Copula-Based Mixtures of Regression Models for Multivariate Response Data

Abstract

In recent years, the use of mixtures of regression models in clustering has gained popularity due to its ability to account for underlying heterogeneity and provide representative interpretations of covariate effects. However, there's a paucity of such models for data with dependent multivariate responses. One approach that has been applied in the case is copula regression models. Copulas are joint distribution functions with uniform margins and can be seen as representing the dependence structure of a random vector. In copula regression, a copula is employed to induce dependence between different responses through the random error term.

In this work, we propose a finite mixture of copula regression models for clustering and interpreting covariate effects in heterogeneous multivariate continuous response data. An ECM algorithm is introduced for estimation. The model's performance is tested through simulations and data analysis on the morphological properties of crabs, demonstrating improved results compared to existing methods.