-------- Original Message --------
Subject: Re: Angle differences in PC axes
Date: Fri, 25 Mar 2011 15:33:20 -0400
From: Dennis E. Slice <[email protected]>
To: [email protected]
Lissa, Hi!...
On 3/25/11 8:42 AM, morphmet wrote:
-------- Original Message --------
Subject: Angle differences in PC axes
Date: Wed, 23 Mar 2011 14:49:43 -0400
From: Lissa Tallman <[email protected]>
To: [email protected]
Hello Morphmetricians,
I am currently working on a project that compares ontogenetic
trajectories in postcranial elements of extant apes using geometric
morphometrics. I performed both a common GPA on the entire sample, as
well as individual GPAs on each taxon and I've looked at the results in
Comparing PCs of groups not jointly superimposed is not meaningful. The
coefficients for GPA PCs are for individual landmark coordinates and
would be orientation-specific. Relative warps doesn't help, either,
since the basis vectors are sensitive functions of the mean
configuration. Orienting to manually adjusted fish PCs (all heads to the
left kind of thing) might help a little, but best not to do it at all.
What should be done is jointly superimpose all groups, then compute PCs
for each in that common space.
both Procrustes shape space and Procrustes form space. In both cases
(particularly once centroid size is included, of course) the bulk of the
shape change occurs along the first PC axis. I would like to determine
Almost by definition, except for the subtlety that in form space PC 1
could represent overwhelming size variation in the face of isometry.
the differences in the angles of those PC axes.
In theory, I believe I need to calculate the dot product of the
eigenvectors (as the sum of all Ux*Vx), and then take the arccos of that
value. If the dot product is greater than 1, I've been assuming that
indicates an angle of over 180 degres, and I've been subtracting 2 to
take the arcccos of the complimentary angle, and then subtracting that
from 180. The problem is that the data from these calculations don't
make geometric sense. If I have three taxa, and I am comparing all
three of them in a pairwise manner, the sum of the two smaller angles
should equal the sum of the largest angle - but that is not what I am
Why? Only if all vectors were coplanar would you expect such a
relationship. Think of two vectors along x, y (90 degrees) and a third
at 45 degrees in their plane. Rotating the third one out of the plane
and towards the z axis increases the two smaller angles, but not the
third until they are all 90 degrees.
Do check your radians vs. degrees as Dr. Adams suggested.
Best, ds
getting. I am wondering if I need to apply some kind of transformation
to my vectors to make sure that they begin in the same place? I did
calculate the magnitude of each vector, and they are all just trivially
different from 1.
Lissa
--
Dennis E. Slice
Associate Professor
Dept. of Scientific Computing
Florida State University
Dirac Science Library
Tallahassee, FL 32306-4120
-
Guest Professor
Department of Anthropology
University of Vienna
-
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