-------- Original Message --------
Subject: RE: Two block partial least squares - interpreting 1st
dimension, and power to detect covariation
Date: Sat, 25 Sep 2010 18:08:01 -0400
From: F. James Rohlf <[email protected]>
Reply-To: [email protected]
Organization: Stony Brook University
To: [email protected]
As in a PCA, it does not make sense to interpret a second axis
separately from the first. If the P-value is small for the second axis
then that means you need to interpret the space spanned by the first two
axes. It will probably help to construct a pair of biplots (as done in
the tpsPLS program) so you can try to figure out what variation in
different directions within the 2D space might mean. That is why the
program allows you to move the red circle around to visualize shapes in
different directions.
It is, perhaps confusing having more than one test for a method. In
canonical correlation analysis, one can have a linear combination of
variables with a very high correlation (and also with a small P-value)
that accounts for very little of the variance. In such cases the
correlation might be considered more of a curiosity than important
because it contributes so little to the explanation of the overall
variance. This is a problem in canonical correlation analysis where one
has the problem of using a powerful method to try to find something in
one set of variables that correlates with something in the other set of
variables. In PLS one finds sets of axes that account for larger
proportions of the between set covariance. They usually are but need not
have high correlations. They usually do but need not account for large
proportions of the variance within sets.
While this does not answer your specific question, I hope it will
suggest a perspective to have about such tests.
----------------------
F. James Rohlf, Distinguished Professor
Dept. Ecology and Evolution, Stony Brook University, NY 11794-5245
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-----Original Message-----
From: morphmet [mailto:[email protected]]
Sent: Friday, September 24, 2010 1:55 PM
To: morphmet
Subject: Two block partial least squares - interpreting 1st dimension,
and power to detect covariation
-------- Original Message --------
Subject: Two block partial least squares - interpreting 1st
dimension,
and power to detect covariation
Date: Fri, 24 Sep 2010 08:36:04 -0400
From: Jen <[email protected]>
To: [email protected]
Hi all,
I'm using 2B-PLS to analyze covariation in male and female shape across
20 populations. There are a couple things that are puzzling me about
2B-PLS and I wonder if anyone can help?
(1) The data I'm working with often give the result that the
co-variation explained by the first dimension is not significant, but
the cumulative P-value for the 2nd dimensions is significant. There's a
significant correlation for both dimensions.
I'm wondering if the significant cumulative P-value for the second
dimension indicates that the first two axes should be interpreted
together (as opposed to the 2nd axis being significant & interpretable
but the first axis not)? I had initially thought that the first
dimension should be significant on its own, if it is to be interpreted.
But I notice that most papers that use 2B-PLS don't seem to report a
significance value for the covariance, but instead report the
significance for the correlation.
I also notice that in the example of simulated data given by Rohlf and
Corti (2000), p. 747, the first axis of covariation is not significant
by the permutation test, whereas the second cumulative P-value is
significant: "cumulative percentages of the squared singular
values...and their percentages from the permutation test were 74.39%
(68.7%), 99.95% (0.1%)..."
And since this is an example of a two covarying sets of data, I take
this to mean that the significance of the first axis alone may not be
particularly meaningful?
(2) I ran two tests: (1) a set of data for male shape against itself
(i.e. the same data), and (2) a set of data for male shape (18
landmarks) against a subset of the same data (5 landmarks), expecting
that in both cases the covariance should be perfect or very high and
significant by a permutation test. However, in both cases the first
dimension of covariation was not significant by a permutation test
(using tpsPLS).
Wondering if my expectation was not corrrect (since the two datasets
were identical & perhaps that is not the same thing as highly
covarying), or if perhaps 20 data points from my 20 populations is not
enough for the permutation test to detect significant covariance?
Many thanks in advance for advice on this!
All best,
Jen Perry
--
****************************************************
Department of Ecology and Evolutionary Biology
25 Willcocks St
University of Toronto
TorontoON M5S 3B2
http://individual.utoronto.ca/jenperry/
