-------- Original Message -------- Subject: Re: PCA and CVA Date: Fri, 5 Sep 2008 01:54:05 -0700 (PDT) From: [EMAIL PROTECTED] To: [email protected] References: <[EMAIL PROTECTED]> I'm still a little confused! In my program Past, I simply compute the eigenvectors of W^(-1)B, with W and B the within and between covariance matrices. The scores are the products of the original data and the eigenvectors. This generally results in correlated scores. I have noticed that some other programs, including Statistica, give basically identical results to Past and must use a similar (simplistic?) approach. Is this not the Done Thing? If so, I would be very grateful if anyone could point me to a step-by-step description of a preferred algorithm! Regards, Oyvind Hammer Natural History Museum University of Oslo
-------- 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 -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
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