Re: [R] question about custom contrasts in ANOVA

          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 

	  Best Wishes,
	  Spencer Graves

> 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@charm.net
>
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-- 
Spencer Graves, PhD
Senior Development Engineer
PDF Solutions, Inc.
333 West San Carlos Street Suite 700
San Jose, CA 95110, USA

spencer.graves@pdf.com
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