[R] Type I and Type III SS in anova

[John Fox]

Dear Menelaos,

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
> Behalf Of Menelaos Stavrinides
> Sent: September-25-08 9:56 PM
> To: r-help at r-project.org
> Subject: [R] Type I and Type III SS in anova
> 
> Hi all,
> I have been trying to calculate Type III SS in R for an unbalanced two-way
> anova. However, the Type III SS are lower for the first factor compared to
> type I but higher for the second factor (see below). I have the impression
> that Type III are always lower than Type I - is that right?

No.

> 
> And a clarification about how to fit Type III SS. Fitting
model<-aov(y~a*b)
> in the base package and then loading car / changing contrasts / running
> Anova(model,type=c("III")) gives different results compared to loading car
/
> changing contrasts / fitting model<-aov(y~a*b) / running
> Anova(model,type=c("III")). However summary(model) gives the same results
in
> both cases. Is this how it is set up?

If you use "type-III" tests in an unbalanced ANOVA, and want to test
sensible hypotheses, you should use an orthogonal row-basis for the effects,
such as is provided by contr.helmert, contr.poly, or contr.sum, but not by
the default contr.treatment. When you fit a model before changing the
contrast type, contr.treatment is used. Changing the contrast type
subsequent to that has no effect on a model that's already fit (how could
it, unless, e.g., the model is updated?). Because the summary method for aov
objects reports "typei-I" (sequential) tests, the results are independent of
the contrast type.

Regards,
 John

> 
> > local({pkg <- select.list(sort(.packages(all.available = TRUE)))
> + if(nchar(pkg)) library(pkg, character.only=TRUE)})
> > options(contrasts=c("contr.helmert","contr.poly"))
> > model2<-aov(tdrate~temp*sex)
> > summary(model2)
>              Df   Sum Sq  Mean Sq   F value  Pr(>F)
> temp          3 0.110137 0.036712 1005.6947 < 2e-16 ***
> sex           1 0.000141 0.000141    3.8593 0.05095 .
> temp:sex      3 0.000154 0.000051    1.4073 0.24206
> Residuals   187 0.006826 0.000037
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> > Anova(model2,type=c"III")
> Error: unexpected string constant in "Anova(model2,type=c"III""
> > Anova(model2,type=c("III"))
> Anova Table (Type III tests)
> 
> Response: tdrate
>              Sum Sq  Df    F value  Pr(>F)
> (Intercept) 0.57549   1 15764.9249 < 2e-16 ***
> temp        0.08571   3   782.6314 < 2e-16 ***
> sex         0.00023   1     6.2851 0.01303 *
> temp:sex    0.00015   3     1.4073 0.24206
> Residuals   0.00683 187
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> --
> Menelaos Stavrinides
> Ph.D. Candidate
> Environmental Science, Policy and Management
> 137 Mulford Hall MC #3114
> University of California
> Berkeley, CA 94720-3114 USA
> Tel: 510 717 5249
> 
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