w.r.t. problem 2. The curvature of shape space, itself, introduces some purely geometric variation that is picked up by PCA. For 2D, you expect to lose 4 dimensions of variation. In fact, you get three exactly zero eigenvalues and one very, very small one. The latter (usually, but I can construct counter examples) reflecting the curvature of GPA space.

-ds

morphmet wrote:


-------- Original Message --------
Subject: Understanding Morphologika
Date: Wed, 3 Mar 2010 09:41:33 +0000
From: <a.vanhete...@roehampton.ac.uk>
To: <morphmet_modera...@morphometrics.org>


________________________________________

Dear Colleagues



I have two unrelated issues, for which I don’t understand what Morphologika is calculating exactly.



Firstly, I am having difficulties with the Procrustes Superimposition performed in Morphologika. I was under the impression that scaling, rotation, reflection and translation could be switched on and off and that the subsequent principal component analysis would be performed on the Procrustes coordinates as you instructed Morphologika to calculate them.

Now my problem is the following:

If I perform Procrustes superimposition without scaling and perform PCA afterwards or Procrustes superimposition with scaling and PCA afterwards, the Procrustes coordinates are different, as would be expected. However, the PC scores are almost identical (a few small differences 5 decimals behind the comma). This is not what I would expect. Since some of my specimens are twice the size of some others, I would expect the first PC to show size (both isometric and allometric), however, it is showing the same signal as the PCA on the full Procrustes superimposition coordinates.

I am confused about what Morphologika calculates exactly to come to these results.

And I have not been able to reproduce either of the PCA plots of Morphologika with SPSS, even though I am forcing SPSS to use the covariance matrix instead of the correlation matrix.

Any help or suggestions of what might be going on would be greatly appreciated.



My second issue relates to the number of principal components calculated by Morphologika.

In the help file it is stated: Principal components analysis of specimens with k landmarks in m dimensions results in km-m-m(m-1)-1 eigenvectors; the principal components of variation of shape.

In my dataset I have 15 landmarks and 3 dimensions, so I think that should result in 15*3-3-3*(3-1)-1=35 principal components. However, Morphologika is giving me 38 principal components in the output. I don’t understand the discrepancy and would appreciate it if anybody could explain where the extra three principal components come from.



Thanking you all in advance.



Best wishes,



Anneke van Heteren


Anneke H. van Heteren
School of Human and Life Sciences
Roehampton University
Whitelands College
Holybourne Avenue
London SW15 4JD
Tel: +44 (0) 20 8392 3728
E-Mail: a.vanhete...@roehampton.ac.uk



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