-------- Original Message --------
Subject: Re: CVA in MorphoJ vs LDA in R
Date: Mon, 13 Jul 2009 10:52:39 -0700 (PDT)
From: Dennis E. Slice <[email protected]>
To: [email protected]
References: <[email protected]>
Some things to think about when considering the output of various programs.
1) Covariance matrices of Procrustes coordinates are guaranteed to be
singular due to the estimation of the superimposition parameters - 4 for
2D data (scale, one angle of rotation, and translation along two
coordinate axes) and 7 for 3D data (one for scale, three angles of
rotation, and translation along three axes). How the programs handle
these singularities - the use of generalized inverses, etc. can affect
the output of a given program.
Relative warp scores (as used by the tps series) have the proper minimum
number of variable dimensions so that singularity is not certain, but
any of these may have singular covariance matrices depending upon actual
covariance structure and sample size relative to landmarks and dimensions.
2) I have, in the past, had students with anomalous PCA results based on
a) a particular program (e.g., SPSS) defaulting to use of the
correlation (instead of covariance) matrix and b) PCA vectors are
defined only up to a reflection.
The above comments are posted with the encouragement of FLB, with whom I
exchanged a couple of short messages on this topic. Any mistakes are, of
course, my own responsibility.
-ds
morphmet wrote:
-------- Original Message --------
Subject: RE: CVA in MorphoJ vs LDA in R
Date: Mon, 13 Jul 2009 03:09:36 -0700 (PDT)
From: Louis Boell <[email protected]>
To: <[email protected]>, <[email protected]>
References: <[email protected]>
<c67cb266.6feb%[email protected]>
Hi Annat,
No, I didn´t receive any answer. I guess that there are not many people
who know enough about both programs to provide the solution.
What I find troublesome in this respect is that your results seem to
depend sometimes from the software you are using. When the software is
intransparent, and you don´t care how it works, and you try only one
program, you might easily end up drawing malinformed conclusions (I
obtained even more bizarre results in SPSS, with most of the CV axes
being identical to those in MorphoJ and four axes being different!).
The only solution I can see for my problem is to try and implement,
e.g., the very same procedure used by MorphoJ in R so that I understand
how it works exactly. I have 13 groups (or even more in some of the
analyses). I hope that I will be able to solve this problem. I expect to
learn a lot while trying! ;-)
Best wishes,
Louis
Louis Boell
MPI für Evolutionsbiologie
August-Thienemannstr.2
24306 Plön
[email protected]
[email protected]
> Date: Fri, 10 Jul 2009 08:55:02 -0500
> Subject: Re: CVA in MorphoJ vs LDA in R
> From: [email protected]
> To: [email protected]
>
> Hi Louis,
> Did you get an answer to your question yet?
> I had a similar problem a while ago and I noticed that if I use the
whole
> configuration I get less separation between the groups then if I use
half of
> it - I'm working with bilateral symmetric objects (skulls) and use
only the
> symmetric component so the two halves are redundant. I didn't
investigate it
> in depth yet, but seems like the redundancy decreases the separation for
> some reason (I don't know enough linear algebra to say why...).
> How many groups do you have btw? The mathematical procedure is
different if
> you have two groups or more. It's a simple calculation in the case of
2 but
> there are several ways for determining the CV's in the case of more
than 2,
> at least in R, so that might be difference between the two softwares
(I only
> had 2).
> I hope that helps somewhat. In any case, I'd be interested to know
what is
> the solution to this.
>
> Best,
> Annat
>
> > From: morphmet <[email protected]>
> > Reply-To: <[email protected]>
> > Date: Tue, 07 Jul 2009 10:06:41 -0400
> > To: morphmet <[email protected]>
> > Subject: CVA in MorphoJ vs LDA in R
> > Resent-From: <[email protected]>
> > Resent-Date: Tue, 7 Jul 2009 07:08:51 -0700 (PDT)
> >
> >
> >
> > -------- Original Message --------
> > Subject: CVA in MorphoJ vs LDA in R
> > Date: Mon, 6 Jul 2009 08:34:07 -0700 (PDT)
> > From: Louis Boell <[email protected]>
> > To: <[email protected]>
> >
> >
> >
> > Dear colleagues,
> >
> > I encountered the following problem: in R, I performed least
> > discriminant analysis (lda) using as the argument Procrustes
coordinates
> > calculated by procGPA . I then used the "predict" function to
calculate
> > Mahalanobis distances between groups. I was, however, surprised to see
> > that the resulting Mahalanobis distances between groups do
fundamentally
> > differ from those calculated using CVA in MorphoJ, based on the
same set
> > of procrustes distances also calculated in R.
> > I had thought that LDA was close to being identical to CVA and had
thus
> > expected very similar results. Did I omit an important step? As far
as I
> > know, the procGPA coordinates have already been projected in the
tangent
> > space, and first calculating a PCA and omitting the last four scores
> > should not much affect the results.
> > I have rechecked both my Procrustes coordinates and the grouping
factor.
> > Everything seems fine.
> > Is there solmething fundamental I might be ignoring?
> > Thanks for advice, best wishes
> >
> > Louis Boell
> >
> >
> >
> > Louis Boell
> > MPI für Evolutionsbiologie
> > August-Thienemannstr.2
> > 24306 Plön
> > [email protected]
> > [email protected]
> >
> >
> >
> >
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> > For more information visit http://www.morphometrics.org
> >
>
>
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Dennis E. Slice
Associate Professor
Dept. of Scientific Computing
Florida State University
Dirac Science Library
Tallahassee, FL 32306-4120
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Department of Anthropology
University of Vienna
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