IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v63y2022i3d10.1007_s00362-021-01253-0.html
   My bibliography  Save this article

A simple and useful regression model for underdispersed count data based on Bernoulli–Poisson convolution

Author

Listed:
  • Marcelo Bourguignon

    (Universidade Federal do Rio Grande do Norte)

  • Diego I. Gallardo

    (Universidad de Atacama)

  • Rodrigo M. R. Medeiros

    (Universidade de São Paulo)

Abstract

Count data is often modeled using Poisson regression, although this probability model naturally restricts the conditional variance to be equal to the conditional mean (equidispersion property). While overdispersion has been intensively studied, there are few alternative models in the statistical literature for analyzing count data with underdispersion. The primary goal of this paper is to introduce a novel model based on Bernoulli-Poisson convolution for modelling count data that are underdispersed relative to the Poisson distribution. We study the statistical properties of the proposed model, and we provide a useful interpretation of the parameters. We consider a regression structure for both components based on a new parameterization indexed by mean and dispersion parameters. An expectation-maximization (EM) algorithm is proposed for parameter estimation and some diagnostic measures, based on the EM algorithm, are considered. Simulation studies are conducted to evaluate its finite sample performance. Finally, we illustrate the usefulness of the new regression model by an application.

Suggested Citation

  • Marcelo Bourguignon & Diego I. Gallardo & Rodrigo M. R. Medeiros, 2022. "A simple and useful regression model for underdispersed count data based on Bernoulli–Poisson convolution," Statistical Papers, Springer, vol. 63(3), pages 821-848, June.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:3:d:10.1007_s00362-021-01253-0
    DOI: 10.1007/s00362-021-01253-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-021-01253-0
    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/s00362-021-01253-0?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
    ---><---

    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. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    2. Marcelo Bourguignon & Diego I. Gallardo, 2020. "Reparameterized inverse gamma regression models with varying precision," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 611-627, November.
    3. Rigby, R.A. & Stasinopoulos, D.M. & Akantziliotou, C., 2008. "A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 381-393, December.
    4. Walmes Marques Zeviani & Paulo Justiniano Ribeiro & Wagner Hugo Bonat & Silvia Emiko Shimakura & Joel Augusto Muniz, 2014. "The Gamma-count distribution in the analysis of experimental underdispersed data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2616-2626, December.
    5. Winkelmann, Rainer, 1995. "Duration Dependence and Dispersion in Count-Data Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 467-474, October.
    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. Douglas Toledo & Cristiane Akemi Umetsu & Antonio Fernando Monteiro Camargo & Idemauro Antonio Rodrigues Lara, 2022. "Flexible models for non-equidispersed count data: comparative performance of parametric models to deal with underdispersion," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(3), pages 473-497, September.
    2. 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.
    3. Alejandra Tapia & Victor Leiva & Maria del Pilar Diaz & Viviana Giampaoli, 2019. "Influence diagnostics in mixed effects logistic regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 920-942, September.
    4. Russo, Cibele M. & Paula, Gilberto A. & Aoki, Reiko, 2009. "Influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4143-4156, October.
    5. Antony Andrews & Omphile Temoso & Sean Kimpton, 2021. "Persistent and Transient Inefficiency of Australian States and Territories in Providing Public Hospital Services: An Application of Bayesian Stochastic Finite Mixture Frontier Analysis," Economic Papers, The Economic Society of Australia, vol. 40(2), pages 104-115, June.
    6. Eugenio J. Miravete, 2004. "The Doubtful Profitability of Foggy Pricing," Working Papers 04-07, NET Institute.
    7. Gurmu, Shiferaw & Rilstone, Paul & Stern, Steven, 1998. "Semiparametric estimation of count regression models1," Journal of Econometrics, Elsevier, vol. 88(1), pages 123-150, November.
    8. Rainer Winkelmann & Klaus Zimmermann, 1998. "Is job stability declining in Germany? Evidence from count data models," Applied Economics, Taylor & Francis Journals, vol. 30(11), pages 1413-1420.
    9. Azizpour, S & Giesecke, K. & Schwenkler, G., 2018. "Exploring the sources of default clustering," Journal of Financial Economics, Elsevier, vol. 129(1), pages 154-183.
    10. Stefano Mainardi, 2003. "Testing convergence in life expectancies: count regression models on panel data," Prague Economic Papers, Prague University of Economics and Business, vol. 2003(4), pages 350-370.
    11. Xiaowen Dai & Libin Jin & Maozai Tian & Lei Shi, 2019. "Bayesian Local Influence for Spatial Autoregressive Models with Heteroscedasticity," Statistical Papers, Springer, vol. 60(5), pages 1423-1446, October.
    12. Xiaowen Dai & Libin Jin & Lei Shi & Cuiping Yang & Shuangzhe Liu, 2016. "Local influence analysis in general spatial models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 313-331, July.
    13. R.A.B. Assumpção & M.A. Uribe-Opazo & M. Galea, 2014. "Analysis of local influence in geostatistics using Student's t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2323-2341, November.
    14. Lee, Sik-Yum & Lu, Bin & Song, Xin-Yuan, 2006. "Assessing local influence for nonlinear structural equation models with ignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1356-1377, March.
    15. Fernanda De Bastiani & Audrey Mariz de Aquino Cysneiros & Miguel Uribe-Opazo & Manuel Galea, 2015. "Influence diagnostics in elliptical spatial linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 322-340, June.
    16. Eugenio J. Miravete, 2009. "Competing with Menus of Tariff Options," Journal of the European Economic Association, MIT Press, vol. 7(1), pages 188-205, March.
    17. Reutterer, Thomas & Platzer, Michael & Schröder, Nadine, 2021. "Leveraging purchase regularity for predicting customer behavior the easy way," International Journal of Research in Marketing, Elsevier, vol. 38(1), pages 194-215.
    18. Alison L. Booth & Hiau Joo Kee, 2009. "Intergenerational Transmission of Fertility Patterns," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(2), pages 183-208, April.
    19. Helton Saulo & Alan Dasilva & Víctor Leiva & Luis Sánchez & Hanns de la Fuente‐Mella, 2022. "Log‐symmetric quantile regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(2), pages 124-163, May.
    20. John D. Rice & Robert L. Strawderman & Brent A. Johnson, 2018. "Regularity of a renewal process estimated from binary data," Biometrics, The International Biometric Society, vol. 74(2), pages 566-574, 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:63:y:2022:i:3:d:10.1007_s00362-021-01253-0. 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.