Modelagem bayesiana flexível em regressão com erros nas variáveis

Abstract

In regression models, the classical normal assumption for the distribution of the measurement errors is often violated, masking some important features of the variability of the data. Some practical actions to overcome this problem, like transformations of the data, sometimes are not effective. In this work we propose a methodology to overcome this problem, in the context of multivariate linear regression with measurement errors. In these models, the covariate is unobservable and the researcher observes a surrogate variable. These measurements are made with an additive error. We extend the classical normal model, by modeling jointly the covariate and the measurement errors by a finite mixture of densities which are in a general family, accommodating skewness, heavy tails and multi-modality at the same time, allowing a degree of flexibility that can not be met by the normal model. We proceed Bayesian inference through a Gibbs-type algorithm. Some proposed models are compared with existing symmetrical models, using a modified DIC criterion, through the analysis of simulated and real data.