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K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model

Author

Listed:
  • Adewale F. Lukman

    (Department of Epidemiology and Biostatistics, University of Medical Sciences, Ondo 220282, Nigeria)

  • B. M. Golam Kibria

    (Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA)

  • Cosmas K. Nziku

    (Department of Statistics, University of Dar es Salaam, Dar es Salaam 65015, Tanzania)

  • Muhammad Amin

    (Department of Statistics, University of Sargodha, Sargodha 40100, Pakistan)

  • Emmanuel T. Adewuyi

    (Department of Statistics, Ladoke Akintola University of Technology, Ogbomoso 210214, Nigeria)

  • Rasha Farghali

    (Department of Mathematics, Insurance and Applied Statistics, Helwan University, Cairo 11732, Egypt)

Abstract

Multicollinearity negatively affects the efficiency of the maximum likelihood estimator (MLE) in both the linear and generalized linear models. The Kibria and Lukman estimator (KLE) was developed as an alternative to the MLE to handle multicollinearity for the linear regression model. In this study, we proposed the Logistic Kibria-Lukman estimator (LKLE) to handle multicollinearity for the logistic regression model. We theoretically established the superiority condition of this new estimator over the MLE, the logistic ridge estimator (LRE), the logistic Liu estimator (LLE), the logistic Liu-type estimator (LLTE) and the logistic two-parameter estimator (LTPE) using the mean squared error criteria. The theoretical conditions were validated using a real-life dataset, and the results showed that the conditions were satisfied. Finally, a simulation and the real-life results showed that the new estimator outperformed the other considered estimators. However, the performance of the estimators was contingent on the adopted shrinkage parameter estimators.

Suggested Citation

  • Adewale F. Lukman & B. M. Golam Kibria & Cosmas K. Nziku & Muhammad Amin & Emmanuel T. Adewuyi & Rasha Farghali, 2023. "K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:340-:d:1029570
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    References listed on IDEAS

    as
    1. Muhammad Amin & Muhammad Qasim & Muhammad Amanullah & Saima Afzal, 2020. "Performance of some ridge estimators for the gamma regression model," Statistical Papers, Springer, vol. 61(3), pages 997-1026, June.
    2. Månsson, Kristofer & Kibria, B.M. Golam & Shukur, Ghazi, 2012. "On Liu estimators for the logit regression model," Economic Modelling, Elsevier, vol. 29(4), pages 1483-1488.
    3. Muhammad Qasim & Muhammad Amin & Talha Omer, 2020. "Performance of some new Liu parameters for the linear regression model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(17), pages 4178-4196, September.
    4. Nagarajah Varathan & Pushpakanthie Wijekoon, 2018. "Optimal generalized logistic estimator," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(2), pages 463-474, January.
    Full references (including those not matched with items on IDEAS)

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