# MANOVA proportion of variance explained

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## MANOVA proportion of variance explained

 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 [hidden email] http://www.the-praise-of-insects.blogspot.com                  _________________________________________________________________ ws Live         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: MANOVA proportion of variance explained

 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 > > [hidden email] > > http://www.the-praise-of-insects.blogspot.com> >   > >   > >   > >   > >   > >   >       > _________________________________________________________________ > > 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.caToronto, ONT  M3J 1P3 CANADA ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: MANOVA proportion of variance explained

 Hi Michael   Thank you very much for the intel regarding eta^2. It is pretty much the sort of thing that I am wanting.   Found a good paper regarding all this:   Estimating an Effect Size in One-Way Multivariate Analysis of Variance (MANOVA) H. S. Steyn Jr; S. M. Ellisa Multivariate Behavioral Research 2009 44: 1, 106 — 129 http://www.informaworld.com/smpp/content~db=all~content=a908623057~frm=titlelink  While the interpretation of univariate eta^2 is pretty intuitive, I'm still having a little bit of trouble getting my head around the exact interpretation of the statistic in the multivariate case. Will have to continue reading around!   Thanks again!   Sam   > Date: Wed, 16 Jun 2010 10:11:05 -0400 > From: [hidden email] > To: [hidden email] > CC: [hidden email] > Subject: Re: MANOVA proportion of variance explained > > 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 >> [hidden email] >> http://www.the-praise-of-insects.blogspot.com>> > -- > 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 >       _________________________________________________________________ [[elided Hotmail spam]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.