[R] When to use quasipoisson instead of poisson family

[Prof Brian Ripley]

On Tue, 10 Apr 2007, Achim Zeileis wrote:

> On Tue, 10 Apr 2007, ronggui wrote:
>
>> It seems that MASS suggest to judge on the basis of
>> sum(residuals(mode,type="pearson"))/df.residual(mode).

Not really; that is the conventional moment estimator of overdispersion
and it does not suffer from the severe biases the unreferenced estimate 
below has (and are illustrated in MASS).

>> My question: Is
>> there any rule of thumb of the cutpoiont value?
>>
>> The paper "On the Use of Corrections for Overdispersion"

Whose paper?  It is churlish not to give credit, and unhelpful to your 
readers not to give a proper citation.

>> suggests overdispersion exists if the deviance is at least twice the 
>> number of degrees of freedom.

Overdispersion _exists_:  'all models are wrong but some are useful' 
(G.E.P. Box).  The question is if it is important in your problem, not it 
if is detectable.

> There are also formal tests for over-dispersion. I've implemented one for
> a package which is not yet on CRAN (code/docs attached), another one is
> implemented in odTest() in package "pscl". The latter also contains
> further count data regression models which can deal with both
> over-dispersion and excess zeros in count data. A vignette explaining the
> tools is about to be released.

There are, but like formal tests for outliers I would not advise using 
them, as you may get misleading inferences before they are significant, 
and they can reject when the inferences from the small model are perfectly 
adequate.

In general, it is a much better idea to expand your models to take account 
of the sorts of departures your anticipate rather than post-hoc test for 
those departures and then if those tests do not fail hope that there is 
little effect on your inferences.

The moment estimator \phi of over-dispersion gives you an indication of 
the likely effects on your inferences: e.g. estimated standard errors are 
proportional to \sqrt(\phi).  Having standard errors which need inflating 
by 40% seems to indicate that the rule you quote is too optimistic (even 
when its estimator is reliable).

-- 
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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595