Liu-type logistic regression coefficient estimation with multicollinearity using the bootstrapping method

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Narumol Sudjai
Monthira Duangsaphon

Abstract

This study proposed new estimators for shrinkage and ridge parameters to overcome the multicollinearity problem in Liu-type logistic regression using the bootstrapping method. Moreover, we compared the performance of four methods for logistic regression coefficient estimation with multicollinearity present: the maximum likelihood estimator, ridge logistic regression, Liu logistic regression, and Liu-type logistic regression, all performed with the bootstrapping method. A simulation study was conducted to compare the performance of the four different estimation methods using the estimated mean square error. The results from both the simulation study and a real data application showed that the Liu-type logistic regression with the bootstrapping method performed best, among the four methods, with a high correlation coefficient. Moreover, the proposed estimators for the shrinkage parameter and ridge parameter showed good performance. In addition, the use of Liu-type logistic regression together using the bootstrapping method was the most robust for correcting the multicollinearity problem.

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