logLik.lm()
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