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-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
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.ca Toronto, ONT M3J 1P3 CANADA ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
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-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
Sam Brown wrote:
> Hi Michael > > Thank you very much for the intel regarding eta^2. It is pretty much the sort of thing that I am wanting. > The latest developer version of the heplots package on R-Forge now includes an initial implementation of etasq() for multivariate linear models. Note that for s>1 dimensional tests, the values of eta^2 differ according to the test statistic: Pillai trace (default), Hotelling-Lawley trace, Wilks' Lambda, Roy maximum root test. See ?heplots:::etasq for details. > # install.packages("heplots",repos="http://R-Forge.R-project.org") > library(heplots) > data(Soils) # from car package > soils.mod <- lm(cbind(pH,N,Dens,P,Ca,Mg,K,Na,Conduc) ~ Block + Contour*Depth, data=Soils) > etasq(Anova(soils.mod)) eta^2 Block 0.5585973 Contour 0.6692989 Depth 0.5983772 Contour:Depth 0.2058495 > etasq(soils.mod) # same eta^2 Block 0.5585973 Contour 0.6692989 Depth 0.5983772 Contour:Depth 0.2058495 > etasq(Anova(soils.mod), anova=TRUE) Type II MANOVA Tests: Pillai test statistic eta^2 Df test stat approx F num Df den Df Pr(>F) Block 0.55860 3 1.6758 3.7965 27 81 1.777e-06 *** Contour 0.66930 2 1.3386 5.8468 18 52 2.730e-07 *** Depth 0.59838 3 1.7951 4.4697 27 81 8.777e-08 *** Contour:Depth 0.20585 6 1.2351 0.8640 54 180 0.7311 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > > 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 > This paper may be more confusing than helpful, since the emphasis is on the use of eta^2 as measures of multivariate 'effect size' and I think they try to blend in too many different threads from the effect-size literature. And they don't discuss what happens in designs with more than one factor or regressor. In the general case, etasq() calculates measures of partial eta^2, reflecting the *additional* proportion of variance associated with a given term in the full model that includes it, relative to the reduced model that excludes it, analogous to partial R^2 in univariate regression models. > >> 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 >> >> > _________________________________________________________________ > Find a way to cure that travel bug MSN NZ Travel > http://travel.msn.co.nz/ -- 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 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
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