inverse prediction and Poisson regression
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 D?veloppement en Agroenvironnement (IRDA) 3300 Sicotte, St-Hyacinthe Qu?bec J2S 7B8 t?l?phone: 450-778-6522 poste 233 courriel: vincent.philion at irda.qc.ca Site internet : www.irda.qc.ca