-------- Original Message --------
Subject: Re: CVA limitations?
Date: Thu, 2 Apr 2009 05:25:21 -0700 (PDT)
From: andrea cardini <[email protected]>
To: [email protected]
Just a quick comment about Philipp's points.
The rule of thumb suggested by textbooks is more restrictive than Jim's
"minimum sample size" as requires N of the smallest group to be larger
than the number of variables. This seems to imply that the minimum
requirement mentioned by Jim is met.
Also, it's true that "CVA will always separate groups even if the share
the same mean configuration" but in that case the cross-validation will
likely produce hit-ratios which are no better than chance (that was
about my last point in the previous message).
Unfortunately most of the time people doing taxonomy like myself are in
the situation exemplified by Paul's case (below) where N is very unequal
across groups and there are at least a few groups with N much smaller
than the number of variables. Then, one may or may not be
computationally able to do a DA/CVA but assumptions are unlikely to be
met, hard to verify and (even more concerning) sampling error may lead
to inaccurate estimates of means, variances etc.
Resampling statistics may help but won't do anything about the accuracy
of estimates and one can only acknowledge that results (at least those
concerning smallest samples) will have to be verified on larger samples.
I'd like also to remember that besides sample size, one should carefully
consider provenance of specimens and maybe also time of specimen
collection. A small sample of individuals collected at the same time and
in the same locality could make things even worse if one is interested
in estimating means and their variation in the whole population. Again,
this is not uncommon for rare species/subspecies from museum collections.
Cheers
Andrea
At 07:43 02/04/2009 -0400, you wrote:
-------- Original Message --------
Subject: Re: CVA limitations?
Date: Thu, 2 Apr 2009 04:26:50 -0700 (PDT)
From: Paul Van Daele <[email protected]>
To: <[email protected]>
References: <[email protected]>
what if total sample size is larger than the number of variables but some
groups have a lower sample size than the number of variables?
Say eg you have 26 variables and three groups with resp. 40, 15 and 5
specimens
Paul Van Daele
Ghent University
Evolutionary Morphology of Vertebrates
KL Ledeganckstraat 35
B-9000 Gent
Belgium
[email protected]
Tel +32 92645233
Fax +32 92645344
Do not go gentle into that good night (D. Thomas)
----- Original Message -----
From: "morphmet" <[email protected]>
To: "morphmet" <[email protected]>
Sent: Thursday, April 02, 2009 1:08 PM
Subject: Re: CVA limitations?
-------- 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
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Dr. Andrea Cardini
Lecturer in Animal Biology
Museo di Paleobiologia e dell'Orto Botanico, Universitá di Modena e Reggio
Emilia
via Università 4, 41100, Modena, Italy
tel: 0039 059 2056532; fax: 0039 059 2056535
Honorary Fellow
Functional Morphology and Evolution Unit, Hull York Medical School
University of Hull, Cottingham Road, Hull, HU6 7RX, UK
University of York, Heslington, York YO10 5DD, UK
E-mail address: [email protected], [email protected],
[email protected]
http://hyms.fme.googlepages.com/drandreacardini
http://ads.ahds.ac.uk/catalogue/archive/cerco_lt_2007/overview.cfm#metadata
More on publications at:
http://www.cons-dev.org/marm/MARM/EMARM/framarm/framarm.html
CLICK ON THE LETTER C AND LOOK FOR "CARDINI" (p. 8-9 until March 2009)
http://hyms.fme.googlepages.com/dr.sarahelton-publications
LOOK FOR "CARDINI"
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