question about custom contrasts in ANOVA

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

-- 
Spencer Graves, PhD
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