[R] inverse prediction and Poisson regression

Vincent Philion vincent.philion at irda.qc.ca
Fri Jul 25 14:07:03 CEST 2003

Hello sir, answers follow...

... Where X is dose and Y is response. the relation is linear for log(response) 
 = b log(dose) + intercept
 *** Is that log(*mean* response), that is a log link and exponential decay with 
I'm not sure I understand what you mean by "mean", (no pun intended!) but Y is a biologicial "growth". Only one "observation" for each X. But this observation is from the growth contribution of about 500 individuals, so I guess it is a "mean" response by design.

the log link is for the Poisson regression, so the GLM is "response ~ log(dose), (family=poisson)"

 ...Response for dose 0 is a "control" = Ymax. So, What I want is the dose for 50% response. 

*** Once you observe Ymax, Y is no longer Poisson.

I don't understand this? What do you mean? Please explain.
 ***What exactly is Ymax?  Is it the response at dose 0? 
Correct. it is measured the same way as for any other Y. (It is also the largest response because the "dose" is always detrimental to growth)

***About the only thing I can actually  interpret is that you want to fit a curve of mean response vs dose, and
 find the dose at which the mean response is half of that at dose 0.

That's it. that sounds right! How? (Confidence interval on log scale and on real scale, etc) Given that the error on Y is Poisson and not "normal"

***That one is easy.

*** I think you are confusing response with mean response, and we can't 
 disentangle them for you.
What else is needed?

bye for now,

Vincent Philion, M.Sc. agr.
Institut de Recherche et de Développement en Agroenvironnement (IRDA)
3300 Sicotte, St-Hyacinthe
J2S 7B8

téléphone: 450-778-6522 poste 233
courriel: vincent.philion at irda.qc.ca
Site internet : www.irda.qc.ca

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