[R] Under-dispersion - a stats question?

Peter Dalgaard p.dalgaard at biostat.ku.dk
Mon Oct 10 22:56:32 CEST 2005

"Martin Henry H. Stevens" <HStevens at muohio.edu> writes:

> 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.

I don't think it is safe to say anything general about this without
knowledge of the model and the subject matter. Residual deviances can
be terribly misleading. Consider for instance this:

y <- c(0,1); w <- c(50,50)
summary(glm(y~1, binomial, weights=w))
y1 <- .5; w1 <- 100
summary(glm(y1~1, binomial, weights=w1))

Notice that coeff. and s.e. is exactly the same, but not the residual

Now, in the first case, did the zeros and ones sort themselves into
two completely separated groups, or was that just because data was
given pre-tabulated? 

   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

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