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.tommasi@unich.it </mc/compose?to=marco.tommasi@unich.it>
tel.: +39 0871 3555890 / fax: + 39 0871 3554163
Web site: www.dni.unich.it
[[alternative HTML version deleted]]
On Mar 21, 2012, at 11:27 , Marco Tommasi wrote:> 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.Well, it would primarily concern the maintainer of the "car" package, which is the one containing the (capital-A) Anova() function. The type III SS don't look right to me either. With aov() we get> M3l <- reshape(M3, direction="long", varying=c("b1","b2","b3"),sep="") > summary(aov(b~fattA*factor(time)+ Error(factor(id)), M3l))Error: factor(id) Df Sum Sq Mean Sq F value Pr(>F) fattA 1 26.042 26.042 16.3 0.00682 ** Residuals 6 9.583 1.597 --- Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 Error: Within Df Sum Sq Mean Sq F value Pr(>F) factor(time) 2 42.33 21.167 23.81 6.65e-05 *** fattA:factor(time) 2 20.33 10.167 11.44 0.00166 ** Residuals 12 10.67 0.889 --- Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1> > 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.tommasi at unich.it </mc/compose?to=marco.tommasi at unich.it> > tel.: +39 0871 3555890 / fax: + 39 0871 3554163 > Web site: www.dni.unich.it > > > > [[alternative HTML version deleted]] > > ______________________________________________ > 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.-- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
>>> El d?a 21/03/2012 a las 11:27, Marco Tommasi<marco.tommasi at unich.it> wrote> 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 typeIII> sum of squares. > > Briefly, I have to do a 2x3 mixed model anova, wherein the firstfactor> is a between factor and the second factor is a within factor. I usethe> command Anova in the list below, because I want to obtain also thesum> 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 thebeteween> 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)You are missing a couple of important points here. First, fattA is a factor according to your description, but you have coded it as a numeric variable. You must coerce it to factor: M3$fattA <- as.factor(M3$fattA) Now, type III SS with Anova() only provides sensible results, if the factor contrasts are orthogonal, e.g. "contr.sum", "contr.poly", or "contr.helmert". This is not the default in R, so you should make it explicit: f5<-lm(cbind(b1,b2,b3)~fattA,data=M3, contrasts=list(fattA="contr.sum")) Now, Anova() gives the same results regardless of the SS type:> > fB<-factor(c(1:3)) > > d2<-data.frame(fB)Try: summary(Anova(f5,idata=d2,idesign=~fB,type=2),multivariate=FALSE) summary(Anova(f5,idata=d2,idesign=~fB,type=3),multivariate=FALSE) I recommend you read Fox's and Weisberg's book that explain many functions of "car", including ANOVA. See specially pages 193 and following. Type carWeb() to go to its webpage. Helios INSTITUTO DE BIOMEC?NICA DE VALENCIA Universidad Polit?cnica de Valencia ? Edificio 9C Camino de Vera s/n ? 46022 VALENCIA (ESPA?A) Tel. +34 96 387 91 60 ? Fax +34 96 387 91 69 www.ibv.org Antes de imprimir este e-mail piense bien si es necesario hacerlo. En cumplimiento de la Ley Org?nica 15/1999 reguladora de la Protecci?n de Datos de Car?cter Personal, le informamos de que el presente mensaje contiene informaci?n confidencial, siendo para uso exclusivo del destinatario arriba indicado. En caso de no ser usted el destinatario del mismo le informamos que su recepci?n no le autoriza a su divulgaci?n o reproducci?n por cualquier medio, debiendo destruirlo de inmediato, rog?ndole lo notifique al remitente.