Improved approximation for transformation diagnostics

The suitability of a normal linear regression model may require transformation of the original response, and transformation diagnostics are designed to detect the need for such transformation. A common approach to transformation diagnostics is to construct an artificial explanatory variable, which is then tested in the augmented linear regression model for the original response. This paper describes corresponding diagnostics based directly on score statistics with accurate approximations for their standard errors. Several transformation models are covered. Some numerical illustrations are given.