-------- Original Message --------
Subject: Re: CVA limitations?
Date: Thu, 2 Apr 2009 10:24:06 -0700 (PDT)
From: F. James Rohlf <[email protected]>
Reply-To: [email protected]
To: Morphmet <[email protected]>
References: <[email protected]>
My earlier comment about the minimum sample size was to provide a
mathematical minimum that permits computing the inverse of the pooled
within covariance matrix. However, a reasonable statistical minimum is
likely to be much larger in order to get stable results.
One cannot just specify some absolute number as being reasonable because
it depends on just how different the groups are. It is useful to do a
pilot study to get an estimate of the differences and then plan a more
definitive study for the actual tests.
Sample sizes also depend on whether you just want to demonstrate that
there is a difference or if you wish to describe the nature of the
difference (which requires a larger n).
--------------------------------
Sent remotely by F. James Rohlf
-----Original Message-----
From: morphmet <[email protected]>
Date: Thu, 02 Apr 2009 12:59:17
To: morphmet<[email protected]>
Subject: Re: CVA limitations?
-------- Original Message --------
Subject: Re: CVA limitations?
Date: Thu, 2 Apr 2009 09:56:01 -0700 (PDT)
From: J. Willacker <[email protected]>
To: [email protected]
References: <[email protected]>
Thanks everyone for your replies.
My landmark suite includes 20 points, therefore I have 40 variables. I
have been doing a minimum of 40 specimens from each population, but if I
understand correctly I should consider doing more. How do I know what
my goal within population N should be? I have more than enough fish
from each population (for most I have 500+ fish) but with this many
populations time becomes an issue when my Ns get too high. A college is
using sample sizes as low as 20 for similar analyses (with the same 20
landmarks), but that doesn't seem valid.
Really, I am very new to these types of analyses and have some trouble
understanding how they do what they do. I realize that no matter how
many fish I include, the CVA could not possibly separate ALL
populations. Ultimately, my goal is to identify populations with unique
head morphologies (very "benthic" or very "limnetic") for use in my
studies of trophic morphology/ecology. Given my purpose, is there a
different analysis that would be more appropriate?
On Thu, Apr 2, 2009 at 4:27 AM, morphmet
<[email protected]
<mailto:[email protected]>> wrote:
-------- Original Message --------
Subject: Re: CVA limitations?
Date: Thu, 2 Apr 2009 05:25:21 -0700 (PDT)
From: andrea cardini <[email protected]
<mailto:[email protected]>>
To: [email protected] <mailto:[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]
<mailto:[email protected]>>
To: <[email protected]
<mailto:[email protected]>>
References: <[email protected]
<mailto:[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] <mailto:[email protected]>
Tel +32 92645233
Fax +32 92645344
Do not go gentle into that good night (D. Thomas)
----- Original Message -----
From: "morphmet" <[email protected]
<mailto:[email protected]>>
To: "morphmet" <[email protected]
<mailto:[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]
<mailto:[email protected]>>
To: [email protected]
<mailto:[email protected]>
References: <[email protected]
<mailto:[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]
<mailto:[email protected]>>
To: [email protected]
<mailto:[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]
<mailto:[email protected]>>
To: Morphmet <[email protected]
<mailto:[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]>
<mailto:[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]
<mailto:[email protected]>
www.virtual-anthropology.com/Members/philippm
<http://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]
<mailto:[email protected]>, [email protected]
<mailto:[email protected]>,
[email protected] <mailto:[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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