A penalty function in binary logistic regression

Abstract

An algorithm is proposed to determine the logistic ridge parameter minimizing the MSE of the estimated parameter estimators, together with a theorem on the upperbound of the optimal logistic ridge parameter to facilitate the nonlinear optimization. A simulation is used to evaluate the relative efficiencies of the proposed estimator and other six well-known ridge estimators with respect to the maximum likelihood estimator. The simulation results confirm that the relative efficiency of the proposed estimator is highest among other well-known estimators. Finally, a real-life data set is used to repeat the evaluation and the conclusion is the same as in the simulation