[R] stepAIC for overdispersed Poisson

[Prof Brian Ripley]

On Mon, 13 Nov 2006, Murray Jorgensen wrote:

> I am wondering if stepAIC in the MASS library may be used for model
> selection in an overdispersed Poisson situation. What I thought of doing
> was to get an estimate of the overdispersion parameter phi from fitting
> a model with all or most of the available predictors (we have a large
> number of observations so this should not be problematical) and then use
> stepAIC with scale = phi. Should this be OK?

Well no, as that quasi-Poisson model does not have an AIC.

Remember AIC assumes maximum likelihood fitting, and you don't have a 
likelihood here (even for fixed phi).  The problem is that an 
'overdispersed Poisson situation' is a situation, not a model (in the 
usual sense of a probability measure over possible outcomes).

You could use a negative binomial GLM (with fixed theta).

-- 
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)
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