Essentially, a Scheffe mixture model is a constrained regression. That is what throws off all of the regular statistics. The main component parameter estimates are constrained by the overall average of the data.

The Scheffe model for three components was created in this fashion:

For three components, a typical regression model would be y=b0 + b1x1 + b2x2 + b3x3. A design to estimate this model (for an unconstrained case) would be the three experiments that are pure component runs. (1, 0, 0), (0, 1, 0), and (0, 0, 1). But I have four parameters in the model. You cannot estimate four things with three trials. So, we rewrite the model as y = b0(x1+x2+x3) + b1x1 +b2x2 + b3x3. Essentially, just rewriting the intercept as b0 times a funny looking one. Multiplying out and regrouping gives the familiar Scheffe form: y = b1*x1 + b2*x2 + b3*x3. The stars indicate that they would be the original coefficients plus b0.

Because of the constraint, if a component has "no effect" (whatever that means in a mixture situation), then the parameter estimate would be the same as the overall mean. The response does not change along that axis of the mixture simplex. For this reason, component D has the largest effect. That parameter estimate of 0.2381 is the FURTHEST AWAY from the overall mean of the data 0.341875.

Although the profiler is helpful, you might also want to consider the Mixture Profiler that is available under the red triangle. That may help.

As for reading more about Scheffe models, the bible of mixture experimentation is the book **Experiments with Mixtures **by John Cornell. Very good book that goes into much more detail on how the Scheffe model was created, how to interpret it, and how to design mixture experiments to estimate such a model. It also discusses alternative mixture models, as the Scheffe model is just one approach to handle the mixture constraint.

Dan Obermiller