A general restricted estimator in binary logistic regression in the presence of multicollinearity

Abstract

The presence of multicollinearity adversely affects the inferential properties of the maximum likelihood (ML) estimator in logistic regression model. It is a well-established fact that the use of restrictions lowers the effect of multicollinearity. In this article, an alternative to the ML estimator has been introduced by combining the exact prior information into the logistic $\mathit{r}-\mathit{k}$ class (Lrk) estimator. The estimator is named a logistic restricted $\mathit{r}-\mathit{k}$ class estimator. Another estimator, logistic restricted PCR estimator, is also developed as a special case of the LRrk estimator. The asymptotic mean squared error (MSE) matrix properties of the estimators are studied and necessary and sufficient conditions are derived. Further, a Monte Carlo simulation study is performed to compare the performance of the estimators in terms of the scalar MSE and the prediction MSE. It is found that the proposed estimators perform better than the existing estimators in most of the cases considered. Moreover, a numerical example has also been presented for comparing the performance of the estimators.