Extensões do resíduo quantílico

Abstract

Regression models have profound importance in analyses that aim to investigate the relationship between a dependent variable and a set of predictor variables. The diagnostic analysis is a fundamental step in validating a regression model, whose objectives are to identify possible discrepant and/or influential points and to verify possible deviations from the assumptions made for modeling. In this case, it is desirable to obtain residuals whose distribution is close to the standard Normal distribution, since their properties and behavior are known. The quantile residual is an important class of residuals with this characteristic, where its distribution is asymptotically standard Normal when the model parameters are consistently estimated. Another common problem in regression analysis is model selection, which consists in selecting the best theoretical model from a set of candidate models. The objective of this work is to develop extensions of the quantile residuals, in aspects of diagnostic analysis and model selection. To check the model fit, an asymptotically distributed standard Normal residual is introduced, which can be used for any parametric circular-linear regression model. For the detection of possible outliers, an extension is proposed on two and three-point inflated beta regression models, whose tail distribution is similar to the standard Normal distribution. Finally, three model selection criteria are introduced by testing goodness of fit using the quantile residuals in a specific context of response variable distribution selection in generalized additive models for location, scale and shape (GAMLSS).