The Modified Logistic Two-Parameter Estimators

Abstract

In this article, we proposed a new estimator, termed the Modified Logistic Two Parameter Estimator (MLTPE), and enhanced it by modifying its coefficients, yielding three variants: Modified Logistic Two-Parameter Estimator1 (MLTPE1), Modified LogisticTwo-Parameter Estimator2 (MLTPE2), and Modified Logistic Two-Parameter Estimator3 (MLTPE3). These estimators are designed for logistic regression models in the presence of multicollinearity. Theoretically, we demonstrated the superiority of the MLTPE over existing estimators, including the Maximum Likelihood Estimator (MLE), Modified Almost Unbiased Ridge Logistic Estimator (MAURLE), and Logistic Two-Parameter Estimator (LTPE), in terms of mean square error (MSE). The superiority of the estimators is examined using a simulation study and a real-world example. In the simulation study, we varied the degree of correlation and sample size. The findings revealed that the efficacy of the estimators is significantly influenced by these factors. Furthermore, we evaluated the prediction performance of these estimators using balanced accuracy. The results suggested that the new estimators, MLTPE1, MLTPE2, and MLTPE3, outperformed the others slightly in terms of balanced accuracy, with MLTPE2 exhibiting superior performance regarding both scalar mean square error (SMSE) and balanced accuracy. Finally, we validated the simulation study using the myopia dataset, which produced satisfactory results