Abstract

In logistic regression models, the maximum likelihood method is commonly used to estimate the model parameters. However, unstable parameter estimates are obtained as a result of multicollinearity. In this article, a new biased estimator is proposed to combat 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. Necessary and sufficient conditions for the superiority of the new 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.

摘要

在逻辑回归模型中，最大似然法通常用于估计模型参数。然而，由于多重共线性，会获得不稳定的参数估计。在本文中，提出了一种新的有偏估计器来对抗二元逻辑回归模型中的多重共线性。所提出的估计量是一个通用估计量，它包括其他有偏估计量，例如 Logistic Ridge、Logistic Liu 和具有两个偏置参数的估计量作为特例。得到了新的有偏估计量优于现有估计量的充要条件。此外，执行蒙特卡罗模拟研究以比较所提出的有偏估计器的性能。最后，给出了一个数值例子来说明一些理论结果。