Date: Wed, 11 Feb 2009 11:32:34 -0500
From: morphmet <[email protected]> Subject: Re:
Canonical variates from first PCs of GPA residuals To: morphmet
<[email protected]>
-------- Original Message --------
Subject: Re: Canonical variates from first PCs of GPA residuals
Date: Wed, 11 Feb 2009 08:28:03 -0800 (PST)
From: Dennis E. Slice <[email protected]>
To: [email protected]
References: <[email protected]>
Relevant to the current posting...
"Is it possible to use rw as variables in multivariate analysis to
differentiate groups?"
Some time ago this question was posed and I answered a simple "Yes."
This is correct since relative warps are a rotation of the partial warp
scores (including the uniform component) and completely describe the
shapes of the sample. If you use all of the relative warps, you should
get the same discrimination as if you used the partial warp scores.
Some background discussion, however, pointed out an important, but
perhaps subtle point (thanks, Fred). That is, you should NOT use a
reduced set of RWs for your analysis. While PCA (e.g., as used to
construct relwarps) makes no reference to group membership, it is
possible that group differences could be a major contributor to sample
variation. This is, after all, the basis for the one-tailed F-test used
in ANOVA - variance among means is tested to see if it is greater than
that expected based on within-sample variation. So, if this were the
case, and you subjected a reduced set of relative warps to MANOVA, CVA,
etc. the results could be misleading. If your only goal is to classify
an unknown, then it doesn't really matter (and may help) that you have
concentrated group differences in the retained components, but in any
statistical testing (even nonparametric testing), p-values for
significance tests of group mean differences will likely be biased,
i.e., too small.
What to do if you need data reduction? Use the initial PCs from the
pooled, within-group shape variation. Their computation is not affected
by group mean differences. Even here, though, it is inappropriate to
select the number of retained PCs based on "noticing" interesting group
separation on one or more of them.
The above holds for GPA coordinates just as it does for relwarps.
-dslice
morphmet wrote:
-------- Original Message --------
Subject: Canonical variates from first PCs of GPA residuals
Date: Tue, 10 Feb 2009 05:15:05 -0800 (PST)
From: Peter Taylor <[email protected]>
To: <[email protected]>
Dear Morphometricians
I am working with data where the number of landmarks (from rodent
skulls) exceeds the smallest sample sizes of my groups. To circumvent
statistical problems with null determinants when using canonical
analysis (CVA) of the weights matrix from GPA, is it permissable to
conduct CVA on the first few PCs from a PCA of the residuals, or aligned
coordinates after least squares, GPA? If so how does one objectively
decide how many PCs to include, should this number be less than the
smallest group sample size, or should it depend on a certain threshold
of cumulative explained variance (70%) or on the eigenvalues (>1?), or
on the degree of separation of groups? Also, is this approach
equivalent, or preferable, to conducting CVA on the first few relative
warps from a relative warps analysis (PCA of weights matrix). I have
seen both approaches in the literature but not sure which is best.
Many thanks
Peter
Dr Peter John Taylor
Curator of Mammals
Durban Natural Science Museum
Ethekwini Libraries & Heritage
P O Box 4085
Durban
4000
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--
Dennis E. Slice
Associate Professor
Dept. of Scientific Computing
Florida State University
Dirac Science Library
Tallahassee, FL 32306-4120
-
Guest Professor
Department of Anthropology
University of Vienna
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