Copula-based mixtures of regression models for multivariate response data

Clustering is a powerful technique for uncovering hidden patterns or subgroups within complex datasets. Recently, the use of mixtures of multiple linear regression models has gained popularity due to their ability to account for underlying heterogeneity in regression-type data and to provide a comprehensive understanding of covariate impacts across latent subgroups. However, models tailored for a multivariate response are relatively rare, especially when the response variables are dependent. Copula regression addresses this issue by employing copulas to model dependencies between response variables. To address this need, a copula-based finite mixture of regression models is proposed for clustering and interpreting covariate effects in heterogeneous multivariate continuous response data. An expectation-conditional-maximization algorithm is used to estimate the model. Simulation studies and real-data analyses illustrate the improved clustering performance of the proposed models compared to existing methods.