ANÁLISE DE DIAGNÓSTICO EM MODELOS DE REGRESSÃO NORMAL E LOGÍSTICA

Abstract

The diagnostic analysis of the quality of the fit is an important phase in regression models, especially with regard to the occurrence of outliers, which can cause substantial distortions in the estimated parameters of the model. In this work, two innovative methods were approached in this area: the method of local influence, which was initially proposed by Cook (1986) and the maximum inclination, proposed by Billor and Loynes (1993). Cook's proposal consists of assessing the normal curvature of a surface, based on the Likelihood Displacement measure (spacing by likelihood), under a small disturbance in the model. Then, Billor and Loynes's (1993) approach was presented, who applied a measure of distance due to the modified likelihood. Thus, the maximum slope is used as a measure of the influence of outliers on the model. Initially, Billor and Loynes's (1993) proposal was applied to the normal model, this proposal was also developed for the logistic model. Two applications were presented, in which diagnostic analysis techniques of the quality of the adjustment were used, by means of graphs and the two proposals: local influence and maximum inclination. In the case of the simple linear normal model, the normal curvature and the maximum inclination showed the same sensitivity in the indication of influential observations. In the second application, the techniques used in this work, did not show a consistent indication in relation to any observation, however some graphics coincided with the indication of observation 13, as the one that stands out the most, being away from the others.