Multinomial logistic regression

[w4rner]

I noticed in the notebook GLMest.ipynb, you don't add a constant column to X. Are you not supposed to?

[khan1792]

In LogisticRegression function of sklearn, you need not to set constant. It's default setting is "fit_intercept = True”. Only for functions of statmodel package, you must ad it.

[w4rner]

Thanks Kanyao!
I manually added a constant column, and my results was: beta 0 = -8.459980007874217e-06
I guess that explains why it is next to 0. Although I'm surprised it even worked given multicollinearity! Any thoughts?

[khan1792]

In sklearn, you can use result.intercept_ to look at the real intercept (even you add the constant column). I think when you add a constant column manually, this column become a variable whose value is constantly 1, and it will provide no information if you already have an intercept. In logistic regression, this kind of variable will serve as an offset for adjusting the intercept, but the coefficients are the same no matter you add the offset or not. I know in oversampling method, we can use this kind of variable to correct the intercept (although the exact constant value of the variable will be calculated in a certain way). In this logic, I speculate that when you add the constant column, the real intercept (no constant column in the model) will become the biased intercept in your model minus beta 0. Since the beta 0 is very small, the biased intercept is very similar the real intercept. You can check my speculation in your code (don't forget to use result.intercept_ to look at the intercept even you add the constant column).