RE: interpretation of WRES of logarithmically transformed data

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com Subject: RE: [NMusers] interpretation of WRES of logarithmically transformed data Date: 11/21/2003 8:28 AM Anthe, The log-transformed model assumes that the residual errors are additive with a constant variance, in your case, sigma2=THETA(10)2. Thus, to calculate the weighted (standardized) residuals you should divide the IRES by sigma (i.e., W=THETA(10)). If the assumptions of your model are correct, these IWRES should be unimodal and symmetric about zero with constant variance. Moreover, if the errors are normally distributed approximately 99% of the residuals should fall between 3 (within 3 standard deviations). Note, there is no need to transform these residuals back to the untransformed scale. Moreover, in doing so you lose the diagnostic properties (symmetry about zero and uniform variance). The whole point to doing the transformation is to find a scale in which it is reasonable to assume that EPS(1) has a symmetric distribution with constant variance. Untransforming the DVs and predictions (PREDs and IPREDs) to the original concentration scale are fine, however, evaluating the goodness of fit in terms of the deviations from the model fit should be performed in the log-transformed scale IF the assumptions of the log-transformed model are valid. Also, I would avoid arbitrarily fixing the prediction to -3 when DV=0. If your model must predict zero (i.e., F=0), such as when an ALAG parameter is included in the model, there is another parameterization of the log-transformed model that introduces a bias parameter to resolve the log(0) problem (see Beal, JPP 2001;28:481-504). There has also been discussion of the pros/cons of this model on Nmusers awhile ago so you might want to search the archives. Ken