[R] question about custom contrasts in ANOVA

[Prof Brian Ripley]

I was puzzled as to what the question actually was. If you set

> options(contrasts=c("contr.sum", "contr.poly"))

the interaction contrasts are precisely those created manually.  Nothing 
fancier is required.  But I am not sure what you want to do with them once 
you have them.

On Tue, 30 Aug 2005, Spencer Graves wrote:

> 	  Since I have not seen a reply to this post, I will attempt a brief
> comment:  I won't comment on the specifics, but your general approach
> seems appropriate.  You already seem to know that a factor with k levels
> is converted into (k-1) separate numerical variables, and a separate
> regression coefficient is estimated for each one.
>
> 	  To see in more detail what you were estimating, I looked at the
> following:
>
> 	  model.matrix(y~xma)
> 	  fit2 <- aov(y~xma)
> 	  attributes(fit2)
>
> 	  From the latter, I identified "contrasts" as something that might be
> interesting to examine, as follows:
>
> 	  fit2$contrasts
>
> 	  For clarity, I think I might reduce the number of observations
> substantially, limiting myself to only 2 or 3 schools and paramterize
> the problem manually, but preserving imbalance.  Then I'd use "lm",
> specifying the terms in different orders.  With imbalance, the answer
> depends on the order unfortunately.  When in doubt, I often experiment
> with changing the order:  If the changes do not affect the conclusions,
> I pick the simplest case to present to my audience.  If the changes do
> affect the conclusions, I know I need to worry about which answer seems
> most correct, and I also know something about the limits of the
> conclusions.
>
> 	  I know this doesn't answer your question, but I hope it helped with a
> solution methodology.
>
> 	  Best Wishes,
> 	  Spencer Graves
>
> Scot W McNary wrote:
>
>> Hi,
>>
>> I have a problem in which I have test score data on students from a number
>> of schools.  In each school I have a measure of whether or not they
>> received special programming.  I am interested in the interaction between
>> school and attendance to the programming, but in a very select set of
>> comparisons.  I'd like to cast the test as one in which students in each
>> school who attend are compared with students who don't across all schools.
>> So, I would be comparing school 1 attenders with school 1 non-attenders,
>> school 2 attenders with school 2 non-attenders, etc.  The reason for the
>> custom contrast is that the between school comparisons (e.g., school 1
>> attenders vs. school 2 non-attenders) are of less interest.
>>
>> This seems to require a custom contrast statement for the interaction
>> term.  I have a toy example that seems to work as it should, but wonder if
>> I've correctly created the contrast needed.
>>
>> Here is a toy example (code put together from bits taken from MASS ch 6,
>> and various R-help postings, (e.g.,
>> http://finzi.psych.upenn.edu/R/Rhelp02a/archive/49077.html)):
>>
>> # toy interaction contrast example, 10 schools, 100 kids, 5 attenders (1)
>> # and 5 non-attenders (2) in each school
>>
>> # make the data
>> school <- gl(10, 10)
>> attend <- gl(2, 5, 100)
>> # creates an interaction with schools 6 and 7
>> y <- c(sample(seq(450, 650, 1), 50), rep(c(rep(650, 5), rep(450, 5)), 2),
>>  	sample(seq(450, 650, 1), 30))
>>
>> # anova
>> summary(aov(y ~ school * attend))
>>
>> # graphically
>> Means <- tapply(y, list(school, attend), mean)
>>
>> plot(Means[,1], col="red", type = "l", ylim = c(400,700))
>>
>> points(Means[,2], col="blue", type = "l")
>>
>> # create contrasts for hypothesis of interest
>> # school i attend j - school i attend j'
>> # for all schools
>> sxa <- interaction(school, attend)
>> sxam <- as.matrix(rbind(diag(1,10), diag(1,10) * -1))
>> contrasts(sxa) <- sxam
>>
>> summary(aov(y ~ sxa), split=list(sxa=1:10), expand.split = T)
>>
>> The actual problem has a few more schools, other covariates, considerably
>> more students, and is somewhat unbalanced.
>>
>> Thanks,
>>
>> Scot
>>
>>
>> --
>>    Scot W. McNary  email:smcnary at charm.net
>>
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>
> -- 
> Spencer Graves, PhD
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>
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-- 
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