Re: Algorithm and visualisation of CVA

[morphmet]

-------- Original Message --------
Subject: Re: Algorithm and visualisation of CVA
Date: Sat, 3 Oct 2009 04:56:52 -0700 (PDT)
From: oyvind.ham...@nhm.uio.no
To: morphmet@morphometrics.org
References: <4ac5ff5e.1020...@morphometrics.org>


Dear Stefan, I would be very grateful if you could email me your R code
for CVA. I can compute W, B etc. myself, but what is then your procedure
for reproducing the MorphoJ CVA ?

Through the years I have used several versions of CVA taken from the
literature for my program "Past", but I never managed to reproduce exactly
the result of any other software package!


Thanks again,

Oyvind Hammer
Natural History Museum
University of Oslo

-------- Original Message --------
Subject:        Re: Algorithm and visualisation of CVA
Date:   Fri, 2 Oct 2009 06:07:53 -0700 (PDT)
From:   Stefan Schlager <stefan.schla...@uniklinik-freiburg.de>
To:     morphmet@morphometrics.org
References:     <4ac38d6e.7040...@morphometrics.org>



Dear all,

I solved the problem: I forgot the weighting of the Between groups SSQ
matrix (and some corrections related to the degrees of freedom involved).
I am now able to reproduce the exact same results as MorphoJ
(calculation and visualization)

Anyhow, I would be glad, if anyone could explain to me (or tell me,
where I can read it), if my explanation for *W%*%CV
*as invertation of the scaling was true. I actually just tried it, as
the adding of an untransformed CV to the mean bore rather grotesque
results. And it seemed logical that there was still some kind of space
deformation "inherent" in the CV.


Another question is, where to put the threshold for a zero eigenvalue of
W, as the inverse inflates minimal differences (for example if
superimposition is done by different software programs): The canonical
roots differ significantly, if the threshold is too low. At the moment I
put it to 1e-7 and gained about the same results, no matter how
superimposition is performed - is there any reliable value I should
chose ore rather let "the thumb rule"?


I would also be thankfull for further detailed literature (my main input
upt to now was: /Zelditch, 2004, Campbell, N. A. and Atchley, W. R.
(1981). The geometry of Canonical Variates analysis. Systematic Zoology,
30, 268?280 and Klingenberg (2005), Distances and directions in
multidimensional shape spaces: implications for morphometric
applications)/

Greetings and a nice weekend
Stefan
**

Stefan Schlager M.A.
Medizinische Fakultät - Anthropologie
Hebelstr. 29
79104 Freiburg
Tel: +49(0)761/203-5522
Fax: +49(0)761/203-6898



morphmet schrieb:

-------- Original Message --------
Subject:     Algorithm and visualisation of CVA
Date:     Wed, 30 Sep 2009 07:15:53 -0700 (PDT)
From:     Stefan Schlager <stefan.schla...@uniklinik-freiburg.de>
To:     morphmet@morphometrics.org
References:     <4ac347c7.8080...@morphometrics.org>



Dear all,

I'm trying to write a script in R for performing a CVA and a couple of
questions came up.

    * let W be the pooled within groups covariance matrix
    * and B the between groups covariance matrix
    * A is a matrix of shape variables
    * ng is the number of groups
    * n is the number of observations


1. as far as I understand, the CVs are:
CV<-eigen(ginv(W)%*%B)$vectors[,1:ng]  ---- ginv=general inverse
the CVscores then are: A%*%CV

when performing a CVA with two groups, I get the exact same results as
in MorphoJ - only on a far smaller scale.
When I have more than two groups, the CVs are completely different -
wheras the plot of the scores are very similar to those of MorphoJ

2. How can I calculate the effects on actual configurations for
visualization?
     I thought of something like: meanshape+x*(W%*%CV[,i]) ----- for the
i-th CV
    for the two-group example I got the same results as MorphoJ (after
scaling W by factor n)

    where W inverts the deformation of the adjusted space  and x is the
CVscore to be displayed.

My questions now:


do I miss something in point 1. when it comes to more than two groups?

is the calculation of the effect of the CV correct?


Thank you very much in advance
Stefan



Stefan Schlager M.A.
Medizinische Fakultät - Anthropologie
Hebelstr. 29
79104 Freiburg
Tel: +49(0)761/203-5522
Fax: +49(0)761/203-6898

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