-------- Original Message --------
Subject: Re: procrustes variances
Date: Tue, 1 Sep 2009 08:41:20 -0700 (PDT)
From: Haber Annat <[email protected]>
To: <[email protected]>
Hello,
Do you (or any one else) mind explaining this in more details?
On the face of it I would think that it makes more sense to superimpose
each sample separately, for exactly the reason that Louis gave. This is
assuming: 1) the samples are based on exactly the same set of landmarks;
2) you're only comparing the total variance within each sample and not
around each landmark, and not anything else; 3) none of the samples
include any of the other samples (and maybe other assumptions I'm
forgetting right now). If that is wrong to do then what about
bootstrapping? After all, as far as I understand, whenever you bootstrap
a sample in order, for example, to get confidence interval of something,
you re-superimpose every bootstrapped sample but you don't superimpose
all 500 or so bootstrapped samples simultaneously, do you? Then if you
pile up all these bootstrapped values into one distribution, that
implies that they are comparable, doesn't it? Even though they're each
based on a somewhat different space. I tried to test it using
simulations as well as looking into my own data. So I generated two
samples with somewhat different mean shape and level of variance (based
on a non-isotropic covariance matrix), but the same sample size, and
compared the variance within each sample when they are superimposed
together as opposed to when they are superimposed separately (repeated
100 times). With the real data I simply took the same number of males
and females from each of 9 species (ruminants, what else) where I know
there is significant sexual dimorphism. With the simulations, the
variances based on the combined GPA correlate very tightly (>0.92) with
the ones based on separate GPA but are consistently slightly
overestimated for both samples in each pair. The higher the variance the
more they are overestimated relative to their variance when superimposed
alone. And also, the higher the difference in mean shape the bigger the
bias. However, when one of the samples is five times bigger, the bigger
sample's variances correlate perfectly while the smaller samples are
vastly overestimated and correlate ~ 0.8.
With the empirical data I get exactly the same variances for each of the
samples either way I calculate it, but that may be because the mean
shape is not that different after all.
So all in all, I can see that the space they're in makes a difference
but I still don't see why it wouldn't be better to compare their
within-sample variance based on separate superimposition for each
sample, especially since there is a consistent bias (although these
brief simulations obviously didn't cover all possible scenarios). And
what does that mean for bootstrapping procedures?
Thanks
Annat
From: morphmet <[email protected]>
Reply-To: <[email protected]>
Date: Fri, 28 Aug 2009 07:42:29 -0400
To: morphmet <[email protected]>
Subject: RE: procrustes variances
Resent-From: <[email protected]>
Resent-Date: Fri, 28 Aug 2009 04:45:01 -0700 (PDT)
-------- Original Message --------
Subject: RE: procrustes variances
Date: Thu, 27 Aug 2009 19:08:25 -0700 (PDT)
From: F. James Rohlf <[email protected]>
Reply-To: [email protected]
Organization: Stony Brook University
To: [email protected]
References: <[email protected]>
You should only compare them when computed after a combined GPA.
Otherwise you are comparing quantities computed in different spaces.
------------------------
F. James Rohlf, Distinguished Professor
Ecology & Evolution, Stony Brook University
www: http://life.bio.sunysb.edu/ee/rohlf
-----Original Message-----
From: morphmet [mailto:[email protected]]
Sent: Thursday, August 27, 2009 11:32 AM
To: morphmet
Subject: procrustes variances
-------- Original Message --------
Subject: procrustes variances
Date: Thu, 27 Aug 2009 07:41:39 -0700 (PDT)
From: Louis Boell <[email protected]>
To: <[email protected]>
Dear colleagues,
I have a question about procrustes variance. I want to compare the
shape
variances of different samples. I have three groups of 77, 96 and 17
specimens, respectively. I calculated the procrustes variance of each
group in two ways: 1) after pooling the raw data of all three groups
into a common total dataset and fitting them together; b) after
calculating the procrustes fit for each dataset/group separately.
The results for the two large samples are quite consistent between both
procedures; however, the estimate of the procrustes variance for the 17
specimen sample is much larger when fitted together with the other two
samples than when fitted separately.
I assume that this is because the procrustes fit is a "democratic"
procedure, which is much more influenced by large samples than by small
samples when they are fitted together. This could potentially result in
a "spreading" of the specimens from the specimens from the small sample
in the space of the procrustes coordinates, if their covariance pattern
is different from the mean covariance pattern of the total dataset
which
will be largely determined by the large samples.
Altogether, my question amounts to whether it is more approriate to
compare procrustes variances from separate procrustes fits or from a
procrustes fit of the pooled total dataset.
Thanks in advance for help
Louis Boell
Louis Boell
MPI für Evolutionsbiologie
August-Thienemannstr.2
24306 Plön
[email protected]
[email protected]
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