[R] Dispersion in summary.glm() with binomial & poisson link

[Prof Brian D Ripley]

On Tue, 9 May 2000, John Maindonald wrote:

> Following p.206 of "Statistical Models in S", I wish to change
> the code for summary.glm() so that it estimates the dispersion
> for binomial & poisson models when the parameter dispersion is
> set to zero.  The following changes [insertion of ||dispersion==0
> at one point; and !is.null(dispersion) at another] will do the trick:

I know S does that, but R is not documented to do so (so your example does
works as documented).  I think this is at best confusing. Once phi is
estimated, they are quasi-likelihood models not binomial nor Poisson and in
particular have no likelihood, so e.g. drop1 becomes inappropriate.  And it
is all too easy to have different treatments of dispersion in different
ancilliary functions (as S managed for many years).

My preference is to treat such models as quasi models.  If enough people
really want them as `binomial' or `poisson' then we need to make much wider
changes to ensure consistency (and incompitibility with S).

There are quite a lot of things in R's glm that are not the same as S's.

> 
> "summary.glm" <-
> function(object, dispersion = NULL,
> 			correlation = FALSE, ...)
> {
>     Qr <- .Alias(object$qr)
>     est.disp <- FALSE
>     df.r <- object$df.residual
>     if(is.null(dispersion)||dispersion==0)	# calculate dispersion if needed
> 	dispersion <-
> 	    if(any(object$family$family == c("poisson",
> "binomial"))&&is.null(dispersion))
> 		1
> 	    else if(df.r > 0) {
> 		est.disp <- TRUE
> 		if(any(object$weights==0))
> 		    warning(paste("observations with zero weight",
> 				  "not used for calculating dispersion"))
> 		sum(object$weights*object$residuals^2)/ df.r
> 	    } else Inf
>     ## calculate scaled and unscaled covariance matrix
> ......
> 
> Here is an example:
> 
> > counts <- c(18,17,15,20,10,20,25,13,12)
> > outcome <- gl(3,1,9)
> > treatment <- gl(3,3)
> > print(d.AD <- data.frame(treatment, outcome, counts))
> > glm.D93 <- glm(counts ~ outcome + treatment, family=poisson())
> > anova(glm.D93)
> > summary(glm.D93,dispersion=0)  #current code
> ......
> Coefficients:
>               Estimate Std. Error z value Pr(>|z|)
> (Intercept)  3.045e+00  0.000e+00     Inf   <2e-16
> outcome2    -4.543e-01  0.000e+00    -Inf   <2e-16
> outcome3    -2.930e-01  0.000e+00    -Inf   <2e-16
> treatment2   1.924e-08  0.000e+00     Inf   <2e-16
> treatment3   8.383e-09  0.000e+00     Inf   <2e-16
> 
> (Dispersion parameter for poisson family taken to be 0)
> 
>     Null deviance: 10.5814  on 8  degrees of freedom
> Residual deviance:  5.1291  on 4  degrees of freedom
> AIC: 56.761
> 
> Number of Fisher Scoring iterations: 3
> 
> Warning message: 
> NAs introduced by coercion 
> 
> > summary(glm.D93,dispersion=0)  # with above change
> .......
> Coefficients:
>               Estimate Std. Error  t value Pr(>|t|)
> (Intercept)  3.045e+00  1.943e-01   15.667  9.7e-05
> outcome2    -4.543e-01  2.299e-01   -1.976    0.119
> outcome3    -2.930e-01  2.192e-01   -1.337    0.252
> treatment2   1.924e-08  2.274e-01 8.46e-08    1.000
> treatment3   8.383e-09  2.274e-01 3.69e-08    1.000
> 
> (Dispersion parameter for poisson family taken to be 1.293029)
> 
>     Null deviance: 10.5814  on 8  degrees of freedom
> Residual deviance:  5.1291  on 4  degrees of freedom
> AIC: 56.761
> 
> Number of Fisher Scoring iterations: 3
> 
> 
> John Maindonald               email : john.maindonald at anu.edu.au        
> Statistical Consulting Unit,  phone : (6249)3998        
> c/o CMA, SMS,                 fax   : (6249)5549  
> John Dedman Mathematical Sciences Building
> Australian National University
> Canberra ACT 0200
> Australia
> 
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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