Regression Transformation Diagnostics Using Local Influence

Abstract Following Box and Cox (1964), the use of transformations in regression analysis is now common; recently there has been emphasis on diagnostic methods for transformation, much of which has involved deletion of data cases. Summaries were given by Cook and Weisberg (1982) and Atkinson (1985). This article obtains diagnostics for the estimated regression parameter of the Box-Cox transformation of the response variable in the linear model. Instead of deleting cases, the more general notions of perturbing assumptions of the model, or components of the data, are employed, as in the local-influence approach of Cook (1986). The diagnostics then arise from local changes to the transformation parameter estimate caused by small perturbations; the case direction in which small perturbations have the greatest effect is the main diagnostic quantity. An appeal of the approach is that it allows simultaneous perturbations affecting all data cases, not just one-at-a-time deletions; it can thus point to groups of in...