Quality of the log transformation for an incorrectly assumed error structure

Abstract

A log transformation is often applied to nonlinear models with an assumed multiplicative error structure. Then the parameters are estimated using ordinary least squares (o. l. s. ) and back transformed predictions made. This paper examines the bias involved with this procedure when the actual error structure is additive and not multiplicative, A correction factor is introduced to help reduce the bias when the back transformed o. l. s. approach is used. We strongly suggest, however, that one should use nonlinear least squares when the analyst believes he is working with an additive error structure.

Keywords:

• transformations
• ordinary least squares regression
• nonlinear regression