[R] Type II and III sum of squares (R and SPSS)
peter dalgaard
pdalgd at gmail.com
Wed Mar 21 18:27:17 CET 2012
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]]
>
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--
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
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