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

[John Maindonald]

PS.  In part, the problem is with the use of the log link, arising  
because the limit of log(mu), as mu goes to 0, is minus infinity.   
This is not an appropriate scale on which to represent a fitted value  
that is zero.  The estimated SE for a fitted value of zero should be  
0.  You will get a more sensible answer if you set family=poisson 
(link="sqrt")

g <- glm(response~traitment, data=mydata, family=poisson(link="sqrt"))
 > summary(g)

Call:
glm(formula = response ~ traitment, family = poisson(link = "sqrt"),
     data = mydata)

Deviance Residuals:
        Min          1Q      Median          3Q         Max
-1.225e+00  -2.730e-05  -2.730e-05   2.745e-01   1.193e+00

Coefficients:
              Estimate Std. Error  z value Pr(>|z|)
(Intercept) 0.0000193  0.0790569 0.000244        1
traitmentB  0.8660061  0.1118034    7.746  9.5e-15

(Dispersion parameter for poisson family taken to be 1)

     Null deviance: 75.485  on 79  degrees of freedom
Residual deviance: 33.896  on 78  degrees of freedom
AIC: 89.579

Number of Fisher Scoring iterations: 14


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