[R] Type I and Type III SS in anova

[Prof Brian Ripley]

Try

library(fortunes); fortune("Type III")

(Try it multiple times as there are two relevant quotes: one is to
http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf)

I would not expect modern statistics courses to discuss this issue (or 
even ANOVA except for historical information), as with an interactive 
computing system you can test any two nested models (and not just linear 
Gaussian models).  It relates to the mindset of batch-mode packages like 
SAS of the 1960s, and seemed old-fashioned even when I first taught the 
area in 1979 (using GLIM).

For Bill Venables' preferred approach see Chapter 6 of MASS (the book, any 
edition).



On Fri, 26 Sep 2008, Stefan Uhmann wrote:

> 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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>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list
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>> PLEASE do read the posting guide 
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>> 
>
> ______________________________________________
> 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.
>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595