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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. 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.
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    4. 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.
    5. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
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    Cited by:

    1. Saeed Aldahmani & Othmane Kortbi & Mhamed Mesfioui, 2024. "Copula-Based Regression with Mixed Covariates," Mathematics, MDPI, vol. 12(22), pages 1-15, November.

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