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. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
