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A Modified Ridge Estimator for the Logistic Regression Model

Year: 2021       Vol.: 70       No.: 2      

Authors: Mazin M. Alanaz, Nada Nazar Alobaidi and Zakariya Yahya Algamal

Abstract:

The ridge estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The logistic regression model is a well-known model in application when the response variable is binary data. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the logistic regression coefficients. To address this problem, a logistic ridge regression model has been proposed by numerous researchers. In this paper, a modified logistic ridge estimator (MLRE) is proposed and derived. The idea behind the MLRE is to get diagonal matrix with small values of diagonal elements that leading to decrease the shrinkage parameter and, therefore, the resultant estimator can be better with small amount of bias. Our Monte Carlo simulation results suggest that the MLRE estimator can bring significant improvement relative to other existing estimators.

Keywords: multicollinearity, ridge estimator, logistic regression model, shrinkage, Monte Carlo simulation

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