-------- 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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