[R] glm or transformation of the response?

[Christoph Scherber]

Dear all,

For an introductory course on glm?s I would like to create an example to show the difference between 
glm and transformation of the response. For this, I tried to create a dataset where the variance 
increases with the mean (as is the case in many ecological datasets):

	poissondata=data.frame(
	response=rpois(40,1:40),
	explanatory=1:40)

	attach(poissondata)

However, I have run into a problem because it looks like the lm model (with sqrt-transformation) 
fits the data best:

##

model1=lm(response~explanatory,poissondata)
model2=lm(sqrt(response+0.5)~explanatory,poissondata)
model3=lm(log(response+1)~explanatory,poissondata)
model4=glm(response~explanatory,poissondata,family=poisson)
model5=glm(response~explanatory,poissondata,family=quasipoisson)
model6=glm.nb(response~explanatory,poissondata)
model7=glm(response~explanatory,quasi(variance="mu",link="identity"))


plot(explanatory,response,pch=16)
lines(explanatory,predict(model1,explanatory=explanatory))
lines(explanatory,(predict(model2,explanatory=explanatory))^2-0.5,lty=2)
lines(explanatory,exp(predict(model3,explanatory=explanatory))-1,lty=3)
lines(explanatory,exp(predict(model5,explanatory=explanatory)),lty=1,col="red")
lines(explanatory,predict(model6,explanatory=explanatory,type="response"),lty=1,col="blue")
lines(explanatory,predict(model7,explanatory=explanatory,type="response"),lty=1,col="green")

##

The only model that performs equally well is model7.

How would you deal with this kind of analysis? What would be your recommendation to the students, 
given the fact that most of the standard glm models obviously don?t seem to produce good fits here?

Many thanks and best wishes
Christoph

(using R 2.8.0 on Windows XP)





-- 
Dr. rer.nat. Christoph Scherber
University of Goettingen
DNPW, Agroecology
Waldweg 26
D-37073 Goettingen
Germany

phone +49 (0)551 39 8807
fax   +49 (0)551 39 8806

Homepage http://www.gwdg.de/~cscherb1