[R-sig-ME] glmer p-values?

[John Maindonald]

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 at 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
> 
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