# [R] MANOVA proportion of variance explained

Michael Friendly friendly at yorku.ca
Wed Jun 16 16:11:05 CEST 2010

```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
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> 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.
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> I can acheive something like what I want by doing the following:
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> 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)))
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> U <- rbind(X,Y,Z)
> m <- manova(U~as.factor(rep(1:3, c(3, 2, 3))))
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> summary(m,test="Wilks")
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> SS<-summary(m)\$SS
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> (a<-mean(SS[[1]]/(SS[[1]]+SS[[2]])))
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> and concluding that 94% of variation is explained.
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> Is my desire misguided? If it is a worthy aim, is this a valid way of acheiving it?
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> Thanks a lot!
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> Sam
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> Samuel Brown
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> Research assistant
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> Bio-Protection Research Centre
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> PO Box 84
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> Lincoln University
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> Lincoln 7647
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> Canterbury
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> New Zealand
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> sam.brown at lincolnuni.ac.nz
>
> http://www.the-praise-of-insects.blogspot.com
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> _________________________________________________________________
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> ws Live
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> 	[[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
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