Design of Experiments Guide • Mixture Designs • Fitting Mixture Designs
Previous
 • 
Next
Fitting Mixture Designs
When fitting a model for mixture designs, take into account that the factors sum to a constant; a traditional full linear model are not fully estimable.
The recommended response surface model is called the Scheffé polynomial (Scheffé 1958). See the discussion of Cox Mixtures and the Scheffé Cubic macro in the Fitting Linear Models book. The Scheffé polynomial model does the following:
•
suppresses the intercept
•
includes all the linear main-effect terms
•
excludes all the square terms (such as X1*X1)
•
includes all the cross terms (such as X1*X2)
To fit a model:
1.
Choose DOE > Mixture Design and make the design data table. To fit a model, the Y column in the data table must contain values. Either assign responses or select Simulate Responses from the red triangle menu before you click Make Table.
2.
The design data table stores the model in the data table as a table property. This table property is a JSL script called Model, located in the left panel of the table.
3.
Right-click the model and select Run Script to open the Fit Model launch window, which is automatically filled with the saved model.
4.
Click Run on the Fit Model window.
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.
The model report usually has several sections of interest, including the whole model tests, Analysis of Variance reports, and response surface reports, which are described below.
Whole Model Tests and Analysis of Variance Reports
In a whole-model Analysis of Variance table, JMP traditionally tests that all the parameters are zero except for the intercept. In a mixture model without an intercept, JMP looks for a hidden intercept, in the sense that a linear combination of effects is a constant. If it finds a hidden intercept, it does the whole model test with respect to the intercept model rather than a zero-intercept model. This test is equivalent to testing that all the parameters are zero except the linear parameters, and testing that they are equal.
The hidden-intercept property also causes the R2 to be reported with respect to the intercept model rather than reported as missing.
Understanding Response Surface Reports
When there are effects marked as response surface effects “&RS,” JMP creates additional reports that analyze the fitted response surface. These reports were originally designed for full response surfaces, not mixture models. However, JMP might encounter a no-intercept model and find a hidden intercept with linear response surface terms, but no square terms. Then it folds its calculations, collapsing on the last response surface term to calculate critical values for the optimum. This can be done for any combination that yields a constant and involves the last response surface term.