-------- Original Message --------
Subject: RE: relative warp question
Date: Tue, 23 Feb 2010 16:00:30 -0000
From: Richards Paul <[email protected]>
To: <[email protected]>
Thank you for your helpful advice. However, I am still a bit confused
and so have rephrased my question, based on what I now know.
I'm now clear analysis of a single variable (i.e. PCA 1) isn’t really
valid. However, is it valid to perform data reduction using PCA (e.g.
take the first 10 axes explaining <90% variation), as can be done prior
to CVA, before carrying out multivariate analyses? If so, can analyses
be performed on PCA (or CVA scores) directly, or must I pick out the
variables from the weight matrix contributing towards my axes of
variation to put into subsequent multivariate analyses? If data
reduction is valid, but not on PCA scores directly, what is the best way
to identify the weight matrix variables contributing towards my chosen
group of PCA axes – can I just regress each PCA against the weight
matrix variables and exclude those that aren’t significantly correlated
or is there a far easier method (I have been using TPSrelw).
I’m sorry this largely repeats my original question, but I have heard
mixed views on whether PCA scores can be statistically analysed
directly. And if data reduction via PCA is used prior to CVA why can it
not be applied prior to carrying out other multivariate tests?
Many thanks,
Paul
----------------
Paul Richards
School of Biology
University of Nottingham
University Park
NG7 2RD
+44 (0)115 8213128
[email protected]
-------- Original Message --------
Subject: Re: Relative warp question
Date: Wed, 10 Feb 2010 08:55:45 +0100
From: andrea cardini <[email protected]>
To: [email protected]
Dear Paul,
RWs are (except in a very special case that rarely if ever occurs in
biological data) just PCs of shapes. Do a PCA using the variance-covariance
matrix on the GPA superimposed (aligned) coordinates and you'll get
exactely the same result. This is why many of us just call it PCA of GPA
superimposed data.
I would not do statistical tests one PC at a time. This is because PCs are
built only to maximize total sample variance but they 'don't know' anything
about groups.
Imagine that you're analysing triangles and you have two groups. Then you
have only two PCs with non-zero eigenvalues (4 d.f. are lost in the GPA).
You test differences one PC at a time and get non-significant results. You
give a look at the scatterplot, however, and you see a good separation of
the two groups but this separation occurs in a direction which is 45° to
your PCs. The differences are not picked up by any PC on its own but you
would have found them if you had done a multivariate analysis.
The fact that PCs sometimes align to some extent with interesting axes of
variation is accidental. You cannot exclude that there's something else
interesting going on in directions which are not collinear with any of the
PCs. PCs maximize TOTAL sample variance and are not optimized to fit any
other model. This does not only concern tests of group differences (that
should be multivariate) but any other a priori model including your "high
spired vs flat and aperture size" which, as you noticed, seem to be
described by several PCs.
The problem with power can often, I fear, only be solved by increasing
sample size. With small samples, you can still do resampling stats (e.g.,
pairwise permutation tests for mean shape differences etc.) but power may
be low and potential issues with sampling error are still there.
MorphoJ does a lot of this kind of resampling stats (see DA/CVA). TPSregr
also can do pairwise tests using permutations. The IMP series has plenty of
resampling stats etc. etc.
Good luck.
Cheers
Andrea
-------- Original Message --------
Subject: RE: Relative warp question
Date: Tue, 09 Feb 2010 21:43:00 -0500
From: F. James Rohlf <[email protected]>
Organization: Stony Brook University
To: [email protected]
References: <[email protected]>
An analysis of relative warps is just a PCA using the weight matrix
(matrix of partial warp scores) as the data matrix. The partial warps
are the variables. If some variable had high loadings on the first few
dimensions then one might be tempted to do a t-test using that variable.
However, in just cases the variable was selected because of its
empirical pattern so the t-test would have to be adjusted to allow for
multiple testing. It is not clear how large the correction should be. It
was selected based on a linear combination and there are an infinite
number of such linear combinations.
One should at least correct for the number of variables (partial warps)
that could possibly be considered for testing. Of course, once you find
that a particular partial warp shows a 'significant' difference it is
unclear what you should do next. Partial warps are usually not too
interesting by themselves. Their purpose is to simply span a space that
captures all possible shape variation for a given set of landmarks.
----------------------
F. James Rohlf, Distinguished Professor
Dept. Ecology and Evolution, Stony Brook University, NY 11794-5245
>-------- Original Message --------
>Subject: Relative warp question
>Date: Mon, 1 Feb 2010 09:29:50 -0500
>From: Richards Paul <[email protected]>
>To: <[email protected]>
>
>
>
>Hi , I am applying relative warp analysis to a population of land
>snails, but I am new to all the theory and methods. Im doing a
>preliminary analysis to see if shell colour (i.e. dark, intermediate,
>light) is associated with differences in shape. I have run the relative
>warp analysis using tpsrelw, but have a few queries about using the
>output and potential analysis.
>
>
>
>RW1 to 3 appear to describe the apparent shape variance I am interested
>in (i.e. high spired vs flat and aperture size). Do the relative warps
>correspond directly to the identical partial warps in the weight matrix
>(e.g. RW1 scores column corresponds to the first variable column in the
>weight matrix)? If so could I take the first variable in the weight
>matrix (assuming it corresponds to RW1) and perform a T test just for
>this variable between my dark and light colour groups? I have tried
>using a MANOVA approach, but because these samples werent collected
>specifically with this analysis in mind I am lacking enough samples in
>each of my colour groups to get sufficient power, but I think a T test
>on a per variable basis should be OK in the first instance.
>
>
>
>I would be most grateful for any advice, and apologise if I have
>overlooked something obvious!
>
>
>
>Thanks, Paul
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