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Regression in a copula model for bivariate count data

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  • Aristidis Nikoloulopoulos
  • Dimitris Karlis

Abstract

In many cases of modeling bivariate count data, the interest lies on studying the association rather than the marginal properties. We form a flexible regression copula-based model where covariates are used not only for the marginal but also for the copula parameters. Since copula measures the association, the use of covariates in its parameters allow for direct modeling of association. A real-data application related to transaction market basket data is used. Our goal is to refine and understand whether the association between the number of purchases of certain product categories depends on particular demographic customers' characteristics. Such information is important for decision making for marketing purposes.

Suggested Citation

  • Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:9:p:1555-1568
    DOI: 10.1080/02664760903093591
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    References listed on IDEAS

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    9. Peter Berkhout & Erik Plug, 2004. "A bivariate Poisson count data model using conditional probabilities," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(3), pages 349-364, August.
    10. Nikoloulopoulos, Aristidis K. & Karlis, Dimitris, 2008. "Copula model evaluation based on parametric bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3342-3353, March.
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    Citations

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    Cited by:

    1. Marra, Giampiero & Wyszynski, Karol, 2016. "Semi-parametric copula sample selection models for count responses," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 110-129.
    2. Bermúdez, Lluís & Karlis, Dimitris, 2012. "A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3988-3999.
    3. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    4. Hendrik van der Wurp & Andreas Groll, 2023. "Introducing LASSO-type penalisation to generalised joint regression modelling for count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 127-151, March.
    5. Giampiero Marra & Matteo Fasiolo & Rosalba Radice & Rainer Winkelmann, 2023. "A flexible copula regression model with Bernoulli and Tweedie margins for estimating the effect of spending on mental health," Health Economics, John Wiley & Sons, Ltd., vol. 32(6), pages 1305-1322, June.
    6. M. Mesfioui & T. Bouezmarni & M. Belalia, 2023. "Copula-based link functions in binary regression models," Statistical Papers, Springer, vol. 64(2), pages 557-585, April.
    7. Tzougas, George & Pignatelli di Cerchiara, Alice, 2021. "The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 602-625.
    8. Faugeras Olivier P., 2017. "Inference for copula modeling of discrete data: a cautionary tale and some facts," Dependence Modeling, De Gruyter, vol. 5(1), pages 121-132, January.
    9. 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.
    10. Giampiero Marra & Rosalba Radice & David Zimmer, 2021. "Did the ACA's “guaranteed issue” provision cause adverse selection into nongroup insurance? Analysis using a copula‐based hurdle model," Health Economics, John Wiley & Sons, Ltd., vol. 30(9), pages 2246-2263, September.
    11. 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.
    12. Giampiero Marra & Rosalba Radice & David M. Zimmer, 2020. "Estimating the binary endogenous effect of insurance on doctor visits by copula‐based regression additive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 953-971, August.
    13. Mamode Khan Naushad & Rumjaun Wasseem & Sunecher Yuvraj & Jowaheer Vandna, 2017. "Computing with bivariate COM-Poisson model under different copulas," Monte Carlo Methods and Applications, De Gruyter, vol. 23(2), pages 131-146, June.
    14. Chen, Zezhun Chen & Dassios, Angelos & Tzougas, George, 2024. "EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects," LSE Research Online Documents on Economics 118826, London School of Economics and Political Science, LSE Library.

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