[R] logLik.lm()

[Prof Brian Ripley]

On Wed, 25 Jun 2003, Spencer Graves wrote:

> Dear Prof. Ripley:
> 
> 	  I gather you disagree with the observation in Burnham and Anderson 
> (2002, ch. 2) that the "complexity penalty" in the Akaike Information 
> Criterion is a bias correction, and with this correction, they can use 
> "density = exp(-AIC/2)" to compute approximate posterior probabilities 
> comparing even different distributions?

That's the derivation of BIC and similar, not AIC.

> 	  They use this even to compare discrete and continuous distributions, 
> which makes no sense to me.  However, with a common dominating measure, 
> it seems sensible to me.  They cite a growing literature on "Bayesian 
> model averaging".  What I've seen of this claims that Bayesian model 
> averaging produces better predictions than predictions based on any 
> single model, even using these approximate posteriors ("Akaike weights") 
> in place of full Bayesian posteriors.
> 
> 	  I don't have much experience with this, but so far, I seem to have 
> gotten great, informative answers to my clients' questions.  If there 
> are serious deficiencies with this kind of procedure, I'd like to know.

Yes, model averaging is useful, but is nothing to do with AIC nor Burnham
& Anderson.  See e.g. my PRNN book for better ways to do it.

Burnham & Anderson (2002) is a book I would recommend people NOT to read
until they have read the primary literature.  I see no evidence that the 
authors have actually read Akaike's papers.

-- 
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