-------- Original Message --------
Subject: PCA and CVA
Date: Thu, 4 Sep 2008 07:06:23 -0700 (PDT)
From: F. James Rohlf <[EMAIL PROTECTED]>
Reply-To: [EMAIL PROTECTED]
Organization: Stony Brook University
To: [email protected]
Norm Campbell has just pointed out to me that I responded a little too
quickly yesterday to one of the questions about orthogonality and
correlation of CVA axes and scores.
CVA scores are uncorrelated even though the CVA axes are not oblique.
The paradox is because the two statements are made with respect to
different coordinate systems.
1) The CVA axes are oblique vectors in the space using the original
variables as an orthogonal coordinate system (even though the variables
may be highly correlated).
2) The CVA scores are uncorrelated in the space defined by using the CVA
axes as an orthogonal coordinate system (i.e., if you simply plot scores
of CVA1 against CVA2 you will not see any correlation). This not simply
a plot of the projections of the data onto the CVA axes of the previous
paragraph because this space has been stretched and compressed by the
standardization by the within-group covariance matrix.
I hope I did not confuse anyone further!
------------------------
F. James Rohlf, Distinguished Professor
Ecology & Evolution, Stony Brook University
www: http://life.bio.sunysb.edu/ee/rohlf
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