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Copula-based link functions in binary regression models

Author

Listed:
  • M. Mesfioui

    (Université du Québec à Trois-Rivières)

  • T. Bouezmarni

    (Université de Sherbrooke)

  • M. Belalia

    (University of Windsor)

Abstract

The paper proposes a new class of link functions for generalized binary regression based on copula models. The idea consists of writing the predictive probability of success (PPOS) in terms of marginal distributions and the conditional distribution for the copula. The proposed link functions provide flexible models and include the probit regression. A remarkable relationship with the logistic regression is also established in the case of a single covariate. To model the PPOS, a parametric family for the copula is considered and either a parametric or a nonparametric estimator for the marginal distributions is used. The asymptotic properties of these estimators are established and a simulation study is carried out to evaluate their performance. Finally, the methodology is illustrated by analyzing a data set on burn injury.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:2:d:10.1007_s00362-022-01330-y
    DOI: 10.1007/s00362-022-01330-y
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    References listed on IDEAS

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    1. Chang, Bo & Joe, Harry, 2019. "Prediction based on conditional distributions of vine copulas," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 45-63.
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    4. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    5. Eric Bouye & Mark Salmon, 2009. "Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 721-750.
    6. Roger M. Cooke & Harry Joe & Bo Chang, 2020. "Vine copula regression for observational studies," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 141-167, June.
    7. Dißmann, J. & Brechmann, E.C. & Czado, C. & Kurowicka, D., 2013. "Selecting and estimating regular vine copulae and application to financial returns," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 52-69.
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