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A simple and useful regression model for fitting count data

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  • 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
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    1. 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.
    2. 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.
    3. 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.
    4. 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, September.
    5. 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.
    6. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
    7. 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.
    8. 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.
    9. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    10. 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.
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    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.

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