A Skew-Normal Copula-Driven GLMM

TL;DR

This paper introduces a flexible method for fitting copula-driven generalized linear mixed models using a skew-normal copula, employing a Monte Carlo EM algorithm, demonstrated through simulations and real data analysis.

Contribution

It develops a novel estimation approach for copula-driven GLMMs with skew-normal copulas, enhancing modeling of dependence structures in mixed models.

Findings

Effective estimation demonstrated via simulations

Successful application to Framingham Heart Study data

Improved modeling of dependence in mixed models

Abstract

This paper presents a method for fitting a copula-driven generalized linear mixed models. For added flexibility, the skew-normal copula is adopted for fitting. The correlation matrix of the skew-normal copula is used to capture the dependence structure within units, while the fixed and random effects coefficients are estimated through the mean of the copula. For estimation, a Monte Carlo expectation-maximization algorithm is developed. Simulations are shown alongside a real data example from the Framingham Heart Study.