Matrix-variate cluster-weighted bilinear factor analyzers

Abstract We develop a unified framework comprising two families of parsimonious models for matrix-variate data, combining the Cluster-Weighted Model (CWM) approach with a bilinear factor-analytic structure. The two families impose factor-analytic constraints on the covariance matrices of either the response or the covariates, resulting in 64 parsimonious configurations for each case. Parameter estimation is performed via an AECM algorithm and implemented in the publicly available MatFacReg package for the R language. Through simulation studies, we evaluate the capability of information criteria to recover the correct model structure, number of components, and latent factors. Estimation accuracy and computational efficiency are also investigated. In an empirical analysis of greenhouse-gas emissions from the agri-food sector, the proposed models achieve superior fit compared to the standard matrix-variate CWM, which does not impose any factor-analytic constraints, revealing four groups of countries mainly differentiated by energy use and population size.