The problem with PC1 is not what I would call a mathematical artifact. I view it as more of a statistical problem.
In traditional morphometric data, variables usually have very large positive correlations between them. This is usually mostly due to the effects of size. Small organisms have small parts and large ones have large parts. The first PC axis is parallel to the direction of greatest variation in the data and thus is usually a direction of variation one can attribute to size variation in traditional morphometric data. One can verify this for a dataset by observing whether small specimens have scores on one end of the PC1 axis and large specimens have scores on the other end. The problem is that the direction of maximum variation for a dataset is also influenced by the presence of sexual dimorphism, geographic variation, etc. These may add large amounts of variation and thus will influence the direction of the PC1 axis. PC1 is not likely to be a pure measure of size in practical applications unless these other influences have been eliminated. In terms of the original question, one cannot assume PC1 represents distortion due to preservation unless one can eliminate other sources of major variation in the data. Jim Rohlf [EMAIL PROTECTED] 3/18/03 > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] Behalf Of > [EMAIL PROTECTED] > Sent: Tuesday, March 18, 2003 8:41 AM > To: [EMAIL PROTECTED] > Subject: RE: question on the use of relative warp scores for statistical > > > Indeed as Jim notes. > > The positive elements of the first latent vector of a positive definite > square matrix is an "artefact". This is incorporated in the > Frobenius-Perron theorem for the spectral properties of non-negative > matrices. Ref. Gantmacher, F. R. Matrizenrechnung II (1966), VEB > Deutscher Verlag der Wissenschaften, Berlin, pp 46-47. Fred Bookstein > was as far as I am aware the first person to expose this non sequitur in > the multivariate morphometric application of PCA. > > Citerat fr�n [EMAIL PROTECTED]: == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
