[R-sig-ME] Can AIC be approximated by -2ln(L) i.e. the deviance, at very large sample size?

[Ben Bolker]

Emmanuel Curis <emmanuel.curis at ...> writes:

> 
> Hi,
> 
> I may be wrong, but I understood that AIC in itself is not as
> important as changes in AIC between models, and some authors says that
> changes in AIC in the order of more than 10 are enough to favor a
> model on another.
> 
> And changes in the 2*k term should be in this order of magnitude when
> comparing different models.
> 
> So my guess would be that it remains important.

  You are exactly right.

  This is exactly equivalent to the initially surprising result
that the maximum (log-)likelihood *decreases* when the sample size 
increases: the probability of any *particular* outcome goes down.
Generally in likelihood-based statistical approaches (including AIC)
we only look at the differences in (log-)likelihood/AIC, not the absolute
number.

  I've started a campaign to try to get people _never_ to produce tables
of raw AIC values; only the delta-AIC values should be presented (if
necessary the minimum AIC value can be put in a footnote somewhere so
people can check for reproducibility of the results, but that's the only
reason one should ever care about the raw value).

  That's not to downplay the issues with AIC in the mixed model context:
http://glmm.wikidot.com/faq#aic