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

From: Christy Anna Hipsley [mailto:chips...@unimelb.edu.au]
Sent: Tuesday, January 23, 2018 9:34 PM
To: MORPHMET <morphmet@morphometrics.org>
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 E: 
christy.hips...@unimelb.edu.au<mailto:christy.hips...@unimelb.edu.au>; 
chips...@museum.vic.gov.au<mailto:chips...@museum.vic.gov.au>
http://blogs.unimelb.edu.au/hipsleylab/
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