Clustering Bivariate Mixed-Type Data via the Cluster-Weighted Model

The cluster-weighted model (CWM) is a mixture model with random covariates that allows for flexible clustering/classification and distribution estimationof a random vector composed of a response variable and a set of covariates. Withinthis class of models, the generalized linear exponential CWMis here introduced especiallyfor modeling bivariate data of mixed-type. Its natural counterpart in the familyof latent class models is also defined. Maximum likelihood parameter estimates are derived using the expectation-maximization algorithm and some computational issuesare detailed. Through Monte Carlo experiments, the classification performance of the proposed model is compared with other mixture-based approaches, consistency of the estimators of the regression coefficients is evaluated, and several likelihood-basedinformation criteria are compared for selecting the number of mixture components. An application to real data is also finally considered.