# [R] how to get inflection point in binomial glm

Rubén Roa rroa at azti.es
Thu Dec 1 15:31:08 CET 2011

```Assuming a logistic model, for each group solve for d at Y=0, or solve for d at p=0.5, where d is your continuous predictor, Y is the logit score, and p is the probability of success in the binomial model. After that you can get the standard error of the inflection point by Taylor series (aka delta method).

Another idea is to re-parameterize the logistic model to include explicitly the inflection point, thus you'll get its estimate and standard error directly as a result of the fit.
For example, disregarding the g factor predictor (or for each group), a logistic model such as
P(d) = 1/(1+exp(log(1/19)(d-d50)/(d95-d50))
includes the inflection point directly (d50) and is a re-parameterized version of the usual logistic model
P(d) =1/(1+exp(b0+b1*d))
where parameters b0 and b1 have been replaced by d95 and d50, the predictor at 50% probability (inflection point), and the predictor at 95% probability, respectively.

HTH

Rubén

-----Mensaje original-----
De: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] En nombre de René Mayer
Enviado el: jueves, 01 de diciembre de 2011 14:25
Para: r-help at r-project.org
Asunto: [R] how to get inflection point in binomial glm

Dear All,

I have a binomial response with one continuous predictor (d) and one factor (g) (8 levels dummy-coded).

glm(resp~d*g, data, family=binomial)

Y=b0+b1*X1+b2*X2 ... b7*X7

how can I get the inflection point per group, e.g., P(d)=.5

I would be grateful for any help.