glm(.) / summary.glm(.); [over]dispersion and returning AIC..
Martin Maechler
Martin Maechler <maechler@stat.math.ethz.ch>
Tue, 3 Feb 1998 11:49:54 +0100
I have been implementing a proposal of Jim Lindsey for glm(.)
to return AIC values, and
print.glm(.) and print.summary.glm(.) printing them....
however:
>>>>> "Jim" == Jim Lindsey <jlindsey@luc.ac.be> writes:
Jim> The problem still remains of getting the correct AIC when the user
Jim> wants the scale parameter to be fixed. (The calculation should use
Jim> the fixed, supplied value, instead of estimating it from the
Jim> deviance.) As I mentioned earlier, the problem is that this is
Jim> specified in summary, after the AIC has already been
Jim> calculated. Would it not be possible to add an option in glm
Jim> itself, allowing the scale parameter to be specified there?
Jim> Otherwise, the AIC should in fact be recalculated every time
Jim> summary is called.
Yes, I think that's what should really happen.
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
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 wouldn't the dispersion also be used in predict.glm(..., se = TRUE) ?].
As a consequence, glm(.) wouldn't (and shouldn't ??) have a
`dispersion = ' argument,
and print.glm(.) maybe also shouldn't print the AIC
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).
-------
Opinions, proposals, please ?
Martin Maechler <maechler@stat.math.ethz.ch> <><
ETH (Federal Inst. Technology) 8092 Zurich SWITZERLAND
http://www.stat.math.ethz.ch/~maechler/
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