Diagnostics in Transformation and Weighted Regression

Abstract

We describe a diagnostic method for assessing the influence of an individual case on the transformation power estimator in the Box–Cox regression model and transform-both-sides regression model (Carroll and Ruppert 1988). We compare the method to those proposed by Cook and Wang (1983) and Hinkley and Wang (1988). The new method takes into account the deletion effect on the Jacobian of the variable's transformation. It provides a more accurate and reliable transformation power estimator. We also extend this method to analyze the case influence on the weighted parameter estimators in both the weighted regression model and the transformed and weighted regression model. Several examples are used to illustrate the results.