Misturas finitas de especialistas de modelos de regressão para dados complexos

Abstract

Traditional regression models start from the premise that all individuals have the same relationship between the explanatory and response variables, but this does not apply to heterogeneous populations. In this context, finite mixtures of regression models aim to identify unobservable groups that behave differently, allowing heterogeneity to be addressed. This paper explores the field of finite regression mixtures, with an emphasis on asymmetric and/or heavy-tailed distributions, which make it possible to build robust models for complex data. The innovation proposed in this study lies in the inclusion of information that improves classification and helps interpret the groups identified, known as expert mixtures. The proposed models were represented hierarchically, along with the corresponding likelihood function, allowing the EM (Expectation-Maximization) algorithm to be applied to obtain the maximum likelihood estimators. Simulation studies were carried out to assess the effectiveness of the algorithm in recovering the parameters. Finally, the proposed model was applied to two sets of real data in order to demonstrate its practical application and the interpretation of the results obtained.