I think you are looking for a multivariate measure of association,
analogous to R^2 for a univariate linear model. If so, there are
extensions of eta^2 from univariate ANOVAs for each of the multivariate
test statistics, e.g.,
for Pillai (-Bartlett) trace and Hotelling-Lawley trace and a given
effect tested on p response measures
eta2(Pillai) = Pillai / s
eta2(HLT) = HLT / (HLT+s)
where s = min(df_h, p)
Alternatively, you could look at the candisc package which, for an
s-dimensional effect, gives a breakdown of the variance reflected in
each dimension of the latents roots of HE^{-1}
Sam Brown wrote:
Hello everybody
After doing a MANOVA on a bunch of data, I want to be able to make some comment
on the amount of variation in the data that is explained by the factor of
interest. I want to say this in the following way: XX% of the data is explained
by A.
I can acheive something like what I want by doing the following:
X <- structure(c(9, 6, 9, 3, 2, 7), .Dim = as.integer(c(3, 2)))
Y <- structure(c(0, 2, 4, 0), .Dim = as.integer(c(2, 2)))
Z <- structure(c(3, 1, 2, 8, 9, 7), .Dim = as.integer(c(3, 2)))
U <- rbind(X,Y,Z)
m <- manova(U~as.factor(rep(1:3, c(3, 2, 3))))
summary(m,test="Wilks")
SS<-summary(m)$SS
(a<-mean(SS[[1]]/(SS[[1]]+SS[[2]])))
and concluding that 94% of variation is explained.
Is my desire misguided? If it is a worthy aim, is this a valid way of acheiving
it?
Thanks a lot!
Sam
Samuel Brown
Research assistant
Bio-Protection Research Centre
PO Box 84
Lincoln University
Lincoln 7647
Canterbury
New Zealand
sam.br...@lincolnuni.ac.nz
http://www.the-praise-of-insects.blogspot.com
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