Modeling and Multivariate Methods - SAS

Chapter 5 Fitting Multiple Response Models 163
Response Specification
Figure 5.4 Test Details
Table 5.6 Description of Test Details
Eigenvalue Lists the eigenvalues of the E – 1 H matrix used in computing the
multivariate test statistics.
Canonical Corr Lists the canonical correlations associated with each eigenvalue. This is the
canonical correlation of the transformed responses with the effects, corrected
for all other effects in the model.
Eigvec Lists the eigenvectors of the E – 1 H matrix, or equivalently of ( E + H) – 1 H .
The Centroid Plot
The Centroid Plot command (accessed from the red triangle next to Species) plots the centroids
(multivariate least squares means) on the first two canonical variables formed from the test space, as in
Figure 5.5. The first canonical axis is the vertical axis so that if the test space is only one dimensional the
centroids align on a vertical axis. The centroid points appear with a circle corresponding to the 95%
confidence region (Mardia, Kent, and Bibby, 1979). When centroid plots are created under effect tests,
circles corresponding to the effect being tested appear in red. Other circles appear blue. Biplot rays show the
directions of the original response variables in the test space.
Click the Centroid Val disclosure icon to show additional information, shown in Figure 5.5.
The first canonical axis with an eigenvalue accounts for much more separation than does the second axis.
The means are well separated (discriminated), with the first group farther apart than the other two. The first
canonical variable seems to load the petal length variables against the petal width variables. Relationships
among groups of variables can be verified with Biplot Rays and the associated eigenvectors.