Just inserting a point into Ben's answer ...

On Fri, Feb 11, 2011 at 4:57 AM, Ben Bolker <bbolker@gmail.com> wrote:

>
>  2. in GLMs (not GLMMs) where we don't estimate the scale parameter
> (e.g. binomial and Poisson) we are not testing deviance
> difference/estimated scale parameter, but just deviance difference
> itself (usually the assumed scale parameter is 1.0).  In this case, the
> badness of the likelihood ratio test approximation comes because the
> deviance difference itself is only approximately chi-squared
> distributed. There are some papers by Cordeiro from the 1980s on
> corrections to the chi-squared assumption that at the level of a crude
> analogy are the same as the Satterthwaite/K-R approaches; find a
> correction term to adjust the reference distribution based on something
> we know about its moments. (I don't know if these approaches have
> actually been implemented in any stats package ...) There is also some
> stuff in McCullagh and Nelder (which I need to bite the bullet and buy)
> on this topic.
>

There is some nice work on getting better-quality inference in GLMs using
higher-order asymptotics.  See the (former) R package HOA, which has been
unbundled.  Described here: http://www.isib.cnr.it/~brazzale/AA/

Cheers

Andrew

-- 
Andrew Robinson
Program Manager, ACERA
Senior Lecturer in Applied Statistics                      Tel:
+61-3-8344-6410
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Email: a.robinson@ms.unimelb.edu.au    Website: http://www.ms.unimelb.edu.au

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