[R] Dispersion in summary.glm() with binomial & poisson link (fwd)

[Prof Brian Ripley]

> From: Jim Lindsey <jlindsey at alpha.luc.ac.be>
> Date: Tue, 9 May 2000 17:12:26 +0200 (MET DST)
> 
> > > That is why I did not submit a bug report.  The problem is that in
> > > many application areas phi is much greater than one.
> > 
> > The gnlr function in my gnlm library (at
> > www.luc.ac.be/~jlindsey/rcode.html) will fit quite a variety of
> > different overdispersed Poisson- and binomial-based distributions
> > (i.e. phi different from one) using their exact likelihoods.
> >   Jim
> 
>   As Bill Venables has kindly pointed out, I was a bit sloppy in the
> above: phi here refers to the appropriate overdispersion parameter in
> the distribution chosed, negative binomial, beta-binomial, double
> exponential, multiplicative Poisson/binomial, etc. For some
> distributions, it can be less than one, i.e. underdispersed. Jim

Yes, that was exactly my concern.  What gnlr does makes sense to me,
but a phi>1 binomial or Poisson only makes sense as a quasi model.  In
the distributions Jim has coded the variance/mean ratio is not
constant (as it is for the phi-Poisson), for example, and the implied
quasi-likelihood (where it exists) differs from those likelihoods.

But GLIM and S and R will in their own ways fit those models, and
I want to look hard to see if what they do in R is sensible (and
some things seem not to be, as Ben Bolker pointed out ca April 19).

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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