Thanks a lot for the detailed comments. Here are some first quick
responses before I look into them in more detail:
As a start, this model is attempting to fit 10 variance-covariance parameters to only 72 observations; while I don't know a great rule of thumb for how big a data set one should have for N var-cov parameters, it should definitely be *more* conservative than the "10-20 observations per parameter" rule of thumb (e.g. see Harrell _Regression Modeling Strategies_) -- var-cov parameters are harder to estimate than location (fixed-effect) parameters.
Yes, I am aware of Harrell's rule. This is not my data set, I am just
trying to check their aov analysis with lmer
Re polynomial/ordered contrast: yes, that's what I was thinking.
SAMPLE is numeric or at least ordinal so I am not really losing dfs
there, plus the way I understand their data the leveling off that is
shown in an effects plot, for instance, seems to make sense because it
would mean that increasing the sample sizes doesn't increase the dep
var. linearly and ad infinitum.
* in general, if you want to correspond to a traditional aov()-style analysis, you want to use a random effect of the form (1|A/B) rather than (B|A)
Ok, THAT I will need to read up on, at present that is over my head.
* the original aov()-style analysis has no room left for residual error: since the experimental design has a single observation per NAME:USED:SAMPLE
Yes, of course.
Finally, if possible (i.e. if the denominator of the 'OVERLAP' variable is known), I would consider a binomial GLMM rather than trying to transform (e.g. see e.g. Warton and Hui "The arcsine is asinine" Ecology 2011) ...
Agreed, they could have done a binomial one but they don't report the
data necessary for that. I only did the arcsine for comparability
because they did it. If any transformation, I'd probably have
preferred the logit, but sure, the binomial one would have been best
Again, thanks a lot!
STG
--
Stefan Th. Gries
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University of California, Santa Barbara
http://www.linguistics.ucsb.edu/faculty/stgries