Help with three-way anova

Hi John

Thanks for your help, that was a very clear answer.  It looks as though,
due to my design, the best way forward is:
contrasts(il4$Infected)
[,1]
I    -1
UI    1
contrasts(il4$Vaccinated)
[,1]
UV   -1
V     1
summary(lm(IL.4 ~ Infected * Vaccinated, il4))
Thanks
Mick

-----Original Message-----
From: John Fox [mailto:jfox at mcmaster.ca] 
Sent: 06 April 2005 12:52
To: michael watson (IAH-C)
Cc: 'r-help'; f.calboli at imperial.ac.uk
Subject: RE: [R] Help with three-way anova

Dear Mick,

For a three-way ANOVA, the difference between aov() and lm() is mostly
in the print and summary methods -- aov() calls lm() but in its summary
prints an ANOVA table rather than coefficient estimates, etc. You can
get the same ANOVA table from the object returned by lm via the anova()
function. The problem, however, is that for unbalanced data you'll get
sequential sums of squares which likely don't test hypotheses of
interest to you.

If you didn't explicitly set the contrast coding, then the out-of-box
default in R [options("contrasts")] is to use treatment.contr(), which
produces dummy-coded (0/1) contrasts. In this case, the "intercept"
represents the fitted value when all of the factors are at their
baseline levels, and it's probably entirely uninteresting to test
whether it is 0.

More generally, however, it seems unreasonable to try to learn how to
fit and interpret linear models in R from the help files. There's a
brief treatment in the Introduction to R manual that's distributed with
R, and many other more detailed treatments -- see
http://www.r-project.org/other-docs.html.

Regards,
 John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
--------------------------------
-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of 
michael watson (IAH-C)
Sent: Wednesday, April 06, 2005 4:31 AM
To: f.calboli at imperial.ac.uk
Cc: r-help
Subject: RE: [R] Help with three-way anova

OK, now I am lost.

I went from using aov(), which I fully understand, to lm()
which I probably don't.  I didn't specify a contrasts matrix 
in my call to lm()....

Basically I want to find out if Infected/Uninfected affects
the level of IL.4, and if Vaccinated/Unvaccinated affects the 
level of IL.4, obviously trying to separate the effects of 
Infection from the effects of Vaccination.

The documentation for specifying contrasts to lm() is a
little convoluted, sending me to the help file for 
model.matrix.default, and the help there doesn't really give 
me much to go on when trying to figure out what contrasts 
matrix I need to use...

Many thanks for your help

Mick

-----Original Message-----
From: Federico Calboli [mailto:f.calboli at imperial.ac.uk]
Sent: 06 April 2005 10:15
To: michael watson (IAH-C)
Cc: r-help
Subject: RE: [R] Help with three-way anova

On Wed, 2005-04-06 at 09:11 +0100, michael watson (IAH-C) wrote:
OK, so I tried using lm() instead of aov() and they give similar
results:

My.aov <-  aov(IL.4 ~ Infected + Vaccinated + Lesions, data)
My.lm  <-   lm(IL.4 ~ Infected + Vaccinated + Lesions, data)
Incidentally, if you want interaction terms you need

lm(IL.4 ~ Infected * Vaccinated * Lesions, data)

for all the possible interactions in the model (BUT you need enough 
degrees of freedom from the start to be able to do this).
If I do summary(My.lm) and summary(My.aov), I get similar
results, but

not identical. If I do anova(My.aov) and anova(My.lm) I get
identical
results.  I guess that's to be expected though.

Regarding the results of summary(My.lm), basically
Intercept, Infected

and Vaccinated are all significant at p<=0.05.  I presume the
signifcance of the Intercept is that it is significantly 
different to
zero?  How do I interpret that?
I guess it's all due to the contrast matrix you used. Check with
contrasts() the term(s) in the datafile you use as independent 
variables, and change the contrast matrix as you see fit.

HTH,

F
--
Federico C. F. Calboli
Department of Epidemiology and Public Health
Imperial College, St Mary's Campus
Norfolk Place, London W2 1PG

Tel  +44 (0)20 7594 1602     Fax (+44) 020 7594 3193

f.calboli [.a.t] imperial.ac.uk
f.calboli [.a.t] gmail.com

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Help with three-way anova

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