In this article, a copula-based method for mixed regression models is proposed, where the conditional distribution of the response variable, given covariates, is modelled by a parametric family of continuous or discrete distributions, and the effect of a common latent variable pertaining to a cluster is modelled with a factor copula. We show how to estimate the parameters of the copula and the parameters of the margins, and we find the asymptotic behaviour of the estimation errors. Numerical experiments are performed to assess the precision of the estimators for finite samples. An example of an application is given using COVID-19 vaccination hesitancy from several countries. Computations are based on R package CopulaGAMM.

翻译：摘要：本文提出了一种基于联结函数的混合回归模型方法，其中响应变量在给定协变量条件下的条件分布通过连续或离散分布的参数族进行建模，而集群中共同潜在变量的效应则通过因子联结函数进行建模。我们展示了如何估计联结函数的参数以及边际分布的参数，并得出了估计误差的渐近行为。通过数值实验评估了有限样本下估计量的精度。以多个国家COVID-19疫苗犹豫情况为例进行了应用分析。计算基于R包CopulaGAMM实现。