-------- Original Message --------
Subject: Re: CVA limitations?
Date: Thu, 2 Apr 2009 04:21:58 -0700 (PDT)
From: Dennis E. Slice <[email protected]>
To: [email protected]
References: <[email protected]>
I put the following out for comment/discussion.
1) To which "within-group" covariance matrix are you referring? CVA uses
the pooled, withinin-group covariance matrix, but comments seem to be
looking at sample size of individual group within covariance. And, I
seem to recall software packages choking if any individual group had a
singular covariance matrix due to sample size. One can easily have the
case where one or more groups are lacking sufficient sample size, but
the pooled, within is more than adequately sampled. Are not the pooled,
within degrees of freedom sufficient to inform you as to the reliability
of your estimates regardless of how they are distributed across samples
(assuming a common covariance structure)?
2) If the pooled, within shows spherical scatter, then mutliplication by
its inverse won't do anything other than rescale all variables by
(more-or-less) the same factor, and the result of the PCA between groups
will be the same as with an overall PCA. Does redoing the analysis as a
straight PCA get you anything other than reclaiming the within-group
degrees of freedom? How important is that?
Best, ds
morphmet wrote:
-------- Original Message --------
Subject: Re: CVA limitations?
Date: Wed, 1 Apr 2009 16:04:19 -0700 (PDT)
From: Philipp Mitteröcker <[email protected]>
To: [email protected]
References: <[email protected]>
Actually, the "rule of thumb" is a computational necessity. More
correct is Jim's formulation that the "degrees of freedom of the
within-group covariance matrix to be greater than the number of
variables". Otherwise you cannot invert the covariance matrix and
hence cannot compute the CVA. But sample size should be much larger
than the number of variables in order to produce interpretable
results. If the sample size is close to the number of variables, CVA
will always separate groups even if the share the same mean
configuration.
But for 65 populations no low-dimensional representation will be
sufficient to distinguish between ALL groups. Furthermore, CVA assumes
equal covariance matrices for all groups, which seems unlikely for so
many populations. If the covariance structures vary considerably, a
pooled estimate may be close to a spherical distribution and the
resulting CVA would be very similar to a principal component analysis
(PCA). I would thus suggest to proceed with a PCA, also because there
are no restriction on sample size and statistical artifacts are less
likely.
I hope this helps,
Philipp
Am 01.04.2009 um 19:33 schrieb morphmet:
-------- Original Message --------
Subject: Re: CVA limitations?
Date: Wed, 1 Apr 2009 09:15:46 -0700 (PDT)
From: andrea cardini <[email protected]>
To: [email protected]
Dear James,
on a similar issue there was an exchange of emails in MORPHMET some time
ago (February, I think) and a few more emails which were not sent to the
list. Jim Rohlf suggested to summarize the main points in an email to
MORPHMET and I agree with him that it's a very good idea.
Unfortunately I am too busy right now for this but hope to do it soon
or later.
Just a couple of quick comments (which greatly oversimplify the
problem).
First of all, give a look at assumptions of DA/CVA. With many groups and
small samples they're often difficult to test.
Second point, from a message that Jim Rohlf sent a couple of years ago:
"... in order use methods that look at difference among groups
relative to
within-group variability one needs the degrees of freedom of the
within-group covariance matrix to be greater than the number of
variables.
With fewer observations the within-group covariance matrix will be
singular. This rule gives a minimum sample size but for reliable results
the sample size should, of course, be much larger". To have more
reliable
results, there's a rule of thumb which is suggested in many textbooks
(and
I am not sure if it is actually supported by studies): this is that
within
each group you should have more specimens than variables.
Last comment, if you really want to do a DA/CVA when N is not very
large,
I'd carefully check if results are stable when you exclude small
groups and
I'd always cross-validate all analyses. If you find that despite
significance, cross-validated hit ratios (i.e., percentages of specimens
correctly classified according to groups) are low, I'd be very cautious
about what those differences really mean (if they do mean anything at
all).
There's plenty of references on this stuff. An old one which I
greatly like
is Neff & Marcus' chapter on DA/CVA in their book on "Multivariate
Methods
for Systematics" (1980).
Good luck with your research.
Cheers
Andrea
At 09:01 01/04/2009 -0400, you wrote:
-------- Original Message --------
Subject: CVA limitations?
Date: Tue, 31 Mar 2009 18:20:40 -0700 (PDT)
From: J. Willacker <[email protected]>
To: Morphmet <[email protected]>
Hi,
I was wondering if there were any limits to the number of groups that
can be distinguished between with CVA? I'm comparing facial morphology
in 65 populations of threespine stickleback fish, but don't know if CVA
is valid with so many groups. Is there a relation between number of
specimens per group and how many groups can be compared? At some point
does the power of the analysis suffer? Really need help with this
since
nobody in our stats department seems to know the answer. Feel free to
respond to [email protected] <mailto:[email protected]> Thanks,
James
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____________________________________
Dr. Philipp Mitteröcker
Department of Theoretical Biology
University of Vienna
Althanstrasse 14
A-1090 Vienna, Austria
Tel: +43 1 4277 56705
Fax: +43 1 4277 9544
[email protected]
www.virtual-anthropology.com/Members/philippm
--
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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