# [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:

> 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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