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：本文提出一种基于连接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，而属于同一集群的公共潜变量效应则通过因子连接函数建模。我们展示了如何估计连接函数参数与边缘分布参数，并推导了估计误差的渐近性质。通过数值实验评估有限样本下估计量的精度，并以多国COVID-19疫苗接种犹豫数据为例进行应用分析。计算基于R包CopulaGAMM实现。