re previous discussion
My old computer program MANOVA has a built in test of parallelism in
multivariate ANCOVA. It's really standard multivariate regression theory
although it isn't widely known. (TW Anderson gave MANOVA and CanR as two
different eigenproblems).
They are easily shown to be equivalent with the same vectors and
eigenvalues related by
R^2 = L/(1+L)
The basic theory is discussed in Bock's multivariate text.
Multivariate regression IS canonical correlation just as multiple
regression IS multiple correlation. The correlations are the natural
measures of association. Add a ANOVA or MANOVA structure and you get
ANCOVA or MANCOVA. The statistical tests are all the standard tests
involving eigenvalues. Partial correlations can be generalized also.
See my papers
Cramer, E. M. (1974). Brief report: The distribution of partial
correlations and generalizations. Multivariate Behavioral Research, 9,
119-122.
Cramer, E. M. (1973). Note: A simple derivation of the canonical
correlation equations. Biometrics, 29, 379-380.
If you write the equations for MANCOVA you see immediately that it
involves Multivariate regression equations for different subgroups and
that the test of parallelism is in fact a test of equality of slopes for
different canonical correlation problems
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