----- Forwarded message from Philipp Mitteröcker <[email protected]> -----
Date: Sun, 16 Jun 2013 17:09:02 -0400
From: Philipp Mitteröcker <[email protected]>
Reply-To: Philipp Mitteröcker <[email protected]>
Subject: Re: Pooled within-group covariance matrix
To: [email protected]
Hi,
The pooled within-group covariance matrix is an average of all the within-group
covariance matrices (weighted by their sample size), i.e, of the variances and
covariances across the individuals of the same group. It thus ignores variation
across the group means and can also be computed as the covariance matrix of the
data after mean-centering each group. When the covariance matrices are
reasonably similar within all groups, one can use their pooled estimate. If
they differ considerably, a pooled estimate might be difficult to interpret
(consider two groups, in one of which two variables are positively correlated
and in the other of which they are negatively correlated; in the pooled
within-group covariance matrix the correlations might cancel).
No other "distortion" of the data occurs than in ordinary PCA or PLS. But of
course, if you try to see group differences in a PCA, estimating the PC axes
from the pooled within-group covariance matrix is not effective, as this
ignores all group mean differences. The same problem probably occurred in your
PLS analysis. Neither version of PCA is particularly well suited for biological
interpretation.
It can be useful to compare patterns of morphological integration or other
correlation patterns within the groups to those between the groups. This might
show, for instance, that genetic/developmental mechanisms accounting for the
correlations across individuals have also affected evolutionary processes.
Best,
Philipp
Am 11.06.2013 um 11:36 schrieb [email protected]:
>
> ----- Forwarded message from [email protected] -----
>
> Date: Mon, 10 Jun 2013 10:59:47 -0400
> From: [email protected]
> Reply-To: [email protected]
> Subject: Pooled within-group covariance matrix
> To: [email protected]
>
> Dear all,
>
> I am performing Partial Least Square analyses to check the association
> between skull shape and climatic variables in a sample of 15 species
> from two different genera of monkeys.
> The association occurs and is significant.
>
> I tried the same analysis but using the pooled within group covariance
> matrix.
> The association does not occur and is not significant.
>
> Can anyone explain me what the "pooled within group covariance matrix"
> analysis really perform and if it generate a distortion to the data
> (like CVA does)?
>
> I tried comparing normal PCA and the one using "pooled within group
> covariance" and what I obtained was a more squeezed distribution so
> that my genera looked much closer in PC plots than they really
> are...it seems to me that this create distortion of original data and
> goes far away from biological interpretation.
>
> All comments and replies about this are welcome,
>
> Thank you in advance
>
> Carlo
>
> ----- End forwarded message -----
>
___________________________________
Dr. Philipp Mitteroecker
Department of Theoretical Biology
University of Vienna
Althanstrasse 14
A-1090 Vienna, Austria
Tel: +43 1 4277 56705
Fax: +43 1 4277 9544
email: [email protected]
homepage: http://theoretical.univie.ac.at/people/mitteroecker
----- End forwarded message -----
