Residuals and Functional Form in Accelerated Life Regression Models

Abstract

This thesis examines misspecifed log-location-scale regression models. Particularily how the models' Cox Snell residuals can be used to infer the functional form of possibly misspecified covariates in the regression. Two different methods are considered. One is using a transformation of the expected value of the residuals. The second is based on estimating the hazard rate function of the residuals using the covariate order method. Simulations and computations in the statistical computing environment R are used to obtain relevant and illustrative results. The conclusion is that both methods are able to recover the functional form of a misspecified covariate, but the covariate order method is best when high levels of censoring are introduced. The Kullback Leibler theory, applied to misspecified regression models, is a part of the basis for the investigations. The thesis shows that a theoretical approach to this theory is consistent with the methods used in R.