Re: [R] MANOVA proportion of variance explained

From: Michael Friendly <friendly_at_yorku.ca>
Date: Mon, 21 Jun 2010 12:09:36 -0400

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: friendly_at_yorku.ca >> To: s_d_j_brown_at_hotmail.com >> CC: r-help_at_r-project.org >> 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 >>> sam.brown_at_lincolnuni.ac.nz >>> 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 >> >>
> _________________________________________________________________
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-- 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 ______________________________________________ R-help_at_r-project.org 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.
Received on Mon 21 Jun 2010 - 16:10:05 GMT

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