[R] lmer t value for 3 levels of fixed factor

[Ben Bolker]

Obermeier Andrew <andrewobermeier <at> me.com> writes:

>  Hello, I just joined this list today, so am worried about proper
> protocol, but would like to post a question about lme4.

  You should probably join/post this question to the r-sig-mixed-models
<at> r-project.org mailing list, which is specialized for those topics.
 
> In Baayen, Davidson, and Bates (2008), Mixed-effects modeling with
> crossed random effects for subjects and items, the authors describe
> steps for a Latin Square Design (p. 402) in which they compare 3
> levels of the experimental conditions. I am considering replicating
> this analysis for my dissertation, I would also like to investigate
> 3 levels of my factor, but wish to confirm how lme4 derives the t
> value.
 
> It is my understanding that t values can only be used to compare 2
> means. For 3 levels, does lme4 do some kind of pairwise comparison?

  If you want to do a single test of the effect of a three-level
factor (i.e. compare otherwise identical models with and without the
factor), then the canonical approach is to do some kind of model
comparison test (likelihood ratio test, conditional F test, etc.).
This is a little bit of a can of worms in the case where the number of
groups is small enough that we would like to take the finite sample
size into account (i.e. we would prefer a conditional F test to the
LRT, but we don't know the denominator degrees of freedom).

  You might want to look at Doug Bates's book draft 
at http://lme4.r-forge.r-project.org/lMMwR/ or at
http://glmm.wikidot.com/faq  ...