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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On
Behalf Of Menelaos Stavrinides
Sent: September-25-08 9:56 PM
To: r-help@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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and provide commented, minimal, self-contained, reproducible code.
