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

René Mayer mayer at psychologie.tu-dresden.de
Thu Dec 1 20:33:58 CET 2011

```Thanks David and Rubén!

@David: indeed 15 betas I forgot the interaction terms, thanks for correcting!

@Rubén:  the re-parameterize would be done within nls()? how to do
this practically with including the factor predictor?

and yes, we can solve within each group for Y=0 getting

0=b0+b1*X |-b0
-b0=b1*X |/b1
-b0/b1=X

but I was hoping there might a more general solution for the case of
multiple logistic regression.

HTH

René

Zitat von "David Winsemius" <dwinsemius at comcast.net>:

>
> On Dec 1, 2011, at 8:24 AM, René Mayer wrote:
>
>> 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
>
> Dear Dr Mayer;
>
> I think it might be a bit more complex than that. I think you should
> get 15 betas rather than 8. Have you done it?
>
>>
>> how can I get the inflection point per group, e.g., P(d)=.5
>
> Wouldn't that just be at d=1/beta in each group? (Thinking, perhaps
> naively, in the case of X=X1 that
>
> (Pr[y==1])/(1-Pr[y==1])) = 1 = exp( beta *d*(X==X1) )  # all other terms = 0
>
> And taking the log of both sides, and then use "middle school" math to solve.
>
> Oh, wait. Muffed my first try on that for sure.  Need to add back
> both the constant intercept and the baseline "d" coefficient for the
> non-b0 levels.
>
> (Pr[y==1])/(1-Pr[y==1])) = 1 = exp( beta_0 + beta_d_0*d +
>                                     beta_n + beta_d_n *d*(X==Xn) )
>
> And just
>
> (Pr[y==1])/(1-Pr[y==1])) = 1 = exp( beta_0 + beta_d_0*d ) # for the
> reference level.
>
> This felt like an exam question in my categorical analysis course 25
> years ago. (Might have gotten partial credit for my first stab,
> depending on how forgiving the TA was that night.)
>
>>
>> I would be grateful for any help.
>>