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

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Published: Sep 29, 2020
DOI: https://doi.org/10.14456/sehs.2020.19
Keywords:
bootstrapping method ridge estimator Liu estimator Liu-type estimator multicollinearity

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Narumol Sudjai
Department of Orthopaedics Surgery, Faculty of Medicine Siriraj Hospital, Mahidol University, Thailand
Monthira Duangsaphon
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Thailand. Corresponding author's e-mail: monthira@mathstat.sci.tu.ac.th

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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How to Cite
Sudjai, N., & Duangsaphon, M. (2020). Liu-type logistic regression coefficient estimation with multicollinearity using the bootstrapping method. Science, Engineering and Health Studies, 14(3), 203–214. https://doi.org/10.14456/sehs.2020.19
Issue
Volume 14, Number 3 (September - December), 2020
Section
Research Articles

References

Asar, Y. (2016). New shrinkage parameters for the Liu-type logistic estimators. Communication in Statistics - Simulation and Computation, 45(3), 1094-1103.

Chernick, M. R., and La Budde, R. A. (2014). An Introduction to Bootstrap Methods with Applications to R, New Jersey: John Wiley & Sons.

Davidson, R., and Mac Kinnon, J. G. (2000). Bootstrap tests: How many bootstraps? Econometric Reviews, 19(1), 55-68.

Efron, B. (1979). Bootstrap methods: another look at the Jackknife. The Annals of Statistics, 7(1), 1-26.

Farghali, R. A., and Abo-El-Hadid, S. M. (2017). Evaluating the performance of Liu logistic regression estimator. Research Journal of Mathematics and Statistics, 9(2), 11-19.

Hoerl, A. E., and Kennard, R. W. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.

Hosmer, D. W., and Lemeshow, S. J. (2000). Applied Logistic Regression, 2nd, New York: Wiley & Sons.

Huang, J. (2012). A Simulation research on a biased estimator in logistic regression model. In Computational Intelligence and Intelligent Systems. ISICA 2012. Communications in Computer and Information Science (Li, Z., Li, X., Liu, Y., and Cai, Z., eds.), pp. 389-395. Berlin, Heidelberg: Springer.

Inan, D., and Erdogan, B. E. (2013). Liu-type logistic estimator. Communications in Statistics - Simulation and Computation, 42(7), 1578-1586.

Kerlinger, F. N., and Pedhazur, E. J. (1973). Multiple Regression in Behavioral Research, New York: Holt, Rinehart & Winston.

Khalaf, G., and Shukur, G. (2005). Choosing ridge parameter for regression problems. Communication in Statistics - Theory and Methods, 34(5), 1177-1182.

Kibria, B. M. G., Månsson, K., and Shukur, G. (2012). Performance of some logistic Ridge regression estimators. Computational Economics, 40(4), 401-414.

Kibria, B. M. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics - Simulation and Computation, 32(2), 419-435.

Kleinbaum, D. G., and Klein, M. (2010). Logistic Regression; A Self-learning Text, 3rd, New York: Springer.

Liu, K. (1993). A new class of biased estimate in linear regression. Communications in Statistics - Theory and Methods, 22, 393-402.

Månsson, K., Kibria, B. M. G., and Shukur, G. (2012). On Liu estimators for the logit regression model. Economic Modelling, 29(4), 1483-1488.

Månsson, K., and Shukur, G. (2011). On ridge parameters in logistic regression. Communications in Statistics - Theory and Methods, 40, 3366-3381.

Muniz, G., and Kibria, B. M. G. (2009). On some ridge regression estimators: an empirical comparisons. Communication in Statistics - Simulation and Computation, 38(3), 621-630.

Newhouse, J. P., and Oman, S. D. (1971). An Evaluation of Ridge Estimators, USA: Rand Corporation.

Pattengale, N. D., Alipour, M., Bininda-Emonds, O. R., Moret, B. M., and Stamatakis, A. (2010). How many bootstrap replicates are necessary? Journal of Computational Biology, 17(3), 337-354.

Petrie, A., and Sabin, C. (2009). Medical Statistics at a Glance, 3rd, Oxford: Wiley Blackwell.

Schaefer, R. L., Roi, L. D., and Wolfe, R. A. (1984). A ridge logistic estimator. Communications in Statistics - Theory and Methods, 13(1), 99-113.

Stoltzfus, J. C. (2011). Logistic regression: a brief primer. Academic Emergency Medicine, 18(10), 1099-1104.

Sudjai, N., and Duangsaphon, M. (2019). Liu logistic regression coefficient estimation with multicollinearity problem by using the bootstrapping method. Veridian E-Journal, Science and Technology, 6(1), 47-61.

Urgan, N. N., and Tez, M. (2008). Liu estimator in logistic regression when the data are collinear. In 20th EURO Mini Conference Continuous Optimization and Knowledge Based Technologies, Neringa, Lithuania.