(Sorry about the double post; it seems the last time I posted this it
didn't show up correctly because of some character encoding issue.)

Hello everyone,

I am testing a model in which I have a two-level factor (let's call it
First [1, 2]) nested under a four-level factor (let's call it Second [A, B,
C, D]). I have used the following model to get coefficients representing
whether, for each level of Second, there is a significant difference (in
the outcome variable, Latency) between the levels of First:

test <- lmer( Latency ~ Second / First + (1|Subject) + (1|Item), data )

This gives me nice output like:

SecondA:First2                          -0.009879   0.008283   -1.19
SecondB:First2                          -0.032136   0.008293   -3.88
SecondC:First2                           0.006748   0.008131    0.83
SecondD:First2                           0.006153   0.008206    0.75

Now, though, I am also interested in directly testing whether those
differences differ between levels of Second. So, for example, whether the
-0.009879 coefficient for SecondA:First2 is significantly different from
the 0.006748 coefficient for SecondC:First2.

Is there a way to specify contrasts for the model that will make it spit
out those comparisons? Or should I do it by hand? I assume I can subtract
one of those coefficients from another and divide by a standard error to
get a new *t*-score, but I'm not sure where I could get the standard error
of the differences between coefficients (my understanding is that the
standard error of the coefficients I would get from ranef(test)$Subject is
not going to be exactly the same as the standard error reported for the
fixed effect [Baayen, 2008:247]).

Thank you very much for your feedback,
Steve Politzer-Ahles

-- 
Stephen Politzer-Ahles
University of Kansas
Linguistics Department
http://www.linguistics.ku.edu/

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