[R] AIC for quasipoisson link

[Bonenfant Christophe]

Ben, I think the reference you're searching for is the one below

@ARTICLE{Lebreton1992,
  author = {Lebreton, J.-D. and Burnham, K. P. and Clobert, J. and Anderson,
	D. R.},
  title = {Modeling survival and testing biological hypotheses using marked
	animals: a unified approach with case studies},
  journal = {Ecological {M}onographs},
  year = {1992},
  volume = {62},
  pages = {67-118},
  keywords = {Modeling, survival, Capture-recapture},
  pdf = {Lebreton1992.pdf}
}

Cheers,

C


Selon Ben Bolker <bolker at ufl.edu>:

> Marc Schwartz <marc_schwartz <at> comcast.net> writes:
>
> >
> > on 10/31/2008 01:07 PM Antonio.Gasparrini <at> lshtm.ac.uk wrote:
>
> > > I'm trying to extract the AIC statistic from a GLM model
> >  >with quasipoisson link.
> > > The formula I'm referring to is
> > >
> > > AIC = -2(maximum loglik) + 2df * phi
> > >
> > > with phi the overdispersion parameter, as reported in:
> > >
> > > Peng et al., Model choice in time series studies os air pollution and
> mortality. J R Stat Soc A, 2006; 162:
> > pag 190.
> > >
> > I was under the impression that there is no log likelihood for quasi*
> > family models, thus no AIC, which is why they are not calculated/printed
> > in the glm() summary outputs.
> >
>
>   Yes, but ... this is a matter of some disagreement.
>
> Long answer: The purist
> position (hi Prof. Ripley) is that quasi-likelihood estimation
> does not produce a likelihood and should not return one.
> A common position in applied statistics (I think starting with
> a paper by Lebreton, but I can't find the ref right now:
> see refs below) is that dividing the log-likelihood of a regular
> likelihood fit by the estimated scale (overdispersion) parameter
> of the quasi- variant gives a "quasilikelihood" that can be
> used to compute a quasi-AIC that can then be used in model
> selection.
>
>  Short answer: I think that if you fit the non-quasi version
> of the model (ie. Poisson family in your case) and extract
> the likelihood from it, then divide by the overdispersion
> parameter estimated from the "quasi" variant, that should
> give you what you want.
>
>   By the way, the formula quoted above looks funny.
> Shouldn't it be
>
>  QAIC = -2(maximum loglik)/phi + 2df
>
> ?  The formula quoted above (phi times my
> version) should give the same ordering, but
> model weights and interpretations of QAIC
> differences will be wrong.
>
>  cheers
>   Ben Bolker
>
>
> Anderson, D. R., K. P. Burnham, and G. C. White. 1994. AIC model selection in
> overdispersed capture-recapture data. Ecology 75, no. 6: 1780-1793.
>
> Richards, Shane A. 2008. Dealing with overdispersed count data in applied
> ecology. Journal of Applied Ecology 45: 218-227.
> doi:10.1111/j.1365-2664.2007.01377.x.
>
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