Performance of some estimators for the multicollinear logistic regression model: theory, simulation, and applications

This article proposes some new estimators, namely Stein's estimators for ridge regression and Kibria and Lukman estimator and compares their performance with some existing estimators, namely maximum likelihood estimator (MLE), ridge regression estimator, Liu estimator, almost unbiased ridge and Liu estimators, adjusted Liu estimator, James stein's estimator, Kibria and Lukman estimator, Dorugade estimator, and modified ridge estimator for the logistic regression model to solve the multicollinearity problem. The bias, covariance matrix, and mean square error matrix for each of the estimators are provided. A Monte Carlo simulation has been conducted to compare the performance of different estimators. We consider the smaller mean squared error value as a performance criterion. From the simulation study, it is evident that all proposed estimators performed better than the MLE. Finally, a real-life data is analyzed to illustrate the findings of the article. Some promising estimators are recommended for the practitioners.