Developing Almost and Modified Almost Unbiased Estimators to Handle Multicollinearity Problem in Logistic Regression Model

Abstract

This paper introduces two biased estimators to avoid problems arising from multicollinearity in the logistic regression model. We investigated the theoretical excellence of the proposed estimators according to the mean square error matrix (MSE) and the scalar mean square error (MSE) criterion. We found that they have the superiority than some existing estimators. Moreover, we run the simulation study, which depended on the simulated MSE (SMSE), squared bias (SB) and generalized cross validation (GCV) as criteria to compare the estimators. The simulation results showed that the proposed estimators have the superiority than the estimators under comparison at several factors and at the same time, they work well at the high level of correlation. In addition, we investigated the behavior of the present estimators applying the real data. Under this trend, the results were consistent with the theoretical results.

Keywords: Maximum likelihood estimator; Multicollinearity; AL estimator; Mean squared error matrix.

Mathematics Subject Classification. Primary: 62J12. 26A25; 26A35