A Two-Parameter Ridge Estimator for Handling Extreme Multicollinearity Problems in Logistic Regression
DOI:
https://doi.org/10.62054/ijdm/0104.15Keywords:
Multicollinearity, Logistic Regression, Robust Estimator, Mean Square Error, Biasing ParameterAbstract
This paper introduces a robust two-parameter ridge estimator that is customized for logistic regression models, which tend to be sensitive to extreme multicollinearity problems. Inflated standard errors and unreliability in the results stem from the problem of multicollinearity characterized by high correlations among predictor variables in logistic regression model. Traditional approaches like the Maximum Likelihood Estimator (MLE) and one-parameter ridge-type estimators often perform poorly under these settings, thus calling for the development of more robust approaches. This new proposal is called New Biased Two Parameter (NBTP), which extends the ridge regression framework by introducing additional biasing parameters customized for an extreme multicollinearity problem. The paper combines a theoretical analysis with extensive Monte Carlo simulations and real application to Pena data. It demonstrates that the new estimator, New Biased Two Parameter (NBTP), provides much more stable and accurate parameter estimates than previous methods. The results underscore the importance of using robust estimation methods within logistic regression, especially when multicollinearity may be widespread in fields such as medical research, finance, and the social sciences.
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