[R-sig-ME] power analysis for multi-level models

[Lee Wurm]

I'm really happy to see the explosion of mixed models in more and more
areas of research, but am now faced with the problem that grant
reviewers (and some journals) insist on seeing effect sizes and power
calculations for these models. I sent my query to the r-help forum and
got a valuable idea, along with the suggestion that I try you folks.

Suppose I want to see if men or women show a stronger word frequency
effect. I have 50 words of varying frequency that I show to 30 men and
30 women, who are supposed to decide as quickly as possible whether
it's a real word. My data object would end up being 3000 lines long,
and look like this:

Subject  Word  Sex  Frequency  ReactionTime
s1 w1 M 23 2543
s1 w2 M 67 1438
s1 w3 M 1 8033
...
s60 w50 F 4 1099

I analyze with:

lmer(ReactionTime ~ (Sex*Frequency) + (1|Subject) + (1|Word)

Can anyone help me get started with calculating effect sizes (or even
better, with attempting power analyses) for such a model? Or with
giving an explanation about why it's an ill-formed question, in terms
that non-experts could understand? Old ways die hard, sometimes, and
grant reviewers control the purse-strings.

Thanks.

--Lee