  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.
