Logistic Regression and modelling probabiliy pi. If the link function is g(pi)=log(pi/(1-pi))=x^T beta

Siemensueqw

Siemensueqw

Answered question

2022-11-07

Logistic Regression and modelling probabiliy π
If the link function is
g ( π ) = log ( π 1 π ) = x T β
show that this is equivalent to modeling the probability π as,
π = e x T β 1 + e x T β
Again I think this is a simply inverse. But I'm not quite sure how to do it.

Answer & Explanation

kliersel12g

kliersel12g

Beginner2022-11-08Added 13 answers

Step 1
You're right, it is just the inverse
ln π 1 π = x T β             π 1 π = e x T β             π = ( 1 π ) e x T β = e x T β π e x T β
Step 2
Now rearrange a bit things
π ( 1 + e x T β ) = e x T β
and from here
π = e x T β 1 + e x T β

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