Double-power transformations to analyze data

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Title: Double-power transformations to analyze data
Author: Sato, Erika
Abstract: Power transformations are commonly used in order to fit simpler and/or more appropriate models to data. These transformations are well-known and well-documented for cases where the predictor variables are not linearly constrained, unlike mixture experiments. In the case of mixture designs, however, for which linear constraints do exist, several linear models proposed in recent literature fall into a power transformation family; this suggests that similar transformations might be useful for mixture experiments, as well. The log-likelihood function for X and y, transformations on the response and predictor variables, was derived for the mixture case where the predictor variables are linearly constrained and was maximized using a specially-written SAS program. To test the effectiveness of this procedure, simulations were done for two different designs and for four different combinations of X, and y. It was found that the 95% confidence region about A and f captured the true values of X and y approximately 90% of the time, regardless of the nature of the design or of the transformation. This procedure appeared to be able to discriminate between the different transformations on the response better than on the predictor variables, particularly when the correct transformation was the log-transformation (i.e., when y = 0). This could be due in part to the fact that the ranges of the predictors chosen was simply not large enough given the amount of replication used.
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Date: 1996-08

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