Re: [S] Comparing non-nested binomial GAMs

Prof Brian Ripley (ripley@toucan.stats)
Mon, 4 May 1998 10:45:23 +0100 (BST)

> From: "Ejrnæs, Rasmus" <>

> I attempt to compare the predictive ability of two different sets of
> predictor variables (environmental gradients) to the same response
> variables (the occurrence of different plant species in grassland
> plots). The dataset is evensized for both setups and contains no missing
> values.
> For this purpose I have used step.gam, family=binomial with options for
> both smoothed (s) and linear responses, and used the AIC-statistic
> (given in step.gam) to assess what set of predictor variables best
> explain each of my response variables.
> Is there any statistical procedure that could be used to estimate the
> significance of the difference in deviance or AIC between the two
> models? Or is there any other obvious way of comparing the two models?
The idea of AIC is to choose the model with smallest AIC. Unfortunately,
step.gam does not give AIC but an approximation, based on an approximation
to the number of parameters (there are several such approximations).

I would use a cross-validation experiment to assess directly the
predictive performance of the two models. This has the advantage of
a direct interpretation and of not depending on dubiously valid theory.

Brian D. Ripley,        
Professor of Applied Statistics,
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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