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Title: Generalized additive cluster weighted model Authors:  Stefano Barberis - University of Milano Bicocca (Italy) [presenting]
Salvatore Ingrassia - University of Catania (Italy)
Giorgio Vittadini - University Milano Bicocca (Italy)
Abstract: An extension of mixture models with random covariates related to the Cluster Weighted Model (CWM) is presented for model-based clustering applications. The Generalized Additive Cluster Weighted Model (GAM-CWM) is a flexible model, able to capture complex relations between a response variable and a set of covariates in each mixture component. The main difference between models related to the CWM and other mixture models is that in CWM the joint probability $p(x,y)$ of a response variable $y$ and a set of explanatory variables $x$ is modelled in each mixture component rather than the conditional $p(y|x)$. The theory of generalized additive model extends the generalized linear model precisely with the aim of making it more flexible introducing a sum of smooth functions of covariates in the linear predictor. In the same way GAM-CWM extends the generalized linear CWM and the polynomial CWM defining a new powerful and very general class of models where the principles of CWM model and the GAM model are combined together. Maximum likelihood estimates are provided via EM algorithm and model selection is carried out using Bayesian Information Criterion (BIC) and Integrated Completed Likelihood (ICL). With simulated and real data are investigated performances, limits and benefits comparing this model with other mixture models related to it.