Fitting Bivariate Mixed-Type Data via the Generalized Linear Exponential Cluster-Weighted Model

TL;DR

This paper introduces a generalized linear exponential cluster-weighted model for effectively clustering and modeling bivariate mixed-type data, utilizing EM algorithm for parameter estimation and BIC for model selection.

Contribution

The paper presents a novel extension of the cluster-weighted model tailored for bivariate mixed-type data, including a latent class model counterpart.

Findings

Successful application to artificial data demonstrating model flexibility.

Real data analysis confirms the model's practical usefulness.

Model selection guided by BIC effectively identifies optimal models.

Abstract

The cluster-weighted model (CWM) is a mixture model with random covariates which allows for flexible clustering and density estimation of a random vector composed by a response variable and by a set of covariates. In this class of models, the generalized linear exponential CWM is here introduced especially for modeling bivariate data of mixed-type. Its natural counterpart, in the family of latent class models, is also defined. Maximum likelihood parameter estimates are derived using the EM algorithm and model selection is carried out using the Bayesian information criterion (BIC). Artificial and real data are finally considered to exemplify and appreciate the proposed model.