Análise do ajuste de modelos utilizando resíduos generalizados de Cox-Snell

Abstract

Once a model is chosen to explain a data set, the researcher is accepting the hypotheses that such data satisfy inherent assumptions of the proposed model. Then it, becomes important the evaluation of the fitted model to the data, so that the results, be reliable. One of the techniques used for such evaluation is residual analysis. Several kinds ofresiduais have been proposed for survival models; among those, the most suitable for this purpose are Cox-Snell (1968) generalized residuais. The objective of this work was to evaluate the adequacy of models by graphical diagnostics using Cox-Snell generalized residuais and to show the whole development in full detail for understanding and application of this theory. To illustrate the theory three appUcations were considered. The fírstapplication sought to illustrate the existent logic by plotting of ordered residuais of three distributions: normal (0,1), logistics (0,1) and extreme value (0,1), versus the expected order statistics of these residuais in consonance with the assumed distributions. The second application consisted of lifetime data of electric insulating, obtained by Nelson (1990). Starting from the verification by graphical diagnostics using Cox-Snell generalized residuais, it was found that the model appropriate for lifetime ofelectric insulating was lognormal. The third application referred to censored data of lifetime of patients, obtained by CoUett (1994). The adequacy of several models was evaluated by Cox-Snell generalized residuais adapted for survival data. The results show that Weibull model was the most appropriate.