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On the bivariate negative binomial regression model

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  • Felix Famoye

Abstract

In this paper, a new bivariate negative binomial regression (BNBR) model allowing any type of correlation is defined and studied. The marginal means of the bivariate model are functions of the explanatory variables. The parameters of the bivariate regression model are estimated by using the maximum likelihood method. Some test statistics including goodness-of-fit are discussed. Two numerical data sets are used to illustrate the techniques. The BNBR model tends to perform better than the bivariate Poisson regression model, but compares well with the bivariate Poisson log-normal regression model.

Suggested Citation

  • Felix Famoye, 2010. "On the bivariate negative binomial regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 969-981.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:6:p:969-981
    DOI: 10.1080/02664760902984618
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    Citations

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    Cited by:

    1. Dong, Chunjiao & Nambisan, Shashi S. & Richards, Stephen H. & Ma, Zhuanglin, 2015. "Assessment of the effects of highway geometric design features on the frequency of truck involved crashes using bivariate regression," Transportation Research Part A: Policy and Practice, Elsevier, vol. 75(C), pages 30-41.
    2. Lluís Bermúdez & Dimitris Karlis, 2022. "Copula-based bivariate finite mixture regression models with an application for insurance claim count data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1082-1099, December.
    3. David B. Audretsch & Albert N. Link & Martijn Hasselt, 2019. "Knowledge begets knowledge: university knowledge spillovers and the output of scientific papers from U.S. Small Business Innovation Research (SBIR) projects," Scientometrics, Springer;Akadémiai Kiadó, vol. 121(3), pages 1367-1383, December.
    4. Mauro Laudicella & Paolo Li Donni, 2022. "The dynamic interdependence in the demand of primary and emergency secondary care: A hidden Markov approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 521-536, April.
    5. Mathews Joseph & Bhattacharya Sumangal & Sen Sumen & Das Ishapathik, 2022. "Multiple inflated negative binomial regression for correlated multivariate count data," Dependence Modeling, De Gruyter, vol. 10(1), pages 290-307, January.
    6. Su Pei-Fang & Mau Yu-Lin & Guo Yan & Li Chung-I & Liu Qi & Boice John D. & Shyr Yu, 2017. "Bivariate Poisson models with varying offsets: an application to the paired mitochondrial DNA dataset," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(1), pages 47-58, March.
    7. Tzougas, George & Makariou, Despoina, 2022. "The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," LSE Research Online Documents on Economics 117197, London School of Economics and Political Science, LSE Library.
    8. Jiang, Yan & Kim, Jeeyeon & Choi, Jeonghye & Kang, Moon Young, 2020. "From clicks to bricks: The impact of product launches in offline stores for digital retailers," Journal of Business Research, Elsevier, vol. 120(C), pages 302-311.
    9. Felix Famoye & Carl Lee, 2017. "Exponentiated-exponential geometric regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 2963-2977, December.
    10. George Tzougas & Despoina Makariou, 2022. "The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 25(4), pages 401-417, December.
    11. Lluís Bermúdez & Dimitris Karlis, 2021. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    12. Koopman, Siem Jan & Lit, Rutger, 2019. "Forecasting football match results in national league competitions using score-driven time series models," International Journal of Forecasting, Elsevier, vol. 35(2), pages 797-809.
    13. Jacek Osiewalski & Jerzy Marzec, 2019. "Joint modelling of two count variables when one of them can be degenerate," Computational Statistics, Springer, vol. 34(1), pages 153-171, March.

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