Dear Peter and Tamre,
I took a closer look at this today, and the infrastructure was there to do
the univariate tests even with a singular SSP matrix, so I modified
Anova.mlm() to accommodate this case. The updates are in the development
version of the car package on R-Forge.
An example (checked against SAS):
--------- snip ------------
> library(car)
Loading required package: MASS
Loading required package: nnet
> phase <- factor(rep(c("pretest", "posttest", "followup"), c(5, 5, 5)),
+ levels=c("pretest", "posttest", "followup"))
> hour <- ordered(rep(1:5, 3))
> idata <- data.frame(phase, hour)
> idata
phase hour
1 pretest 1
2 pretest 2
3 pretest 3
4 pretest 4
5 pretest 5
6 posttest 1
7 posttest 2
8 posttest 3
9 posttest 4
10 posttest 5
11 followup 1
12 followup 2
13 followup 3
14 followup 4
15 followup 5
>
> mod.ok <- lm(cbind(pre.1, pre.2, pre.3, pre.4, pre.5,
+ post.1, post.2, post.3, post.4, post.5,
+ fup.1, fup.2, fup.3, fup.4, fup.5) ~
gender,
+ data=OBrienKaiser[1:5,])
> av.ok.2 <- Anova(mod.ok, idata=idata, idesign=~phase*hour)
> av.ok.3 <- Anova(mod.ok, idata=idata, idesign=~phase*hour, type=3)
> summary(av.ok.2, multivariate=FALSE)
Univariate Type II Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 1323.00 1 91.111 3 43.5622 0.00708 **
gender 0.89 1 91.111 3 0.0293 0.87505
phase 2.00 2 30.556 6 0.1964 0.82679
gender:phase 7.44 2 30.556 6 0.7309 0.51990
hour 35.07 4 6.333 12 16.6105 7.796e-05 ***
gender:hour 1.93 4 6.333 12 0.9158 0.48597
phase:hour 3.73 8 41.667 24 0.2688 0.97012
gender:phase:hour 5.27 8 41.667 24 0.3792 0.92125
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning message:
In summary.Anova.mlm(av.ok.2, multivariate = FALSE) :
Singular error SSP matrix:
non-sphericity test and corrections not available
> summary(av.ok.3, multivariate=FALSE)
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 1283.56 1 91.111 3 42.2634 0.007391 **
gender 0.89 1 91.111 3 0.0293 0.875049
phase 0.78 2 30.556 6 0.0764 0.927365
gender:phase 7.44 2 30.556 6 0.7309 0.519900
hour 36.07 4 6.333 12 17.0842 6.779e-05 ***
gender:hour 1.93 4 6.333 12 0.9158 0.485966
phase:hour 3.93 8 41.667 24 0.2832 0.965130
gender:phase:hour 5.27 8 41.667 24 0.3792 0.921247
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning message:
In summary.Anova.mlm(av.ok.3, multivariate = FALSE) :
Singular error SSP matrix:
non-sphericity test and corrections not available
--------- snip ------------
I think that it should also be possible to get the GG and HF epsilons but I
think that would require a different approach than is currently used.
Best,
John
> -----Original Message-----
> From: r-help-boun...@r-project.org [mailto:r-help-bounces@r-
> project.org] On Behalf Of peter dalgaard
> Sent: March-05-12 11:29 AM
> To: Tamre Cardoso
> Cc: r-help@r-project.org; John Fox
> Subject: Re: [R] new to repeated measures anova in R
>
>
> On Mar 5, 2012, at 16:05 , Tamre Cardoso wrote:
>
> > Thank you.
> >
> > I have attached the data:
>
> The list software seems to have scrubbed it though...
>
> > The error message from Anova is:
> >
> >> pressure.aov = Anova(multmodel, idata=fact.idata, idesign = ~Shoe *
> >> Region, type="III")
> > Error in linearHypothesis.mlm(mod, hyp.matrix, SSPE = SSPE, idata =
> idata, :
> > The error SSP matrix is apparently of deficient rank = 9 < 14
>
> Oho. Yes that can be a problem. I it is not actually required to have a
> full rank SSP to do the F tests, but the design of Anova() is such that
> it tries to do multivariate analyses somewhere along the way, and I
> don't think there's a way to tell it not to (John?).
>
> I don't think plain anova.mlm has this particular restriction. It's
> basically the same issue as this:
>
> > X <- matrix(rnorm(12),3,4)
> > idata <- data.frame(gg = factor(1:4))
> > anova(m,idata=idata, X=~1, test="Spherical")
> Analysis of Variance Table
>
>
> Contrasts orthogonal to
> ~1
>
> Greenhouse-Geisser epsilon: 0.4312
> Huynh-Feldt epsilon: 0.8876
>
> Df F num Df den Df Pr(>F) G-G Pr H-F Pr
> (Intercept) 1 0.3376 3 6 0.79935 0.66045 0.77968
> Residuals 2
> > Anova(m,idata=idata, idesign=~gg, type="III")
> Error in linearHypothesis.mlm(mod, hyp.matrix, SSPE = SSPE, idata =
> idata, :
> The error SSP matrix is apparently of deficient rank = 2 < 3
> > anova(m,idata=idata, X=~1) # Full MV test fails here too
> Error in anova.mlm(m, idata = idata, X = ~1) : residuals have rank 2 <
> 3
>
>
> --
> Peter Dalgaard, Professor
> Center for Statistics, Copenhagen Business School Solbjerg Plads 3,
> 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Email: pd....@cbs.dk Priv: pda...@gmail.com
>
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