[R] Type II and III sum of squares (R and SPSS)

[Helios de Rosario]

>>> El día 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 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)

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

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