Maximum Likelihood Estimation of Gaussian Cluster Weighted Models and\n Relationships with Mixtures of Regression

2012/07/12 by Salvatore Ingrassia, Ingrassia, Salvatore, Simona C. Minotti +1
Computer Science · Mathematics · #Advanced Clustering Algorithms Research #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences

paper · pdf · doi:10.48550/arxiv.1207.3106

openalex publication_date 2012/07/12 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

Cluster-weighted modeling (CWM) is a mixture approach for modeling the joint\nprobability of a response variable and a set of explanatory variables. The\nparameters are estimated by means of the expectation-maximization algorithm\naccording to the maximum likelihood approach. Under Gaussian assumptions, we\nanalyse the complete-data likelihood function of cluster weighted models.\nFurther, under suitable hypotheses we show that the maximization of the\nlikelihood function of Gaussian cluster weighted models leads to the same\nparameter estimates of finite mixtures of regression and finite mixtures of\nregression with concomitant variables. In this sense, the latter ones can be\nconsidered as nested models of Gaussian cluster weighted models.\n

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