[R] Difference between AIC in GLM and GLS - not an R question

Prof Brian Ripley ripley at stats.ox.ac.uk
Tue Nov 27 16:12:54 CET 2007

On Tue, 27 Nov 2007, Geertje Van der Heijden wrote:

> I have fitted a model using a glm() approach and using a gls() approach
> (but without correcting for spatially autocorrelated errors).  I have
> noticed that although these models are the same (as they should be), the
> AIC value differs between glm() and gls(). Can anyone tell me why they
> differ?

First, what estimation method are you using in gls()?  It happily quotes 
'AIC' for REML fits (the default), for which it is not defined in the 
strict sense (and can be misleading).

Beyond that, AIC is only defined up to an additive constant, as 
log-likelihoods are.  You should find differences in AIC for nested models 
are the same however you compute them by maximum likelihood.

> Thanks,
> Geertje
> ~~~~
> Geertje van der Heijden
> PhD student
> Tropical Ecology
> School of Geography
> University of Leeds
> Leeds LS2 9JT

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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)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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