-------- Original Message --------
Subject: Algorithm and visualisation of CVA
Date: Wed, 30 Sep 2009 07:15:53 -0700 (PDT)
From: Stefan Schlager <[email protected]>
To: [email protected]
References: <[email protected]>
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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