Logistic Regression with multicollinearity

Question

I really stuck on Logistic Regression. I have 3 models (Binary Logistic);

1. Logistic Regression.
2. RIDGE Logistic Regression
3. LASSO Logistic Regression

My data has multicollinearity. So I can't use Model 1. But when I use Model 1, I get better result than other two.

My question is; If I use Model 1, will I do wrong?

EDIT: I am using R.

Answer 1

If you can estimate Model $1$, then your multicolinearity is not complete, hence it isn't wrong to use this model. There is no assumption of non-colinearity, hence there is no theoretical problem and practically you have one global minima, albeit maybe not-so stable. If the stability of the model bothers you, you can use RIDGE or LASSO. Both methods result in biased but more stable (smaller variance) estimators. There is no way to tell which one is better without further information.