IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v31y2022i3d10.1007_s11749-022-00801-6.html
   My bibliography  Save this article

A simple and useful regression model for fitting count data

Author

Listed:
  • Marcelo Bourguignon

    (Universidade Federal do Rio Grande do Norte)

  • Rodrigo M. R. Medeiros

    (Universidade Federal do Rio Grande do Norte)

Abstract

We present a novel regression model for count data where the response variable is BerG-distributed using a new parameterization of this distribution, which is indexed by mean and dispersion parameters. An attractive feature of this model lies in its potential to fit count data when overdispersion, equidispersion, underdispersion, or zero inflation (or deflation) is indicated. The advantage of our new parameterization and approach is the straightforward interpretation of the regression coefficients in terms of the mean and dispersion as in generalized linear models. The maximum likelihood method is used to estimate the model parameters. Also, we conduct hypothesis tests for the dispersion parameter and consider residual analysis. Simulation studies are conducted to empirically evidence the properties of the estimators, the test statistics, and the residuals in finite-sized samples. The proposed model is applied to two real datasets on wildlife habitat and road traffic accidents, which illustrates its capabilities in accommodating both over- and underdispersed count data. This paper contains Supplementary Material.

Suggested Citation

  • Marcelo Bourguignon & Rodrigo M. R. Medeiros, 2022. "A simple and useful regression model for fitting count data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 790-827, September.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:3:d:10.1007_s11749-022-00801-6
    DOI: 10.1007/s11749-022-00801-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-022-00801-6
    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/s11749-022-00801-6?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. Kazuki Aoyama & Kunio Shimizu & S. Ong, 2008. "A first–passage time random walk distribution with five transition probabilities: a generalization of the shifted inverse trinomial," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(1), pages 1-20, March.
    2. Puig, Pedro & Valero, Jordi, 2006. "Count Data Distributions: Some Characterizations With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 332-340, March.
    3. Marcelo Bourguignon & Christian H. Weiß, 2017. "An INAR(1) process for modeling count time series with equidispersion, underdispersion and overdispersion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 847-868, December.
    4. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    5. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, April.
    6. Zijian Guo & Dylan S. Small & Stuart A. Gansky & Jing Cheng, 2018. "Mediation analysis for count and zero‐inflated count data without sequential ignorability and its application in dental studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(2), pages 371-394, February.
    7. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    8. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    9. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
    10. Hyoyoung Choo-Wosoba & Steven M. Levy & Somnath Datta, 2016. "Marginal regression models for clustered count data based on zero-inflated Conway–Maxwell–Poisson distribution with applications," Biometrics, The International Biometric Society, vol. 72(2), pages 606-618, June.
    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. Célestin C. Kokonendji & Sobom M. Somé & Youssef Esstafa & Marcelo Bourguignon, 2023. "On Underdispersed Count Kernels for Smoothing Probability Mass Functions," Stats, MDPI, vol. 6(4), pages 1-15, November.

    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. Darcy Steeg Morris & Kimberly F. Sellers, 2022. "A Flexible Mixed Model for Clustered Count Data," Stats, MDPI, vol. 5(1), pages 1-18, January.
    2. Fábio M. Bayer & Francisco Cribari‐Neto & Jéssica Santos, 2021. "Inflated Kumaraswamy regressions with application to water supply and sanitation in Brazil," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(4), pages 453-481, November.
    3. 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.
    4. Bilal Barakat, 2017. "Generalised count distributions for modelling parity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 36(26), pages 745-758.
    5. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    6. Gauss Cordeiro & Josemar Rodrigues & Mário Castro, 2012. "The exponential COM-Poisson distribution," Statistical Papers, Springer, vol. 53(3), pages 653-664, August.
    7. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    8. Yayan Hernuryadin & Koji Kotani & Tatsuyoshi Saijo, 2020. "Time Preferences of Food Producers: Does “Cultivate and Grow” Matter?," Land Economics, University of Wisconsin Press, vol. 96(1), pages 132-148.
    9. Alp Atakan & Mehmet Ekmekci & Ludovic Renou, 2021. "Cross-verification and Persuasive Cheap Talk," Papers 2102.13562, arXiv.org, revised Apr 2021.
    10. Mhamed Ben Salah & Cédric Chambru & Maleke Fourati, 2022. "The colonial legacy of education: evidence from of Tunisia," ECON - Working Papers 411, Department of Economics - University of Zurich, revised Sep 2024.
    11. Ameztegui, Aitor & Coll, Lluís & Messier, Christian, 2015. "Modelling the effect of climate-induced changes in recruitment and juvenile growth on mixed-forest dynamics: The case of montane–subalpine Pyrenean ecotones," Ecological Modelling, Elsevier, vol. 313(C), pages 84-93.
    12. Sokolova, Maria V., 2016. "Exchange Rates, International Trade and Growth: Re-Evaluation of Undervaluation," Conference papers 332790, Purdue University, Center for Global Trade Analysis, Global Trade Analysis Project.
    13. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    14. Grün, Bettina & Kosmidis, Ioannis & Zeileis, Achim, 2012. "Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i11).
    15. Ashrafi, M. & Khanjani, M.J. & Fadaei-Kermani, E. & Barani, G.A., 2015. "Farm drainage channel network optimization by improved modified minimal spanning tree," Agricultural Water Management, Elsevier, vol. 161(C), pages 1-8.
    16. Dries P.J. Kuijper & Jakub W. Bubnicki & Marcin Churski & Bjorn Mols & Pim van Hooft, 2015. "Context dependence of risk effects: wolves and tree logs create patches of fear in an old-growth forest," Behavioral Ecology, International Society for Behavioral Ecology, vol. 26(6), pages 1558-1568.
    17. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    18. Vincenzo Verardi, 2013. "Semiparametric regression in Stata," United Kingdom Stata Users' Group Meetings 2013 14, Stata Users Group.
    19. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2016. "No-arbitrage bounds for the forward smile given marginals," Papers 1603.06389, arXiv.org, revised Oct 2016.
    20. Szidarovszky, Ferenc & Luo, Yi, 2014. "Incorporating risk seeking attitude into defense strategy," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 104-109.

    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:testjl:v:31:y:2022:i:3:d:10.1007_s11749-022-00801-6. 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.