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I am applying logistic regression to predict a target variable ( success or no-success).I added some new features, tested my AUC.My AUC initially was 0.6, and it increased to 0.7 when I added polynomial features (degree=2).

I was building an app to test my model and calculated the probability of success ( using predict_prob_).But when I was building the app, I realized that when I increase the values of the most predictive feature in the model, the probability of success continues to increase.There seems to be no plateau ( meaning the probability doesn't remain constant after a the predictive feature crosses a certain threshold).

Is this expected? I cannot seem to solve this problem.I assumed the adding polynomial features would help reach a plateau.Any advice? or am I understanding the concept wrong?

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Graph and function of inverse of logistic function

$${\displaystyle \operatorname {logit} ^{-1}(\alpha )=\operatorname {logistic} (\alpha )={\frac {1}{1+\operatorname {exp} (-\alpha )}}={\frac {\operatorname {exp} (\alpha )}{\operatorname {exp} (\alpha )+1}}}$$

From graph and function, if your "plateau" means the probability remains constant after a the predictive feature crosses a certain threshold, then there is no plateau. If your "plateau" means the probability changes very little when covariates change, then when p is close to 0 or 1, there are plateaus. When you increase the value of covariates whose regression coefficients are positive, the probability will increase; When you increase the value of covariates whose regression coefficients are negative, the probability will decrease.

Adding more covariates (including polynomial) generally does not increase the speed of increasing the probability, because it is possible the added covariates have negative coefficients, and even the coefficeint is positive, it is possible that other positive regression coefficients decrease.

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