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Title: Parsimonious seemingly unrelated linear cluster-weighted models for contaminated data Authors:  Gabriele Soffritti - University of Bologna (Italy)
Gabriele Perrone - Department of Statistical Sciences, University of Bologna (Italy) [presenting]
Abstract: Nowadays, in several areas, it is frequent for a researcher to be involved in the task of systematically extracting information from data sets that are too large or complex to be dealt with by traditional statistical methods. This is also true in multivariate linear regression analysis when samples are characterised by unobserved heterogeneity. A modern approach to this problem is represented by the Gaussian linear cluster-weighted models, which allow to simultaneously perform model-based cluster analysis and multivariate linear regression analysis with random predictors. Robustified models have been recently developed, based on the use of the contaminated Gaussian distribution, which can manage the presence of mildly atypical observations. A more flexible class of contaminated Gaussian linear cluster-weighted models is specified, in which the researcher is free to use a different vector of covariates for each response. The novel class also includes parsimonious models, where parsimony is attained by imposing suitable constraints on the component-covariance matrices of either the responses or the covariates. Identifiability conditions are illustrated and discussed. An expectation-conditional maximisation algorithm is provided for the maximum likelihood estimation of the model parameter. The effectiveness and usefulness of the proposed models are shown through the analysis of simulated and real datasets.