Python中的有限逻辑回归

Question

The standard logistic regression solver in scikit-learn assumes the regression equation:

P(X) = 1/ (1 + exp(b0 + b1*X1 + ... + bn*Xn))

.. and solves for the b 's using various solver routines.

For a specific project, I'd like to bound the regression equation between 0-a (instead of 0-1) and add a variable c to center an independent variable Xk , eg

P(X) = a / (1 + exp((b0 + b1*X1 + .. + bn*Xn) * (Xk  - c)))

and solve for a , b 's and c .

Any thoughts/ideas on how to modify logistic.py to achieve this? I thought of modifying the expit function to reflect the changed equation. But how do a let the solvers know to also include the new variables a and c ? Any scripts available that are able to handle my modified logistic regression equation?

Answer 1

It is not totaaly clear what you need but

P(X) = a / (1 + exp(b0 + b1*X1 + .. + bn*Xn) * (Xk  - c))

that's the same as

P(X) = a / (1 + exp(b0 + b1*X1 + .. + bn*Xn + log(Xk)/log(c))

so replace c by exp(1/bk)