Flexible mixture modelling with the polynomial Gaussian cluster-weighted model. (June 2014)

• Record Type: Journal Article
• Authors: Punzo, Antonio
• Is Part Of: Statistical modelling. Volume 14:Number 3(2014)
• Page Start: 257
• Page End: 291
• Publication Date: 2014-06
• Subjects: mixtures of distributions -- mixtures of regressions -- EM algorithm -- polynomial regression -- model-based clustering -- model-based classification -- random covariates -- cluster-weighted models; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X13503455
• Languages: English
• ISSNs: 1471-082X

Abstract

In the context of mixture models with random covariates, this article presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. First, it allows for possible nonlinear dependencies in the mixture components by considering a polynomial regression. Second, it is not restricted to be used for model-based clustering only being contextualized in the most general model-based classification framework. Maximum likelihood parameter estimates are derived using the EM algorithm and model selection is carried out using the Bayesian information criterion (BIC) and the integrated completed likelihood (ICL). The article also investigates the conditions under which the posterior probabilities of component-membership from a polynomial Gaussian CWM coincide with those of other well-established mixture-models which are related to it. When applied to artificial and real data, the polynomial Gaussian CWM has shown to outperform the mixture of polynomial Gaussian regressions, which is its natural competitor in the class of mixture models with fixed covariates.