On the relationship between multicollinearity and separation in logistic regression

Multicollinearity and separation are two major issues in logistic regression. In this paper, for the first time we study the relationship between multicollinearity and separation. We analytically prove that multicollinearity implies quasi-complete separation. Through counter examples, we show that multicollinearity does not always imply complete separation and that separation does not always imply multicollinearity. We also present the consequences of multicollinearity and separation. We analytically prove that multicollinearity means no finite solution to maximum likelihood estimate and that separation means no finite solution to maximum likelihood estimate.

Automated summary

In this paper, the relationship between multicollinearity and separation in logistic regression is studied for the first time. The analysis shows that multicollinearity implies quasi-complete separation, but not always complete separation. Similarly, separation does not always imply multicollinearity. Additionally, the consequences of multicollinearity and separation are presented, including the lack of finite solutions to maximum likelihood estimate in both cases.