Modeling and Multivariate Methods - SAS

166 Fitting Multiple Response Models Chapter 5
Multivariate Tests
Figure 5.7 Multivariate Test Reports
The M Matrix report gives the response design that you specified. The M-transformed Parameter
Estimates report gives the original parameter estimates matrix multiplied by the transpose of the M matrix.
Note: Initially in this chapter, the matrix names E and H refer to the error and hypothesis cross products.
After specification of a response design, E and H refer to those matrices transformed by the response design,
which are actually M´EM and M´HM.
The Extended Multivariate Report
In multivariate fits, the sums of squares due to hypothesis and error are matrices of squares and cross
products instead of single numbers. And there are lots of ways to measure how large a value the matrix for
the hypothesis sums of squares and cross products (called H or SSCP) is compared to that matrix for the
residual (called E). JMP reports the four multivariate tests that are commonly described in the literature. If
you are looking for a test at an exact significance level, you may need to go hunting for tables in reference
books. Fortunately, all four tests can be transformed into an approximate F test. If the response design yields
a single value, or if the hypothesis is a single degree of freedom, the multivariate tests are equivalent and
yield the same exact F test. JMP labels the text Exact F; otherwise, JMP labels it Approx. F.
In the golf balls example, there is only one effect so the Whole Model test and the test for Brand are the
same, which show the four multivariate tests with approximate F tests. There is only a single intercept with
two DF (one for each response), so the F test for it is exact and is labeled Exact F.
The red triangle menus on the Whole Model, Intercept, and Brand reports contain options to generate
additional information, which includes eigenvalues, canonical correlations, a list of centroid values, a
centroid plot, and a Save command that lets you save canonical variates.
The effect (Brand in this example) popup menu also includes the option to specify contrasts.