Multivariate response and parsimony for Gaussian cluster-weighted models

A family of parsimonious Gaussian cluster-weighted models (CWMs) is presented. This family concerns a multivariate extension to cluster-weighted modelling that can account for correlations between multivariate response. Parsimony is attained by constraining parts of an eigen-decomposition imposed on the component covariance matrices. A sufficient condition for identifiability is provided and an expectation-maximization algorithm is presented for parameter estimation. Model performance is investigated on both synthetic and classical real data sets and compared with some popular approaches. Finally, it is shown that accounting for linear dependencies in the presence of a linear regression structure offers better performance, vis-\`{a}-vis clustering, over existing methodologies.