Diagnostics and Robust Estimation When Transforming the Regression Model and the Response

Abstract

In regression analysis, the response is often transformed to remove heteroscedasticity and/or skewness. When a model already exists for the untransformed response, then it can be preserved by applying the same transform to both the model and the response. This methodology, which we call “transform both sides,” has been applied in several recent papers and appears highly useful in practice. When a parametric transformation family such as the power transformations is used, then the transformation can be estimated by maximum likelihood. The maximum likelihood estimator, however, is very sensitive to outliers. In this article, we propose diagnostics to indicate cases influential for the transformation or regression parameters. We also propose a robust bounded-influence estimator similar to the Krasker-Welsch regression estimator:

KEY WORDS:

• Power transformations
• Bounded-influence estimator
• M estimation
• Casedeletion diagnostics
• Nonlinear models
• Fisheries analysis