[R-sig-eco] ICC confidence intervals and power analysis for random effects in lmer?

[Bob O'Hara]

On 04/12/2012 03:50 AM, Bradley Carlson wrote:
> I'm performing an analysis of behavioral variation among individual
> tadpoles, using individual ID as a random effect and time as a continuous
> fixed covariate in the lmer function in lmer4 package. I'm really
> interested in making inferences about the random effect (i.e. the extent of
> variation among individuals). I'd like to do two things that I can't seem
> to find straightforward answers about and I'm hoping someone can help or
> point me to a good resource.
>
> 1) The intraclass correlation coefficient is of particular interest to me,
> as it describes the proportion of variation that occurs among individuals.
> Ideally I'd like to report a confidence interval of the ICC but I can't
> find any way to calculate one, other than a function in the psychometric
> package that appears to only work when there are no covariates in the model
> (random effect only).
MCMC has already been mentioned and lme4 still has its mcmcsamp() 
function. Failing that, you could try a parametric bootstrap, which 
requires a little bit of coding but simulate() makes it much easier.
> 2) A reviewer requested a power analysis of the ability to detect a
> significant random effect. Any tips on how to approach that?
Report the random effect and confidence intervals. Retrospective power 
analyses are pretty pointless (e.g. see 
http://beheco.oxfordjournals.org/content/14/3/446.full), unless you're 
planning to repeat the experiment.

Bob

-- 
Bob O'Hara

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