[R] Under-dispersion - a stats question?

[Prof Brian Ripley]

On Mon, 10 Oct 2005, Martin Henry H. Stevens wrote:

> Hello all:
> I frequently have glm models in which the residual variance is much
> lower than the residual degrees of freedom (e.g. Res.Dev=30.5, Res.DF
> = 82). Is it appropriate for me to use a quasipoisson error
> distribution and test it with an F distribution? It seems to me that
> I could stand to gain a much-reduced standard error if I let the
> procedure estimate my dispersion factor (which is what I assume the
> quasi- distributions do).
>
> Thank you for any input at all.

This usually indicates a deviation from the large-sample theory because of 
small counts.  See e.g. MASS4 p.208.  Then estimator

 	residual variance
 	-----------------
     residual degrees of freedom

is unreliable.  If the better methods discuss there confirm 
under-dispersion, then you probably have some form of negative correlation 
and need to look at your experimental setup.  (But it is usually are false 
alarm.)

-- 
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