A Modified Ridge-Type Logistic Estimator

The binary logistic regression (BLR) model is used as an alternative to the commonly used linear regression model when the response variable is binary. As in the linear regression model, there can be a relationship between the predictor variables in a BLR, especially when they are continuous, thus giving rise to the problem of multicollinearity. The efficiency of maximum likelihood estimator (MLE) is low in estimating the parameters of BLR when there is multicollinearity. Alternatively, the ridge estimator and the Liu estimator were developed to replace MLE. However, in this study, we developed a new estimator also to mitigate the effect of multicollinearity. We established the superiority of this new estimator over the existing ones in terms of their corresponding MSE. Finally, a numerical example and simulation study were conducted to illustrate the theoretical results. The result shows that the new estimator outperforms the existing estimators.