Statistical Papers ( IF 1.3 ) Pub Date : 2022-06-14 , DOI: 10.1007/s00362-022-01330-y M. Mesfioui, T. Bouezmarni, M. Belalia
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.
中文翻译:
二元回归模型中基于 Copula 的链接函数
本文提出了一类新的基于 copula 模型的广义二元回归链接函数。这个想法包括根据边际分布和 copula 的条件分布来编写预测成功概率 (PPOS)。建议的链接函数提供了灵活的模型并包括概率回归。在单个协变量的情况下,也建立了与逻辑回归的显着关系。为了对 PPOS 进行建模,需要考虑 copula 的参数族,并使用边缘分布的参数或非参数估计量。建立了这些估计器的渐近特性,并进行了模拟研究以评估它们的性能。最后,通过分析烧伤数据集来说明该方法。