Comparison of Test Statistics for Testing the Regression Coefficients in the Ridge, Liu and Kibria-Lukman Logistic Regression Models: Simulation and Application

Abstract

Ridge, Liu and Kibria- Lukman regression are methods that have been proposed to solve the multicollinearity problem for both linear and non-linear regression models. This paper studies different Ridge, Liu and Kibria-Lukman regression z-type tests of the individual coefficients for logistic regression model. A simulation study was conducted to evaluate and compare the performance of the test statistics with respect to their empirical sizes and powers under different simulation conditions. Our simulations allowed us to identify among the proposed tests, which ones maintain type I error rates close to the 5% nominal level, while at the at same time showing considerable gain in statistical power over the standard Wald z-test commonly used in logistic regression model. Our paper is the first of its kind in comparing the z-type tests for these different shrinkage approaches to estimation in logistic regression. The results will be of value for applied statisticians and researchers in the area of regression models.