[R] unexpected result in glm (family=poisson) for data with an only zero response in one factor

[John Maindonald]

The Wald statistics that are returned as "z value" can be a very  
rough approximation.  The standard error is radically different, on a  
logarithmic scale, between log(mu) = -20.30 [the best glm() managed  
in approximating -infinity] and log(mu) + log(a) = -0.29.  It is  
actually worse than might appear; the SE=2457.38 is an approximation  
to infinity!  The phenomenon is an extreme version, now with a  
poisson error model, of the Hauck-Donner effect (Modern Applied  
Statistics with S, 4th edn, pp.197-199) that occurs with binomial  
data.  Use the result from the anova likelihood ratio test, where the  
approximations that are involved are usually much better behaved (but  
it would not hurt to do a simulation as a check.)

There is an example of this phenomenon with a poisson error model in  
Subsection 8.4.2 (the same subsection number both for the 1st edn and  
the forthcoming 2nd edn) of Data Analysis & Graphics using R, CUP,  
2003 and 2006. Install and attach the DAAG package and try

example(moths)

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.

> Dear members,
> here is my trouble: My data consists of counts of trapped insects  
> in different attractive traps. I usually use GLMs with a poisson  
> error distribution to find out the differences between my  
> traitments (and to look at other factor effects). But for some  
> dataset where one traitment contains only zeros, GLM with poisson  
> family fail to find any difference between this particular  
> traitment and anyother one (even with traitment that have trapped a  
> lot of insects). GLMs with gaussian family does not seem to have  
> the same problem but GLMs with binomial family does.
> I'm not sure if it is a statistical problem or if it comes from  
> R... in the latter case I think some solution exists (perhaps in  
> the options of the glm() function ?).
> Thank you for your help.
>
>
> Here I figure out an exemple to past in the console:
>
> ## START  
> ###################################################################### 
> ########
> # Take a data set of counts for two traitments, one containing only  
> zeros
> A=c 
> (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 
> ,0,0,0,0,0)
> B=c 
> (1,0,0,0,2,1,0,0,1,2,0,0,0,1,2,2,0,1,1,0,1,0,2,1,1,0,1,2,0,1,0,1,1,1,0 
> ,1,1,1,0,1)
> traitment=c(rep("A",40),rep("B",40))
> response=c(A,B)
> mydata=data.frame(traitment ,response)
>
>
> # Make a GLM on this dataset , with "family=poisson"
>
>  g=glm(response~traitment, data=mydata, family=poisson)
>  anova.glm(g,test="Chisq")
> # There is an effect of the traitment ...
>
>  summary(g)
> # But traitment A does not differ from traitment B ! ! ! (the  
> pvalue is always close from 1 in such cases)
>
> # Now if you replace only one zero of the A reponse to 1, the GLM  
> works properly:
>  mydata[1,2]=1
>  g=glm(response~traitment, data=mydata, family=poisson)
>  anova.glm(g,test="Chisq")
>  summary(g)
> ###################################################################### 
> ###############  END ##
>
>
>
> Antonin Ferry (PhD)
>
> "Laboratoire d'Ecobiologie des Insectes Parasitoides"
> http://www.parasitoides.univ-rennes1.fr
> Université de Renes1, FRANCE