Enhancing Predictive Performance of the Logistic Two-Parameter Estimator under Multicollinearity

Abstract

This study aimed to propose a new estimator named Modified Logistic Two-Parameter Estimator (MLTPE) with the best predictive performance in logistic regression when multicollinearity exists. The performance of the proposed estimator was compared with existing estimators: Maximum Likelihood Estimator (MLE), Modified Almost Unbiased Ridge Logistic Estimator (MAURLE), Modified Almost Unbiased Ridge Logistic Liu Estimator (MAULLE) and Logistic Two-Parameter Estimator (LTPE), in terms of the scalar mean squared error (SMSE) and balanced accuracy. The performance of the estimators was evaluated using Monte Carlo simulations. In the design of the experiment, factors such as the degree of correlation and sample size were varied. The results showed that the performance of the estimators depended on these factors. Finally, the theoretical results were applied to a myopia real world dataset and observed that the results agreed with the simulation study's results. It was noticed that the MAURLE performs well in terms of SMSE; however, the proposed estimator showed slightly better performance in terms of balanced accuracy.