Type I and Type III SS in anova
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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