Diagnostic Tests for Transformations

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Abstract
The evidence for transformation of the response in a regression model may sometimes depend crucially on one or a few observations. Expressions are derived for estimating the effect of deletion of observations on both the score test and the estimate of the transformation parameter. The estimates are presented as index plots, which are as easy to calculate as the wellknown added-variable plots of constructed variables. One advantage of the new procedure is that the importance of individual observations is not masked by the presence of leverage. A second is that the plots refer directly to score statistics and parameter estimates, both quantities of prime inferential importance. Examples are given for the power transformation and for the shifted power transformation with unknown origin.

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