# [R] When to use quasipoisson instead of poisson family

ronggui ronggui.huang at gmail.com
Tue Apr 10 11:20:09 CEST 2007

On 4/10/07, Prof Brian Ripley <ripley at stats.ox.ac.uk> wrote:
> 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.

Thanks for pointing this out. There is the citation:
@article{lindsey1999,
title={On the use of corrections for overdispersion},
author={Lindsey, JK},
journal={Applied Statistics},
volume={48},
number={4},
pages={553--561},
year={1999},
}

> >> 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
>
> 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.

Which is the better (or ) best way to expand the existing model?
by adding some other relevant independent variables or by using other
more suitable model like "Negative Binomial Generalized Linear Model"?

Thanks!

> 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
>

--
Ronggui Huang
Department of Sociology
Fudan University, Shanghai, China