-------- 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
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
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
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
--
Lissa Tallman, Ph.D.
Post-Doctoral Associate, CUNY/Lehman
@ Department of Vertebrate Paleontology
American Museum of Natural History
79th St. at Central Park West
New York, NY 10024
phone: 212-769-5553
Adjunct Assistant Professor
Hunter College
Department of Anthropology
email: [email protected] <mailto:[email protected]>
