[R] deviance in glm

[Prof Brian D Ripley]

On Thu, 8 Mar 2001, Chong Gu wrote:

>
> Folks,
>
> I am not sure if it's a feature or a "bug".  The same is observed in
> Splus.
>
> Suppose I have Poisson counts, and I would like to estimate the
> parameter using glm.  I would assume I can feed it the individual
> counts, or I can feed it the distinctive counts with the frequency as
> the weights, and I would get the same results.  I do, but the deviance
> df are returned differently.  Here is a short session.
>
> y<-rpois(1000,5)
> fr<-as.vector(table(y))
> yy<-0:(length(fr)-1)
> glm(y~1,poisson)
> glm(yy~1,poisson,weight=fr)
>
> I believe the first call to glm gives the correct df, but with real
> data, do I have to break up the tabulated data to get it right from R
> (or Splus), or I just have to manually calculate the df?  Can this be
> potentially misleading to practitioners?
>
> Or maybe my thinking was off?

The deviance is by comparison with a saturated model, and because the data
are different, so is the saturated model.  For this problem, the saturated
model has one parameter per x observation, not one per y observation.  So
in the second case you are specifying that there are 14 (in my run) (x,y)
pairs that occurred a number of times *and* this would always have
occurred.   Given that you grouped on y, that seems invalid except as a
computational device.

> I tried similar things with Bernoulli data and got similar results.

Grouping data can also affect the likelihood and the MLE in other problems.
It's neither a feature nor a bug, but part of the definitions.

-- 
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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