The Generalized Linear Mixed Cluster-Weighted Model

Cluster-weighted models (CWMs) are a flexible family of mixture models for fitting the joint distribution of a random vector composed of a response variableand a set of covariates. CWMs act as a convex combination of the products ofthe marginal distribution of the covariates and the conditional distribution of the responsegiven the covariates. In this paper, we introduce a broad family of CWMs inwhich the component conditional distributions are assumed to belong to the exponentialfamily and the covariates are allowed to be of mixed-type. Under the assumptionof Gaussian covariates, sufficient conditions for model identifiability are provided.Moreover, maximum likelihood parameter estimates are derived using the EM algorithm.Parameter recovery, classification assessment, and performance of someinformation criteria are investigated through a broad simulation design. An applicationto real data is finally presented, with the proposed model outperforming otherwell-established mixture-based approaches.