The response design forms the M matrix. The columns of an M matrix define a set of transformation variables for the multivariate analysis. The Choose Response button contains the options for the M matrix.
The most typical response designs are Repeated Measures and Identity for multivariate regression. There is little difference in the tests given by the Contrast, Helmert, Profile, and Mean options, since they span the same space. However, the tests and details in the Least Squares means and Parameter Estimates tables for them show correspondingly different highlights.
The Repeated Measures and the Compound options display dialogs to specify response effect names. They then fit several response functions without waiting for further user input. Otherwise, selections expand the control panel and give you more opportunities to refine the specification.
Set up custom tests of effect levels using the Custom Test option.
Note: For instructions on how to create custom tests, see Custom Test in Standard Least Squares Report and Options.
Saves variables called Canon[1], Canon[2], and so on, as columns in the current data table. These columns have both the values and their formulas. For an example, see Save Canonical Scores. For technical details, see Canonical Details.


Note: The Contrast command is the same as for regression with a single response. See the LSMeans Contrast in Standard Least Squares Report and Options, for a description and examples of the LSMeans Contrast commands.

1.

The Iris data (Mardia, Kent, and Bibby 1979) have three levels of Species named Virginica, Setosa, and Versicolor. There are four measures (Petal length, Petal width, Sepal length, and Sepal width) taken on each sample.
2.

Select Analyze > Fit Model.

3.

4.

5.

6.

Click Run.

7.

8.

Click Run.

9.

From the red triangle menu next to Species, select Test Details.

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 Centroid Plot and Centroid Values. 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. See Details for Centroid Plot.
Click the Centroid Val disclosure icon to show additional information, shown in Centroid Plot and Centroid Values.
Saves columns called Canon[i] to the data table, where i refers to the ith canonical score for the Y variables. The canonical scores are computed based on the matrix used to construct the multivariate test statistic. Canonical scores are saved for eigenvectors corresponding to nonzero eigenvalues.
1.

2.

From the red triangle menu next to Whole Model, select Test Details.

3.

From the red triangle menu next to Whole Model, select Save Canonical Scores.

The details list the canonical correlations (Canonical Corr) next to the eigenvalues. The saved variables are called Canon[1], Canon[2], and so on. These columns contain both the values and their formulas.
To obtain the canonical variables for the X side, repeat the same steps, but interchange the X and Y variables. If you already have the columns Canon[n] appended to the data table, the new columns are called Canon[n] 2 (or another number) that makes the name unique.
1.

2.

Select Analyze > Fit Model.

3.

4.

5.

6.

Click Run.

7.

8.

Click Run.

9.

From the red triangle menu next to Whole Model, select Test Details.

10.

From the red triangle menu next to Whole Model, select Save Canonical Scores.

The output canonical variables use the eigenvectors shown as the linear combination of the Y variables. For example, the formula for canon[1] is as follows: