Abstract:

Power transformations are commonly used in order to fit simpler and/or more appropriate
models to data. These transformations are wellknown and welldocumented 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 loglikelihood
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 speciallywritten 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 logtransformation
(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. 