To whom it may concern
I made some analysis with R using the command Anova. However, I found
some problmes with the output obtained by selecting type II o type III
sum of squares.
Briefly, I have to do a 2x3 mixed model anova, wherein the first factor
is a between factor and the second factor is a within factor. I use the
command Anova in the list below, because I want to obtain also the sum
of squares of the linear and quadratic contrast between the levels of
the within factor.
Below I report the list of commands used in R ("fattA" is the beteween
factor and "fB" is the within factor):
> a1b1<-c(10,9,8,7)
> a1b2<-c(7,6,4,5)
> a1b3<-c(3,2,3,4)
> a2b1<-c(9,9,8,7)
> a2b2<-c(8,7,9,7)
> a2b3<-c(7,8,8,6)
>
> M3<-matrix(0,8,4)
> M3[,1]<-cbind(a1b1,a2b1)
> M3[,2]<-cbind(a1b2,a2b2)
> M3[,3]<-cbind(a1b3,a2b3)
> M3[,4]<-rep(c(1,2),each=4)
>
> colnames(M3)<-c("b1","b2","b3","fattA")
>
> M3<-as.data.frame(M3)
>
> require(car)
Loading required package: car
Loading required package: MASS
Loading required package: nnet
> f5<-lm(cbind(b1,b2,b3)~fattA,data=M3)
> a5<-Anova(f5)
> f6<-lm(c(b1,b2,b3)~rep(fattA,3),data=M3)
>
>
> fB<-factor(c(1:3))
> d2<-data.frame(fB)
> a6<-Anova(f5,idata=d2,idesign=~fB,type=2)
> summary(a6,multivariate=F)
Univariate Type II Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 1080.04 1 9.5833 6 676.200 2.133e-07 ***
fattA 26.04 1 9.5833 6 16.304 0.006819 **
fB 42.33 2 10.6667 12 23.812 6.645e-05 ***
fattA:fB 20.33 2 10.6667 12 11.438 0.001660 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Mauchly Tests for Sphericity
Test statistic p-value
fB 0.87891 0.7242
fattA:fB 0.87891 0.7242
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
fB 0.89199 0.0001474 ***
fattA:fB 0.89199 0.0026452 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
HF eps Pr(>F[HF])
fB 1.2438 6.645e-05 ***
fattA:fB 1.2438 0.00166 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning message:
In summary.Anova.mlm(a6, multivariate = F) : HF eps > 1 treated as 1
I repated the anlysis by setting type III sum of squares and I obtained:
> a6<-Anova(f5,idata=d2,idesign=~fB,type=3)
> summary(a6,multivariate=F)
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 30.817 1 9.5833 6 19.294 0.004606 **
fattA 26.042 1 9.5833 6 16.304 0.006819 **
fB 40.133 2 10.6667 12 22.575 8.57e-05 ***
fattA:fB 20.333 2 10.6667 12 11.438 0.001660 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Mauchly Tests for Sphericity
Test statistic p-value
fB 0.87891 0.7242
fattA:fB 0.87891 0.7242
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
fB 0.89199 0.0001851 ***
fattA:fB 0.89199 0.0026452 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
HF eps Pr(>F[HF])
fB 1.2438 8.57e-05 ***
fattA:fB 1.2438 0.00166 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Warning message:
In summary.Anova.mlm(a6, multivariate = F) : HF eps > 1 treated as 1
As you can see, the sum of squares of the within factor "fB" and of the
intercept obtained by setting type II sum of squares are dofferent form
those obtained by setting type III sum of squares. I repeated the
analysis by using SPPS (type II and III) and i obtained the same sum of
squares for both types., which I report below:
within factor and interaction
source Sum of squares (type II and III)
fB 42.33333333
fB * fattA 20.33333333
Error(fattB) 10.66666667
between factor
Source Sum of squares (type II and III)
intercept 1080.041667
fattA 26.04166667
Error 9.583333333
The most strange thing, for me, is not only that R gives different
outputs both for type II and III sum of squares, but that the output
obtained with type II sum of squares in R coincides with the output
obtained with type III of SPSS.
As I remember, with balanced design, type II and III sum of squares
should give the same output.
Is there anybody that can help me about this point?
thank you for your kind attention.
Marco Tommasi, Ph/D.
Department of Neuroscience and Imaging
"G. D'Annunzio" University of Chieti-Pescara
Via dei Vestini 31
66100 Chieti
ITALY
e-mail: marco.tomm...@unich.it </mc/compose?to=marco.tomm...@unich.it>
tel.: +39 0871 3555890 / fax: + 39 0871 3554163
Web site: www.dni.unich.it
[[alternative HTML version deleted]]
______________________________________________
R-help@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.
