R help - Nov 2006 - stepAIC for overdispersed Poisson

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?

Murray Jorgensen
-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    Home +64 7 825 0441    Mobile 021 1395 862

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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