[R] add1() and glm

Prof Brian Ripley ripley at stats.ox.ac.uk
Sat Apr 1 09:06:49 CEST 2006

See McCullagh and Nelder (1989) (and the source code).

On Fri, 31 Mar 2006, Chad Reyhan Bhatti wrote:

> Hello,
> I have a question about the add1() function and quasilikelihoods for GLMs.
> I am fitting quasi-Poisson models using  glm(, family = quasipoisson).
> Technically, with the quasilikelihood approach the deviance does not have
> the interpretation as a likelihood-based measure of sample information.
> Functions such as stepAIC() cannot be used.  The function add1() returns
> the change in the scaled deviance between the null model and the
> alternative model along with a chi-sq p-value.

Not true.  You choose a suitable test, and for quasipoisson the F test is 
the appropriate choice and that does not give `a chi-sq p-value'.

If the dispersion is estimated, it is estimated via the residual deviance 
(as it says on the help page) and that has a degrees of freedom in the 
model output.  The test is done in exactly the same way as a lm fit, just 
replacing sums of squares by deviances (and indeed, exactly as a Gaussian 
glm fit).

> Agresti, (Categorical Data Analysis p.140 last sentence before Section
> 4.5.2), makes the statement "For some GLMs the scaled deviance has an
> approximate chi-squared distribution." with no details, no references, and
> no degrees of freedom.
> Does anyone know:
> 1) How the p-value is computed in add1(), ie degrees of freedom and maybe
> a reference?
> 2) A reference for using the scaled deviance for model comparison.
> Thanks,
> Chad R. Bhatti

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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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