Estimação Bayesiana em modelos de mistura de regressões com censura ou dados faltantes utilizando misturas de escala de distribuições normais assimétricas

Abstract

The use of mixed regression models comes from the need to study data with heterogeneous behavior, where there are distinct populations (groups), whose linear relationships between the response variable and the predictor variables differ, between the groups, by the coefficients of the regression model. In this context, it is very common to use models of mixtures in which the components have a normal distribution, but the use of distributions from a family of Scale Mixture of Skew-Normal - SMSN, instead of the normal distribution, it is a common practice when the data have characteristics such as asymmetry and heavy tails, aspects that the normal model does not support. The absence or loss of some observations in a data set is a very important pattern and is much discussed in the literature. If such data are not treated correctly, for example, when they are ignored, they can cause great damage to the parameter estimates. For this reason, in part of this text, we propose the use of mixtures of regression models whose errors are distributed from the SMSN family, as a way of adjusting this type of data, specifically when absences are found in the response variable and in the covariates. Another enough recurrent problem refers to the existence of a censored structure in the response variables within each group. We propose to deal with these problems using a mixture of tobit models with random errors distributed in the SMSN family. The modeling using this family also accommodates possible multimodal behaviors generated by the structure of the groups. We developed an MCMC algorithm to perform Bayesian estimation. The proposed models are compared with their symmetric equivalents, such as those contained in the SMN (scale mixtures of normal) family, using some model selection criteria. We show the efficiency of the proposed method through the analysis of simulated and real data.