[R-sig-ME] GLMER - p values proportion data

[Ben Bolker]

Rebecca Ross <ricr2 at ...> writes:

> 
> Dear All,
> 
> I would like to analyse proportion data (number of trials, number of
> successes) with one fixed effect (continuous) and one random effect
> (categorical). I believe (using Bolker TREE paper analysis) that I should
> be using a GLMER model. Can I trust the p-values produced by this, and if
> not, what should I be doing?
> 
> I have tried to follow up on various R mailing lists, but I am not 100%
> sure what the right answer is.
> 

  Using glmer (i.e. a GLMM) seems perfectly reasonable.  The p values
produced by summary() for a glmer model are (as is typical in the context
of generalized linear models) asymptotic Wald test statistics.  They
may be OK for large, well behaved data sets.  To get more reliable
likelihood ratio test statistics, either fit reduced models and use
anova(), or use drop1().  However, these are still asymptotic.
If you have a large number of random-effect blocks (>40 or so) these
should be very reliable.  If you have a smaller number and you really
want reliable p-values you will probably need to do some form of
resampling (parametric or non-parametric bootstrap, MCMC, etc.).