[R] Overdispersion in count data

[Achim Zeileis]

On Wed, 2 Apr 2008, Gavin Simpson wrote:

> On Wed, 2008-04-02 at 12:03 -0400, Wade Wall wrote:
> > Hi all,
> >
> > I have count data (number of flowering individuals plus total number of
> > individuals) across 24 sites and 3 treatments (time since last burn).
> > Following recommendations in the R Book, I used a glm with the model y~
> > burn, with y being two columns (flowering, not flowering) and burn the time
> > (category) since burn.  However, the residual deviance is roughly 10 times
> > the number of degrees of freedom, and using the quasibinomial distribution
> > doesn't change this.  Any suggestions as to why the quasibinomial
> > distribution doesn't change the residual deviance and how I should proceed.
> > I know that this level of residual deviance is unacceptable, but not sure is
> > transformations are in order.
>
> The quasi families estimate the dispersion parameter rather than assume
> it is fixed. This doesn't change the estimates for the coefficients, but
> it may change their standard errors if the estimated dispersion
> parameter is different from 1, and hence the test statistics and their
> p-values. As such the residual deviance doesn't change, you are just
> adjusting the interpretation of coefficients to take account of the
> over-dispersion.
>
> If you are not happy with the fitted model there are numerous options
> you could try, including fitting a negative binomial (NB) GLM (see
> glm.nb() in package MASS) or a zero-inflated Poisson or NB model or a
> Hurdle model. Functions to fit the ZIP/ZINB or Hurdle models can be
> found in the pscl package.

The pscl also provides
  vignette("countreg", package = "pscl")
which discusses Poisson, quasi-Poisson, negative binomial models and
zero-augmented versions of these.
Z

> HTH
>
> G
>
> >
> > Needless to say that I am at the outer limits of my statistical knowledge.
> >
> > Thanks for any help,
> >
> > Wade Wall
> >
> > 	[[alternative HTML version deleted]]
> >
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>
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