-------- Original Message --------
Subject: Re: Comparing Segments of Developmental Trajectories
Date: Tue, 13 Mar 2012 13:40:46 -0400
From: Philipp Mitteröcker <mitte...@univie.ac.at>
To: morphmet@morphometrics.org
Dear Michelle,
In a high-dimensional space, angles tend to be very large. They can be
close to 90 degrees and still not be significant.
This is the same paradox as for a chi-square distribution: the more
dimensions, the larger the average (squared) distance between the points.
You can try to project your data onto the first few principal components
and compute the angles from these PC scores.
Plotting the trajectories in a PCA plot or some other ordination might
also be helpful.
Best,
Philipp
Am 12.03.2012 um 23:29 schrieb morphmet:
-------- Original Message --------
Subject: Comparing Segments of Developmental Trajectories
Date: Mon, 12 Mar 2012 18:15:09 -0400
From: Michelle Singleton <msingle...@midwestern.edu>
To: morphmet@morphometrics.org
Dear Colleagues,
As part of a study of ontogenetic shape change in a group of related
species, I wish to compare patterns of shape change between successive
developmental stages. My intention was to compare angular differences
between species vectors obtained from multivariate regression of
Procrustes residuals on my developmental variable.
When I apply this approach to the full developmental series (juvenile to
adult) I get interspecies angles comparable to those obtained by myself
and others in prior studies, but when I look at individual segments
(e.g., Stage 1 to Stage 2) the resulting angles are very large,
apparently because the amount of variation between stages is too small
to allow accurate vector estimates, although the smaller sample sizes
probably contribute as well. The large angles do, nevertheless, return
the same qualitative result (in terms of relative vector similarity) as
the angles for the full ontogenetic series.
My questions are: 1) have I correctly identified the source of the
discrepancy in angle magnitudes? 2) can permutation significance tests
based on these angles be meaningful; or, 3) is this the wrong approach
and is there perhaps a more appropriate method for this comparison?
Many thanks for your thoughts on this problem.
Best regards,
Michelle
--
Michelle Singleton, Ph.D.
Professor of Anatomy
Midwestern University
555 31st Street
Downers Grove, IL 60515
Phone: 630.515.6137 <tel:630.515.6137>
Fax: 630.515.7199 <tel:630.515.7199>
e-mail: msingle...@midwestern.edu <mailto:msingle...@midwestern.edu>
___________________________________
Dr. Philipp Mitteroecker
Department of Theoretical Biology
University of Vienna
Althanstrasse 14
A-1090 Vienna, Austria
Tel: +43 1 4277 56705
Fax: +43 1 4277 9544
email: philipp.mitteroec...@univie.ac.at
homepage: http://theoretical.univie.ac.at/people/mitteroecker
