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.brown at lincolnuni.ac.nz
>
> http://www.the-praise-of-insects.blogspot.com
>
>
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>
>
> _________________________________________________________________
>
> ws Live
>
> [[alternative HTML version deleted]]
>
--
Michael Friendly Email: friendly AT yorku DOT ca
Professor, Psychology Dept.
York University Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele Street Web: http://www.datavis.ca
Toronto, ONT M3J 1P3 CANADA