Logistic average maximum likelihood-centered penalized estimator: a new estimator to better address multicollinearity in Logistic regression

Logistic ridge estimator (LRE) is a common method to address multicollinearity in Logistic regression (LR), shrinking the parameters towards zero. However, LRE contradicts the actual association and tends to become an inadequate solution for multicollinearity where the true value of the parameter is not equal to zero. In this work, a new estimator, Logistic average maximum likelihood-centered penalized estimator (LAMLPE), was proposed to better address multicollinearity. LAMLPE shrinks the parameters towards the weighted average of maximum likelihood estimators. A simulation study and case study indicate that LAMLPE can obtain a more accurate estimate than existing estimators where the true parameters have same sign and small variation. Therefore, LAMLPE is recommended to address multicollinearity in LR when the true parameters are known to have the same sign in advance.