[R] glm or transformation of the response?

[Peter Dalgaard]

Christoph Scherber wrote:
> 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)
> 

Any good reason that you're not transforming both sides when
transforming? and that you're not looking at

model8 <- glm(response~log(explanatory),poissondata,family=poisson)
(etc.)

??

BTW, your predict call seems to be missing data.frame() around
"explanatory=explanatory". The predict() methods do not have an argument
called "explanatory", so this is just ignored (a buglet if you ask me).

-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
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