A new Jackknifing ridge estimator for logistic regression model

The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The logistic regression model is a well-known model in application when the response variable is binary data. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the logistic regression coefficients. To address this problem, a logistic ridge estimator has been proposed by numerous researchers. In this paper, a new Jackknifing logistic ridge estimator (NLRE) is proposed and derived. The idea behind the NLRE is to get diagonal matrix with small values of diagonal elements that leading to decrease the shrinkage parameter and, therefore, the resultant estimator can be better with small amount of bias. Our Monte Carlo simulation results suggest that the NLRE estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the NLRE estimator outperforms both logistic ridge estimator and maximum likelihood estimator in terms of predictive performance.