Abstract
<jats:p>Logistic regression is one of the most important and widely applied statistical models for analyzing binary response data in various scientific and applied fields. Nevertheless, parameter estimation using Maximum Likelihood Estimation (MLE) may become unstable and yield high-variance estimates when explanatory variables are strongly multicollinear. This problem negatively affects model reliability, prediction accuracy, and interpretation of regression coefficients. To overcome these limitations, several biased estimation approaches have been proposed, among which the Liu estimator has demonstrated promising performance. This study proposes an improved, efficient Liu shrinkage estimator for logistic regression to reduce mean squared error (MSE) and improve estimation efficiency under multicollinearity. The proposed estimator extends existing Liu-based methods by introducing an optimised procedure for selecting the shrinkage parameter and enhancing coefficient stability. The performance of the proposed method was evaluated using an extensive Monte Carlo simulation study under different combinations of sample sizes, numbers of explanatory variables, and correlation levels. Comparative analysis was carried out against the classical MLE and several existing Liu estimators. In addition, the proposed approach was validated using a real dataset related to anti-hepatitis C virus activity. The results demonstrated that the proposed estimator consistently achieved lower MSE and more stable estimates, indicating superior accuracy and effectiveness under severe multicollinearity.</jats:p>