Ben and John, thank you for your feedback.  This is a much more complicated
issue than I expected (or I should say hoped).

John, you were correct in assuming I am fitting using a binomial
family/logit link function.

Is anyone aware of papers describing this issues for the GLM case?  Or
perhaps use cases of large-sample/asymptotic approaches or MCMC approaches
that Ben mentioned?

Thanks again,

Luke

On Wed, Dec 1, 2010 at 11:36 PM, John Maindonald <john.maindonald@anu.edu.au
> wrote:

> Perhaps it is worth adding that there are two kinds of issues:
>
> 1) there are the issues that arise in connection with the
> asymptotic (large sample) approximations used in GLMs.
> Adding in components of normal error may ameliorate
> these somewhat, but at the cost of leading to distributions
> that are more complicated to characterise.  In any case,
> these issues do not arise for lmer models, not at all events
> if the distributional assumptions are correct.
>
> 2) there are the issues on which my message focused,
> where adding in components of normally distributed variation
> invokes issues, just as for gaussian lmer models, about how
> to allow for uncertainty in the standard error estimates.
> ----
>
> In some ways maybe better, in some ways worse!  Certainly,
> in this no man's land between the normal distributions of
> gaussian lmer models, and GLM models with an exponential
> error term that has a theoretical variance, the complications
> are greater.
>
> John Maindonald             email: john.maindonald@anu.edu.au
> phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
> Centre for Mathematics & Its Applications, Room 1194,
> John Dedman Mathematical Sciences Building (Building 27)
> Australian National University, Canberra ACT 0200.
> http://www.maths.anu.edu.au/~johnm
>
> On 02/12/2010, at 2:57 PM, Ben Bolker wrote:
>
> > On 10-12-01 09:42 PM, Lucas Kid wrote:
> >> Am I correct in assuming that the p-values returned by glmer do not
> suffer
> >> from the same issues as those that are not returned by lmer (addressed
> quite
> >> famously before by Dr. Bates)?
> >>
> >  Unfortunately, you're incorrect.
> >
> >  The situation is possibly even worse than for linear mixed models.  To
> > **very** briefly recap, for classical linear mixed models, we know that
> > certain ratios of sums of squares are F-distributed with certain degrees
> > of freedom under the null hypothesis.  This goes away once one leaves
> > the classical (balanced, orthogonal, nested ...) case.
> >
> >  For generalized (NOT mixed) linear models, we don't even have a good
> > (or at least widely used) finite-sample correction (that I know of).
> > For models with overdispersion there are some cases where you may use an
> > F test (or at least Venables and Ripley say so), but even that use is
> > "with caution".
> >
> >  The usual choices (use large-sample/asymptotic approaches and hope for
> > the best; MCMC approaches, non-parameteric or parametric bootstrap)
> apply.
> >
> >   I would be happy to be corrected by someone.
> >
> >  Ben Bolker
> >
> > _______________________________________________
> > R-sig-mixed-models@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>

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