Stephen,

You are looking for the nesting of the FirstFactor within the SecondFactor.
Here is an example for your two-way design.
The model.matrix shows the dummy variables.
The last four columns show the two-level comparisons of Fir within each
level of Sec

Rich



tmp <- data.frame(y=rnorm(16),
                  Sec=rep(LETTERS[1:4], each=4),
                  Fir=rep(factor(1:2), 4, each=2))
contrasts(tmp$Fir) <- c(1, -1)
tmp.aov <- aov(y ~ Sec/Fir, data=tmp)
anova(tmp.aov)
cbind(tmp, model.matrix(tmp.aov)[, -1])


On Fri, Sep 7, 2012 at 2:46 PM, Stephen Politzer-Ahles <
politzerahless@gmail.com> wrote:

> Hello everyone,
>
> I am running a mixed effects model where I have two fixed factors, one with
> 2 levels and one with 4, and their interaction. Let's say these are my
> factors and their levels:
>
> FirstFactor: 1, 2
> SecondFactor: A, B, C, D
>
> For the interaction, I am interested in the four two-way comparisons, not
> the two four-way comparisons. In other words, I want to test whether 1A is
> significantly different than 2A, whether 1B is significantly different than
> 1B, etc; I am not interested in the comparison of 1A~1B~1C~1D.
>
> However, the latter comparisons are what the coefficients seem to give me
> when I summarize my model. For instance, the coefficient for the
> interaction term "FirstFactor2:SecondFactorB" doesn't tell me how different
> 2B is from 1B, it tells me how different 2B is from 2A.
>
> Is there a straightforward way to code the contrasts so that the
> coefficients I get for the interaction terms do the comparisons I'm
> interested in?
>
> Thank you for your advice,
> Steve Politzer-Ahles
>
> --
> Stephen Politzer-Ahles
> University of Kansas
> Linguistics Department
> http://www.linguistics.ku.edu/
>
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>
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