Some new methods to solve multicollinearity in logistic regression

The binary logistic regression is a widely used statistical method when the dependent variable is binary or dichotomous. In some of the situations of logistic regression, independent variables are collinear which leads to the problem of multicollinearity. It is known that multicollinearity affects the variance of maximum likelihood estimator (MLE) negatively. Thus, this article introduces new methods to estimate the shrinkage parameters of Liu-type logistic estimator proposed by Inan and Erdogan (2013 Inan, D., Erdogan, B. E. (2013). Liu-type logistic estimator. Communications in Statistics-Simulation and Computation 42(7):1578–1586. [Google Scholar]) which is a generalization of the Liu-type estimator defined by Liu (2003 Liu, K. (2003). Using Liu-type estimator to combat collinearity. Communications in Statistics: Theory and Methods 32(5):1009–1020. [Google Scholar]) for the linear model. A Monte Carlo study is used to show the effectiveness of the proposed methods over MLE using the mean squared error (MSE) and mean absolute error (MAE) criteria. A real data application is illustrated to show the benefits of new methods. According to the results of the simulation and application proposed methods have better performance than MLE.