# Would there be any alternatives to a Logistic Regression or way to modify the Regression for what I'm looking for?

To provide more information I am looking for an alternative to logistic Regression or a way to modify it. This is because of two reasons:

• My data is widely dispersed across the X axis for both my 1s and 0s however there is slightly more 1s the higher the X and slightly more 0s the lower the X. So the probabilities listed in a standard Logistic regression I feel are over/understated on both ends of the X axis.
• I'm not very concerned with classifying future outcomes accurately, I'm more concerned in how movement along the X increases the probability for my 1 outcomes.

My main concern with a Logistic Regression is that the starting off point the probability of a 1 is close to 0% while the ending point the probability is 100% (given a positive relationship with the x).

With my data this isn't accurate as the probability of a 1 outcome would never hit 100%. I am wondering if there would a better method for me to utilize that would allow me to map out the relationship between my X variable against my 1 and 0 Y variables? Or a way to modify the regression to take into account that for my max X variable I will never have a 100% probability of getting a 1?

Basically I'm interested in knowing what my probability of a 1 outcome is for my max X while getting an accurate representation of how the probability will change with movement across my X axis.

Edit: Picture for example of a Logistic Regression (Not a picture of my actual data though)

• Try plotting this with confidence or prediction intervals and see if that eases your concerns. Also, it would help if you could add a plot of your actual data, so we could see exactly what the problem is.
– mkt
Sep 20, 2022 at 16:13
• I am not seeing the problem with logistic regression yet - maybe you underestimate it's flexibility. Does it have to be a parametric model or will lowess do? Sep 20, 2022 at 16:28
• But does the logistic regression run over your data actually predict the probabilities like 100%? That would be the case if you have no negative examples in your data for such cases--so from the data point of view, it is a reasonable answer. If you want to constrain it, you can always do arbitrary things like "rounding down" the probabilities to arbitrary values--it doesn't have much sense, but it illustrates the arbitrariness of such solutions. Better alternative is a Bayesian model, but do you have enough prior knowledge to decide on informative priors?
– Tim
Sep 20, 2022 at 16:29
• "My main concern with a Logistic Regression is that the starting off point the probability of a 1 is close to 0% while the ending point the probability is 100% (given a positive relationship with the x)." - this is not a true statement about logistic regression. Sep 20, 2022 at 16:29
• "the starting off point the probability of a 1 is close to 0% while the ending point the probability is 100%" That fact that this is false, that is already shown in your image. The end points are close but not exactly equal to 0% and 100%. Sep 20, 2022 at 16:53