[R] question about AIC

Renaud Lancelot renaud.lancelot at free.fr
Thu Aug 1 14:16:28 CEST 2002

Kyriakos Kachrimanis wrote:
> Please, forgive my ignorance on statistics, but I have a rather simple
> question concerning AIC. Small values of AIC mean good fit of the model. How
> about negative values of AIC? Is a model with AIC=0.5 considered to have
> better fit than a model with AIC=-500?
> I couldn't find anything explaining this in the documentation or any
> elementary statistics textbook that I have at my disposal.
> Thanks in advance,
> Kyriakos Kachrimanis.

AIC is a measurement of the distance between the current model and the
"true", unknown model, given the data. Therefore, it is not meaningful
by itself, but only when compared to other models (difference in AIC and
other derived statistics). Moreover, all the compared models must have
been fitted (with a maximum-likelihood method) on the same data set, and
with the same response (i.e. you can't directly compare y = f(x) and
log(y) = f(x)), but they don't need to be nested. In these conditions, a
model with AIC = -500 is much, much better than a model with AIC = 0.5.

A very good textbook is:
Burnham, K.P., Anderson, D.R., 1998. Model selection and inference: a
practical information-theoretic approach. New-York, Springer-Verlag, 353
The second edition should be available soon.



Dr Renaud Lancelot, vétérinaire
CIRAD, Département Elevage et Médecine Vétérinaire (CIRAD-Emvt)
Programme Productions Animales

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