-------- Original Message --------
Subject: Re: regression of Procrustes coordinates on classifiers
Date: Fri, 27 Feb 2009 07:29:36 -0800 (PST)
From: Joseph Kunkel <[email protected]>
To: [email protected]
CC: Joseph Kunkel <[email protected]>
References: <[email protected]>
Louis,
My first comment is about using Mahalanobis D as a 'distance'. That
is really a misnomer. Mahalanobis D is a sum of independent F-tests
when you look at how it is calculated. The true distance is perhaps
the mean Euclidean distance and Mahalanobis D is the test of whether
that Euclidean Distance is actually significantly different from
zero. Using Mahalanobis D as a distance is like using a t-test value
as a measure of a difference-of-interest. If that is what you want,
an abstraction of how many standard deviations you are away from zero
that is fine. But remember that F-tests explode (they are ratios of
squares so if the denominator is unstable the explosion is greater)
when the the null hypothesis is not true! Sorry for sawing an old
horse, or am I wrong in a more basic way in this instance?
I would export the aligned coordinates, analyze then in a GLM
factorial design, remove your 'desert vs forest "factor"' before and
after calculating your distance and testing for their significance.
To be pedantic for the sake of novice readers of this list: As you
suggest, in the General Linear Model, Y = XB, your factors belong on
the right in the design matrix X. They are corrected for as factors.
Continuous variables belong on the left as columns of the Y matrix and
should be eliminated by the generalized test of additional
information. (Rao, 1965, Linear Statistical Inference and its
Applications)
I would avoid the perhaps easier route of analysis and suggest that if
MorphoJ wants to include correcting for factors within a comparison
group that it be done in a formally correct way. Doing things in
convenient ways will take us down the same road traveled by the
Windows operating System.
Joe
On Feb 27, 2009, at 9:01 AM, morphmet wrote:
-------- Original Message --------
Subject: regression of Procrustes coordinates on classifiers
Date: Fri, 27 Feb 2009 05:55:11 -0800 (PST)
From: Louis Boell <[email protected]>
To: <[email protected]>
Dear colleagues,
I wish to investigate how strongly the fact that a sample of specimens
belongs to a given class, say, samples from desert vs samples from
forest, influences the Mahalanobis distances between my samples. This
amounts to "correcting" for the desert vs forest "factor"
and checking how much smaller the Mahalanobis distances between desert
and forest samples get when calculated from the residuals of the
"correction".
I have about 10 samples per class (each sample in itself consisting of
enough specimens given the number of landmarks) from each class).
In this situation, I tried "correction" by using a dummy-coded
regression (desert=1, forest=2) of Procrustes coordinates on my factor
in MorphoJ. The results are appealing. Now I know that for a
noncontinoous independent variable, you´d prefer to use logistic
regression instead of simple regression, because the fit will be more
appropriate in this case.
My question is: is there a statistical reason not to use this
procedure?
Or caution about the interpretation of the results?
I´d be grateful for any advice
Best wishes
Louis
Louis Boell
MPI für Evolutionsbiologie
August-Thienemannstr.2
24306 Plön
[email protected]
[email protected]
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Joseph G. Kunkel, Professor
Biology Department
University of Massachusetts Amherst
Amherst MA 01003
http://www.bio.umass.edu/biology/kunkel/
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