[R] Help with three-way anova

[John Fox]

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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