[R] GLM function with poisson distribution

[Thomas Lumley]

On Tue, 25 Jan 2005, Florian Menzel wrote:

> Hello all,
> I found a weird result of the GLM function that seems
> to be a bug.

No, the problem is that you are using the Wald test when the mle is 
infinite, which is always going to be unreliable.  It's even worse because 
you are using data that couldn't really have come from a Poisson 
distribution (because for a=1 you have mean 3 and variance 0).

If you used anova(model) to get a likelihood ratio test the p-value would 
be 4e-10.

 	-thomas

> The code:
>  a=c(rep(1,8),rep(2,8))
>  b=c(rep(0,8),rep(3,8))
>  cbind(a,b)
>  model=glm(b~a, family=poisson)
>  summary(model)
> generates a dataset with two groups. One group
> consists entirely of zeros, the other of 3‘s (as
> happened in a dataset I’m analyzing right now). Since
> they are count data, one should apply a poisson
> distribution. A GLM with poisson distribution delivers
> a p value > 0.99, thus, completely fails to detect the
> difference between the two groups. Why not and what
> should I do to avoid this error? A quasipoisson
> distribution detects the difference but I’m not sure
> whether it’s appropriate to use it.
> Thanks a lot to everybody who answers!
> 		 Florian
>
> Version information:
> version 1.9.0 (2004-4-12)
> os mingw32
> arch i386
>
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Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle