I'm not sure on what kind of dataset would be most appropriate, but following code I used to create a dataset with a linear response and an increasing variance (the megaphone type, common in ecological datasets if I'm right) :
beta0 <- 10 beta1 <- 1 x <- c(1:40) y <- beta0 + x*beta1 +rnorm(40,0,1)*seq(0.1,10,length.out=40) Data=data.frame(x,y) I won't win the price for most elegant programming with this, but it surely works fine for my simulations. Kind regards Joris On Tue, Nov 25, 2008 at 3:52 PM, Christoph Scherber <[EMAIL PROTECTED]> 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) > > > > > > -- > 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 > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
