R devel - Feb 1998 - glm(.) / summary.glm(.); [over]dispersion and returning AIC..

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
stat.math.ethz.ch/~maechler
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On Tue, 3 Feb 1998, Martin Maechler wrote:
> 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:
<snip>
> 
> 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
> 
How about overdispersion as estimated by the mean squared Pearson
residual. Unlike the deviance estimate this works for quasilikelihood (ie
when only first two moments are specified correctly), at least according
to McCullagh & Nelder.


Thomas Lumley
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>>>>> "Jim" == Jim Lindsey <jlindsey@luc.ac.be>
writes:
  MM>> S has adopted the concept that the glm(.) model is always the same,
  MM>> the dispersion being an orthogonal nuisance parameter,
  MM>> which the user should specify in
  MM>> 	summary(....) , i.e.,
  MM>> 	summary.glm(object, dispersion = NULL, correlation=FALSE, ..)
  MM>> 			    ^^^^^^^^^^^^^^^^^

    Jim> But in fact it is unity for binomial and poisson so some action must
    Jim> be taken in summary. The orthogonality is a characteristic of
    Jim> exponential dispersion models.
Sure; the above meant:  
	-  dispersion  *is* an optional parameter to  summary.glm(.).
	-  it has a default depending on the model fitted (e.g. =1 for binomial)
	-  if the user specifies a different value, that one is used ...

  MM>> [but wouldn't the dispersion also be used in predict.glm(...,
se=TRUE) ?]

    Jim> Dispersion does not affect predictions, only their precision.

Exactly, and the point is that ``predict( ... , se = TRUE )
						^^^^^^^^^^
			asks for 'standard errors' !
 it is short for  'se.fit' and actually
 not (yet) available in R, but in S-plus  predict.lm & predict.glm.

The question remains (actually an S-plus only question for the current R):

  How to get standard errors for predicted values
  WITH user-specified / non-standard estimated dispersion value?
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