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Jim, I am relating your message to R-devel.
This should be discussed in a broader audience;
I am not an expert on GLM's, I know you are
and others on this group also...
R-develers, please CC to Jim Lindsey (on this topic), since he hasn't
been part of the R-devel list for a while..
BTW: I will be gone to the snowy mountains,
for two weeks by end of Friday....
- Martin
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Return-Path: jlindsey@luc.ac.be
From: Jim Lindsey <jlindsey@luc.ac.be>
Subject: Re: glm(.) / summary.glm(.); [over]dispersion and returning AIC..
To: maechler@stat.math.ethz.ch
Date: Wed, 4 Feb 1998 10:15:50 +0100 (MET)
In-Reply-To: <199802031049.LAA00411@sophie.ethz.ch> from "Martin Maechler" at Feb 3, 98 11:49:54 am
For binomial and poisson,
there are even three possibilities:
1. no dispersion (as by the proper GLM)
2. overdispersion estimated by the deviance (ratio)
3. overdispersion specified by the user
None of these except the first give true AICs. Hence, the AIC for
these models is always correct and should not be touched.
S has adopted the concept that the glm(.) model is always the same,
the dispersion being an orthogonal nuisance parameter,
which the user should specify in
summary(....) , i.e.,
summary.glm(object, dispersion = NULL, correlation=FALSE, ..)
^^^^^^^^^^^^^^^^^
But in fact it is unity for binomial and poisson so some action must
be taken in summary. The orthogonality is a characteristic of
exponential dispersion models.
[but wouldn't the dispersion also be used in predict.glm(..., se = TRUE) ?].
Dispersion does not affect predictions, only their precision.
As a consequence, glm(.) wouldn't (and shouldn't ??) have a
`dispersion = ' argument,
Agreed. Basically, I was lazy in implementing the AIC and did not try
to pass the function to summary, only the calculated value.
and print.glm(.) maybe also shouldn't print the AIC
I think it should, because it is always correct for the best model, ie
that using the estimated dispersion parameter. The AIC for a fixed
value of the dispersion parameter will always be poorer (except for
the penalty of 2 perhaps).
BTW, V&R's MASS library contains the following functions
> apropos("[Aa][Ii][Cc]")
[1] "extractAIC" "extractAIC.aov" "extractAIC.coxph"
[4] "extractAIC.glm" "extractAIC.lm" "extractAIC.negbin"
[7] "extractAIC.survreg" "stepAIC"
where "stepAIC" is the main function, calling the generic "extractAIC"
(and one of its methods).
Maybe we should try look adopt what they've done.
(haven't looked at it really).
I don't think the AIC should need to be extracted. It should always be
available. I think it is much more fundamental than z statistics or P-values.
Jim
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