An efficient generalized ridge estimator for logistic regression model

In the logistic regression model (LRM), the maximum likelihood estimator (MLE) is commonly employed to estimate unknown model parameters. However, when substantial multicollinearity exists among the explanatory variables, the MLE produces unstable parameter estimates with large variances, wide confidence intervals, and low statistical power, which in turn complicates reliable inference and prediction. To alleviate these drawbacks, this study investigates a generalized ridge logistic regression (GRL) estimator based on introducing a ridge parameter matrix K that controls the amount of shrinkage and reduces the variance of the regression coefficient estimates. The parameters of the GRL model are estimated via the maximum likelihood approach, and the performance of the GRL estimator is then compared with that of the traditional MLE under different patterns and degrees of multicollinearity using a Monte Carlo simulation framework. The simulation experiment evaluates several recently proposed methods for selecting the GRL ridge parameter k and examines their impact on the mean squared error (MSE) of the coefficient estimates. The findings indicate that the generalized ridge estimator for logistic regression consistently yields lower MSE values than the conventional ML estimator across all investigated correlation structures and noise levels, confirming its practical usefulness for classification and predictive modeling in the presence of multicollinearity.