Copula-based link functions in binary regression models

M. Mesfioui, T. Bouezmarni and M. Belalia ()
Additional contact information
M. Mesfioui: Université du Québec à Trois-Rivières
T. Bouezmarni: Université de Sherbrooke
M. Belalia: University of Windsor

Statistical Papers, 2023, vol. 64, issue 2, No 9, 557-585

Abstract: 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.

Keywords: Copula; Discrete response; Link function; Logistic regression; Semi-parametric estimation; Bootstrap (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-022-01330-y

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