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An appropriate response surface model for mixture responses is the Scheffé polynomial (Scheffé 1958). See the discussion of Cox Mixtures and the Scheffé Cubic macro in Cox Mixtures in the Fitting Linear Models book. The Scheffé polynomial model does the following:
In this model, the parameters are easy to interpret (Cornell 1990). The coefficients on the linear terms are the fitted response at the extreme points where the mixture consists of a single factor. The coefficients on the cross terms indicate the curvature across each edge of the factor space.
For a mixture model with third-degree polynomial terms, the Scheffé Cubic model can be used. The Scheffé Cubic model includes terms of the form X1*X2*(X1-X2).

Help created on 3/19/2020