Dear Paul:
Sorry for my ignorance, but just to
clarify things further (I post this to the web
server, since it might be a question of interest for others, too) .
Does it make sense to interpret these PC loadings
(i.e., eigenvectors) directly to evaluate the
influence of each landmark and its dimension (x,
y, or z) on a specific PC? For example, variable
1 represents the x coordinate of landmark 1, var
2 = y coord. of lm1, var 3 = z coord of lm1, var 4 = x coord. of lm2, etc.
If this is the case, what about the lacking
variables 76-78, since these should refer to the
x-, y-, and z-coordinates of landmark 26)?
Oliver
Dear all,
Oliver Betz asked earlier this week why when he carried out a PCA of
shapes with 26 landmarks (=78 variables - x,y and z coords)the output in
morphologika shows PC loadings for only 75 variables.
I misunderstood his question and thought he was referring to the reduced
dimensionality of the shape space consequent on removing size, rotation
and translation (ie a loss of 3 dimensions when working in 2D or 7 in
3D)
In fact the issue is simply that in tangent projecting, the
dimensionality of the data submitted to PCA (the tangent coordinates as
opposed to the original Procrustes registered coordinates) is reduced by
3 for 3D data and 2 for 2D data. Thus 78-3=75.
Morphologika knows when tangent projection has been carried out and
reverses this before plotting shapes in the output window when exploring
PCs etc. This is why almost no-one ever notices.
I hope this clarifies things
Paul O'Higgins
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Prof. Dr. Oliver Betz
Zoologisches Institut
Abt. Evolutionsbiologie der Invertebraten
Auf der Morgenstelle 28E
D-72076 Tübingen
Germany
phone: 0049-(0)7071-2972995
E-mail: [EMAIL PROTECTED]
http:/www.uni-tuebingen.de/agbetz
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