[R] inverse prediction and Poisson regression
Vincent Philion
vincent.philion at irda.qc.ca
Fri Jul 25 15:10:35 CEST 2003
Hello again, sorry for the notation. Again, I'm just a biologist!!!
;-)
But I'm enjoying this problem quite a bit! I'm very grateful for all the input. This is great.
On 2003-07-25 08:38:00 -0400 Prof Brian Ripley <ripley at stats.ox.ac.uk> wrote:
Answers:
> Ymax is the maximum observation in your example, and also the observation at
> zero. I was asking which you meant: if you meant Y at 0 (and I think you do)
> then it is somewhat misleading notation.
I will clean up my notation!
>
> You have a set of Poisson random variables Y_x at different values of x.
> Poisson random variables have a mean (I am using standard statistical
> terminilogy), so let's call that mu(x). Then you seem to want the value of x
> such that mu(x) = mu(0)/2 *or* mu(x) = Y_0/2,
OK, I want x for mu(x) = mu(0)/2.
> that in your model mu(0) would be infinity, and so the
> model cannot fit your data (finite values of Y_0 have zero probability).
Correct, This is part of the problem! The model does not "hold" for X = 0.
> the largest response because the "dose" is always detrimental to growth)
>
> The last is not true, given your assumptions, It could have the largest mean
> response, but 0 is a possible value for Y_0.
Yes, you are right, but then there is no growth, nad no LD50 value, so we reject this sample...
>
> Fit a model for the mean response (one that actually can fit your data), and
> solve the estimated mu(x) = mu()/2 or Y_0/2. That gives you an estimate, and
> the delta method will give your standard errors.
Then you suggest using another model that will account for zero dose, OK. I think I saw something similar in another reply. I need to read it more carefully.
--
Vincent Philion, M.Sc. agr.
Phytopathologiste
Institut de Recherche et de Développement en Agroenvironnement (IRDA)
3300 Sicotte, St-Hyacinthe
Québec
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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