Modeling and Multivariate Methods - SAS

42 Introduction to the Fit Model Platform Chapter 2
Construct Model Effects
Table 2.3 Descriptions of the Macros Options (Continued)
Scheffé Cubic
Radial
Creates main effects, interactions, and Scheffé Cubic terms.
When you fit a 3rd degree polynomial model to a mixture, you need to take
special care not to introduce even-powered terms because they are not
estimable. When you get up to a cubic model, this means that you cannot
specify an effect like X1*X1*X2. However, it turns out that a complete
polynomial specification of the surface should introduce terms of the form:
X1*X2*(X1 – X2)
which we call Scheffé Cubic terms.
In the Fit Model window, this macro creates a complete cubic model. The
Scheffé Cubic terms are included if you either (a) enter a 3 in the Degree
box, then do a “Mixture Response Surface” command on a set of mixture
columns, or (b) use the Scheffe Cubic command in the Macro button.
Fits a radial smoother using the selected variables. The number of knots is
the number of unique values of the smoothing variable. The smoother is
based on the automatic smoother in Ruppert, Wand, and Carroll (2003,
Chapter 13.4–13.5).
The GLIMMIX procedure in SAS/STAT can produce the same results if the
following options are included in the RANDOM statement:
• TYPE = RSMOOTH
• KNOTMETHOD = DATA
Response Surface Curvature
Often in industrial experiments, the goal is to find values for one or more factors that maximize or minimize
the response. JMP provides surface modeling with special reports that show the critical values, the surface
curvature, and a response contour plot.
The Response Surface selection in the Effect Macros popup menu automatically constructs all the linear,
quadratic, and cross product terms needed for a response surface model.
The same model can be specified using the Add and Cross buttons to create model effects in the Fit Model
dialog. You then select a model term and assign it the Response Surface effect attribute found in the
Attributes popup menu. The response surface effects show with &RS after their name in the Construct
Model Effects list, as shown in Figure 2.4.
Note: Curvature analysis is not shown for response surface designs of more than 20 factors in the Fit Model
platform. No error message or alert is given. All other analyses contained within the report are valid and are
shown. For additional information about response surface designs, see Design of Experiments.