David,
Yes, fixing the angle first allows for a single GPA, which then retains
relative size information across the substructures. And yes, it puts things in
a common orientation. Both have major advantages for downstream PLS, and its
interpretation. Many PLS-based integration analyses in GMM examine covariation
in substructures from a single larger object subjected to a single GPA. I
point to the classic paper of Bookstein et al. 2003 as an exemplar.
I would argue that it is in such cases where integration patterns are most
interpretable, as with a single GPA one is able to characterize covariation
patterns among sets of variables whose spatial relationships have been retained
throughout the analysis. This is rather important. When this isn’t the case, it
is much more challenging to derive interpretable estimates. This is what I was
alluding to in the last part of my previous post.
Dean
Dr. Dean C. Adams
Professor
Department of Ecology, Evolution, and Organismal Biology
Department of Statistics
Iowa State University
www.public.iastate.edu/~dcadams/<http://www.public.iastate.edu/~dcadams/>
phone: 515-294-3834
From: [email protected] [mailto:[email protected]] On Behalf Of David Katz
Sent: Wednesday, January 24, 2018 11:48 AM
To: Adams, Dean [EEOBS] <[email protected]>
Cc: Christy Anna Hipsley <[email protected]>; MORPHMET
<[email protected]>
Subject: Re: [MORPHMET] relative positions of landmark partitions in
integration tests - how important?
I read Christy's question a little differently, and requiring some
clarification.
First, Dean, doesn't Dean & Felice fix the angle between jaw and cranium so
that you can subject a craniomandibular dataset to a common GPA, which at the
PLS step has the benefit of preserving relative size relationships between the
two structures? On the other hand, it's not clear if Christy obtained landmarks
in a way that allows her to do this as easily. For instance, her sample may
have had crania and mandibles dissected out and landmarked separately, in which
case she subject the cranium and mandible to separate GPAs. Christy?
If GPA was performed separately for the cranium and mandible, then couldn't
Christy's issue simply be that cranium and mandible have differently oriented
principal axes (as determined by gpagen)?
Also, Christy, are you using the "plot.pls" function (warpgrids=TRUE) for
plotting? If so, then I think one option would be to make shapes=TRUE in that
function. This will give you an output that includes the coordinates of the
extreme shapes (I assume as p*3 matrices). After that, you just have to choose
which two columns from crania extremes and which two columns from mandible
extremes provide you with common cranial and mandibular views. You can then
make 2D plots your landmarks using the base R plotting functions.
Unfortunately, you won't have warpgrids. But you can overlay two (e.g.,
mandible) configurations to show the difference between extremes. Or you can
plot one extreme as the ball-and-stick wireframe and the change to the other
extreme as displacement vectors emanating from the wireframe.
David
On Wed, Jan 24, 2018 at 10:15 AM, Adams, Dean [EEOBS]
<[email protected]<mailto:[email protected]>> wrote:
Christy,
That data example contained variation in relative jaw position among specimens,
which could affect shape estimates, as well as down-stream shape analyses.
Several approaches have been proposed for dealing with such rotational
variation (see Adams 1999; also Bookstein’s Orange book). One approach is to
rotate one subset of landmarks so the angle between subsets is invariant across
specimens. The geomorph function ‘fixed.angle’ performs this operation for 2D
landmark datasets.
As to your comment on whether or not such positional variation makes a
difference, yes it can. PLS examines the degree of covariation between blocks
of variables and estimates of the between block covariation will differ if one
set of variables is rotated relative to the other. Whether this results in a
large or small difference in r-PLS values is data-dependent, but the values
will not be the same.
For this reason, prior to any PLS analysis for evaluating integration and
covariation patterns, one must first carefully consider what type of variables
are being utilized, how they were generated, and whether it even makes sense to
interpret the results biologically.
Dean
Dr. Dean C. Adams
Professor
Department of Ecology, Evolution, and Organismal Biology
Department of Statistics
Iowa State University
www.public.iastate.edu/~dcadams/<http://www.public.iastate.edu/~dcadams/>
phone: 515-294-3834<tel:(515)%20294-3834>
From: Christy Anna Hipsley
[mailto:[email protected]<mailto:[email protected]>]
Sent: Tuesday, January 23, 2018 9:34 PM
To: MORPHMET <[email protected]<mailto:[email protected]>>
Subject: [MORPHMET] relative positions of landmark partitions in integration
tests - how important?
Hi all,
I'm trying to run an integration test in geomorph, or rather phylo.integration
on 2 sets of Procrustes aligned coordinates for cranium and jaws of lizards,
landmarked on both sides. When I plot the results I get graphs of the landmarks
for the positive and negative extremes of PLS1&2, but for the cranium they are
in lateral view while for the mandibles they are in frontal view.
I'm wondering if this is an issue for the estimation of r-PLS, since in Adams &
Felice 2004 (PLoS ONE: Assessing Trait Covariation and Morphological
Integration on Phylogenies Using Evolutionary Covariance Matrices), they write
"the position of the jaw was standardized relative to the skull by rotating the
jaw to a common articulation angle among specimens".
If it is an issue, how do I rotate the position of one of the partitions to be
in the same orientation as the other?
Thanks for any advice!
Christy
Dr Christy Anna Hipsley | ARC DECRA Fellow
School of BioSciences, University of Melbourne/
Museums Victoria
GPO Box 666
Melbourne, Victoria 3001 Australia
T: +61 3 8341 7423<tel:+61%203%208341%207423> E:
[email protected]<mailto:[email protected]>;
[email protected]<mailto:[email protected]>
http://blogs.unimelb.edu.au/hipsleylab/
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David C. Katz, Ph.D.
Postdoctoral Fellow
Benedikt Hallgrimsson Lab
University of Calgary
Research Associate
Department of Anthropology
University of California, Davis
ResearchGate profile<https://www.researchgate.net/profile/David_Katz29>
Personal webpage
<https://davidckatz.wordpress.com/>
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