[R] Type I and Type III SS in anova

[Stefan Uhmann]

Dear list,

slightly OT: can you recommend me any sources where I can find more 
about this Type I - II - III anova problem? It seems as my statistics 
courses did not cover this issue, so I feel rather naive and have this 
sort of feeling that some of my analyses might be complete nonsense.

Regards,
Stefan

John Fox schrieb, Am 26.09.2008 12:36:
> 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
>>
>> 	[[alternative HTML version deleted]]
>>
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