Joint regression analysis of correlated data using Gaussian copulas

This article concerns a new joint modeling approach for correlated data analysis. Utilizing Gaussian copulas, we present a unified and flexible machinery to integrate separate one-dimensional generalized linear models (GLMs) into a joint regression analysis of continuous, discrete, and mixed correlated outcomes. This essentially leads to a multivariate analogue of the univariate GLM theory and hence an efficiency gain in the estimation of regression coefficients. The availability of joint probability models enables us to develop a full maximum likelihood inference. Numerical illustrations are focused on regression models for discrete correlated data, including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes. In the simulation studies, the proposed copula-based joint model is compared to the popular generalized estimating equations, which is a moment-based estimating equation method to join univariate GLMs. Two real-world data examples are used in the illustration.