-------- Original Message --------
Subject: Re: Canonical variates from first PCs of GPA residuals
Date: Wed, 11 Feb 2009 12:30:32 -0800 (PST)
From: Michael Collyer <[email protected]>
To: [email protected]
References: <[email protected]>
Dear Dominique, Peter,
It seems to me that the reason for performing CVA needs to be stated a
priori. What will CVA accomplish for you? Below I can think of a few
reasons, and I provide what I personally think might be appropriate ways
to proceed.
1) Graphical description of group differences. If the purpose is to
have an ordination plot that projects values on 2-3 canonical axes
(which best describe group differences relative to within-group
variation), then there seems to be no reason to reduce the number of
PCs. The number of canonical axes with positive eigen values is perhaps
constrained, but it should be possible to still compute the canonical
axes and project the data (at least I do not see how the linear algebra
would change). Perhaps certain statistical software packages might
prevent the procedure if the number of variables exceeds the smallest
group size, but that is probably related more so to an associated
statistical test, which brings me to the next reason.
2) Statistical evaluation of group differences. Often, a one-factor
MANOVA is performed as part of a CVA. This is probably the big reason
to reduce data to a few PCs -- to make sure that there are sufficient
degrees of freedom for the MANOVA. That is one way to solve the
problem, although I would recommend a non-parametric approach, like a
randomization/permutation test. But this only allows one to perform the
MANOVA and by using reduced dimensions of data, you might inadvertently
affect the estimation of your canonical axes.
3) Post-hoc classification. Perhaps another reason to do CVA is that
most software packages will assign, post-hoc, the expected group
association of all objects in the analysis based on shortest generalized
distances to group means. If there is an apparently high correct
classification, it suggests that groups are tightly clustered in e.g.,
the shape space. Again, I think it would be a mistake to include only a
portion of the available information, as it will affect the calculation
of generalized distances. However, I could see an argument that if the
first fews PCs estimated from shape data roughly correspond to e.g., an
environmental gradient, then one might wish to ask if classification is
high (or low) with respect to a constrained interpretation of shape
variation. This, however, seems to be a rare case and not a good
general rule to follow.
As a personal bias, I seldom feel that CVA offers more than PCA (as a
graphical representation of shape variation) and a separate statistical
test of group differences (or group clustering). Others might have a
different opinion.
good luck!
Mike
Dear all,
We are currently dealing with exactly the same problem as Peter. One
idea I had was to perform a backward stepwise discriminant function
analysis, so to let the model decide which variables (in this case
PC's instead of partial warps) are relevant to be included and which
not (hence reducing the number of variables in this way). So, I would
also be interested to know from the morphmet group any suggestions on
whether this is an acceptable approach to follow.
Best
Dominique
Prof. Dr. Dominique Adriaens
Ghent University
Evolutionary Morphology of Vertebrates & Zoology Museum
K.L. Ledeganckstraat 35, B-9000 Gent
BELGIUM
tel: +32 9 264.52.19, fax: +32 9 264.53.44
E-mail: [email protected]
URL: http://www.fun-morph.ugent.be/
http://www.zoologymuseum.ugent.be/
--
Michael Collyer
__________________________________________________
Assistant Professor
Department of Biology
Stephen F. Austin State University
PO Box 13003 SFA Station
Nacogdoches, TX 75962-3003
Phone (936) 468-2322 Fax (936) 468-2056
Email [email protected]
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