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 +
From:
To:
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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Florida State University
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