Ridge Estimator in Logistic Regression under Stochastic Linear Restrictions

Abstract

In the logistic regression, it is known that multicollinearity affects the variance of Maximum Likelihood Estimator (MLE). To overcome this issue, several researchers proposed alternative estimators when exact linear restrictions are available in addition to sample model. In this paper, we propose a new estimator called Stochastic Restricted Ridge Maximum Likelihood Estimator (SRRMLE) for the logistic regression model when the linear restrictions are stochastic. Moreover, the conditions for superiority of SRRMLE over some existing estimators are derived with respect to Mean Square Error (MSE) criterion. Finally, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Ridge Type Logistic Estimator (LRE) and Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model by using Scalar Mean Squared Error (SMSE).