glm(.) / summary.glm(.); [over]dispersion and returning AIC..

[Martin Maechler]

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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