersion and that present structural zeros due to the existence of a non-users group. A simulation study demonstrates the capability of the model to detect over- and under-dispersion of the potential users group of the dataset in relation to the value of covariates, and to estimate the proportion of structural zeros with great accuracy. An application of the model to fit the number of children per family in relation to several covariates confirms the presence of structural zeros in fertility data at the same time as it detects under-dispersion in most of the levels determined by the covariates.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0683-1
    DOI: 10.1007/s00362-015-0683-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-015-0683-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-015-0683-1?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. Markus Jochmann, 2013. "What belongs where? Variable selection for zero-inflated count models with an application to the demand for health care," Computational Statistics, Springer, vol. 28(5), pages 1947-1964, October.
    2. Chen, Xue-Dong & Fu, Ying-Zi, 2011. "Model selection for zero-inflated regression with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 765-773, January.
    3. Luigi Aldieri & Concetto Paolo Vinci, 2012. "Education and fertility: an investigation into Italian families," International Journal of Social Economics, Emerald Group Publishing, vol. 39(4), pages 254-236, March.
    4. Zeileis, Achim & Kleiber, Christian & Jackman, Simon, 2008. "Regression Models for Count Data in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i08).
    5. 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.
    6. Angers, Jean-Francois & Biswas, Atanu, 2003. "A Bayesian analysis of zero-inflated generalized Poisson model," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 37-46, February.
    7. Kevin E. Staub & Rainer Winkelmann, 2013. "Consistent Estimation Of Zero‐Inflated Count Models," Health Economics, John Wiley & Sons, Ltd., vol. 22(6), pages 673-686, June.
    8. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    9. Feng-Chang Xie & Jin-Guan Lin & Bo-Cheng Wei, 2010. "Testing for varying zero-inflation and dispersion in generalized Poisson regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1509-1522.
    10. Claudia Czado & Holger Schabenberger & Vinzenz Erhardt, 2014. "Non nested model selection for spatial count regression models with application to health insurance," Statistical Papers, Springer, vol. 55(2), pages 455-476, May.
    11. Weiren Wang & Felix Famoye, 1997. "Modeling household fertility decisions with generalized Poisson regression," Journal of Population Economics, Springer;European Society for Population Economics, vol. 10(3), pages 273-283.
    12. Luigi Aldieri & Concetto Paolo Vinci, 2012. "Education and fertility: an investigation into Italian families," International Journal of Social Economics, Emerald Group Publishing Limited, vol. 39(4), pages 254-263, March.
    13. Hossein Zamani & Noriszura Ismail, 2013. "Score test for testing zero-inflated Poisson regression against zero-inflated generalized Poisson alternatives," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 2056-2068, 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. Ajiferuke, Isola & Famoye, Felix, 2015. "Modelling count response variables in informetric studies: Comparison among count, linear, and lognormal regression models," Journal of Informetrics, Elsevier, vol. 9(3), pages 499-513.
    2. 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.
    3. Kong, Maiying & Xu, Sheng & Levy, Steven M. & Datta, Somnath, 2015. "GEE type inference for clustered zero-inflated negative binomial regression with application to dental caries," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 54-66.
    4. Marjan Qazvini, 2019. "On the Validation of Claims with Excess Zeros in Liability Insurance: A Comparative Study," Risks, MDPI, vol. 7(3), pages 1-17, June.
    5. Helai Huang & Hong Chin, 2010. "Modeling road traffic crashes with zero-inflation and site-specific random effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 445-462, August.
    6. 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.
    7. Hossein Zamani & Pouya Faroughi & Noriszura Ismail, 2016. "Bivariate generalized Poisson regression model: applications on health care data," Empirical Economics, Springer, vol. 51(4), pages 1607-1621, December.
    8. Volition Tlhalitshi Montshiwa & Ntebogang Dinah Moroke, 2017. "The Effect of Sample Size on the Efficiency of Count Data Models: Application to Marriage Data," Journal of Economics and Behavioral Studies, AMH International, vol. 9(3), pages 6-18.
    9. John Haslett & Andrew C. Parnell & John Hinde & Rafael de Andrade Moral, 2022. "Modelling Excess Zeros in Count Data: A New Perspective on Modelling Approaches," International Statistical Review, International Statistical Institute, vol. 90(2), pages 216-236, August.
    10. Totterman, Stephen, 2021. "Vehicle-based recreation and compliance for three beaches in northern New South Wales," OSF Preprints ja8h6, Center for Open Science.
    11. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    12. 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.
    13. Fatima Olanike Kareem & Olayinka Idowu Kareem, 2014. "Specification and Estimation of Gravity Models: A Review of the Issues in the Literature," RSCAS Working Papers 2014/74, European University Institute.
    14. Jong-Hyun Kim & Yong-Gil Lee, 2021. "Factors of Collaboration Affecting the Performance of Alternative Energy Patents in South Korea from 2010 to 2017," Sustainability, MDPI, vol. 13(18), pages 1-25, September.
    15. Gamba, Simona & Magazzini, Laura & Pertile, Paolo, 2021. "R&D and market size: Who benefits from orphan drug legislation?," Journal of Health Economics, Elsevier, vol. 80(C).
    16. Olga Alipova & Lada Litvinova & Andrey Lovakov & Maria Yudkevich, 2018. "Inbreds And Non-Inbreds Among Russian Academics: Short-Term Similarity And Long-Term Differences In Productivity," HSE Working papers WP BRP 48/EDU/2018, National Research University Higher School of Economics.
    17. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    18. Sewando, Ponsian T. & Mdoe, N. Y. S. & Mutabazi, K. D. S, 2011. "Farmers’ preferential choice decisions to alternative cassava value chain strands in Morogoro rural district, Tanzania," MPRA Paper 29797, University Library of Munich, Germany.
    19. Payandeh Najafabadi Amir T. & MohammadPour Saeed, 2018. "A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(2), pages 1-31, July.
    20. 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.

    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:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0683-1. 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.