[R] AIC in glm()

[Jim Lindsey]

> 
> Hi all,
> 
> I am trying to understand how is calculated the AIC returned by glm(). I
> have a model object m1 which fitting results are:
> 
> > summary(m1)
> [...]
> (Dispersion parameter for gaussian family taken to be 3.735714)
> 
>     Null deviance: 1439.8  on 15  degrees of freedom
> Residual deviance:   52.3  on 14  degrees of freedom
> AIC: 70.357
> 
> 
> Since there are 2 parameters, I would naively compute: AIC = Dev + 2*2 =
> 56.3, or possibly scaling the deviance by the dispersion parameter: AIC =
> Dev/3.735 + 2*2 = 18.00. I do not see how is computed the value 70.357. I
> have read ?extractAIC and looked in the base package, but did not find a clue.

The AIC in glm is based on (2x) the full likelihood including all
constants. The parameter count includes the dispersion parameter for
those distributions that have one different from 1. Differences in AIC
should be the same under the two approaches. Jim

> 
> Any help appreciated.
> 
> Emmanuel Paradis
> 
> 
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