Another New Two Parameter Estimator in Dealing with Multicollinearity in the Logistic Regression Model

Abstract

In logistic regression models, the maximum likelihood method is always one of the commonly used to estimate the model parameters. However, unstable parameter estimates are obtained due to  the problem of multicollinearity. In this article, a new two parameter biased estimator is proposed to combat the issue of multicollinearity in the binary logistic regression models. The proposed estimator is a general estimator which includes other biased estimators, such as the Logistic Ridge, Logistic Liu and the estimators with two biasing parameters as special cases. The properties of the proposed estimator were derived, and six (6) forms of biasing parameter
k (generalized, maximum, median, mid-range, arithmetic and harmonic means) were used in this study. Necessary and sufficient conditions for the superiority of the new two parameter biased estimator over the existing estimators are obtained. Also, Monte Carlo simulation studies are executed to compare the performance of the proposed biased estimator. Finally, a
numerical example is given to illustrate some of the theoretical results. The proposed estimator outperforms all the other estimators in the various design of experiment used in this study.