Liu estimator in logistic regression when the data are collinear

Abstract

The logistic regression model is used to predict a binary response variable. Logistic regression using maximum likelihood estimation has gained widespread use but it is found that multicollinearity among the independent variables inflates the variance of this estimator. Previously, Ridge, Principal Component and Stein estimators were proposed instead of maximum likelihood estimator when the data are collinear. And in this study a Liu type estimator is proposed that will have smaller mean squared error than the maximum likelihood estimator. And Liu type estimator and several alternative estimators in logistic regression, such as Ridge, Stein, principal component, are compared under the mean squared error criterion.