International Journal of Nonlinear Analysis and Applications
A new Jackknifing ridge estimator for logistic regression model
Document Type : Research Paper
Authors
1 Department of management Information systems, College of Administration and Economics, University of Mosul, Mosul, Iraq.
2 Department of Statistics and Informatics, University of Mosul, Mosul, Iraq.
Abstract
In reducing the effects of collinearity, the ridge estimator (RE) has been consistently demonstrated to be an attractive shrinkage method. In application, when the response variable is binary data, the logistic regression model (LRM) is a well-known model. However, it is known that collinearity negatively affects the variance of maximum likelihood estimator of the LRM. To address this problem, a logistic ridge estimator was proposed by several authors. In this work, a Jackknifing logistic ridge estimator (NJLRE) is proposed and derived. The Monte Carlo simulation results recommend that the NJLRE estimator can bring significant improvement relative to other existing estimators. Furthermore, the real application results demonstrate that the NJLRE estimator outperforms both LRE and MLE in terms of predictive performance.
Keywords
[2] M. Arashi, B. M. G. Kibria and T. Valizade, On ridge parameter estimators under stochastic subspace hypothesis, J. Stat. Comput. Simul., 87(5)(2017) 966–983.
[3] Y. Asar and A. Gen¸c, New shrinkage parameters for the Liu-type logistic estimators, Commun. Stat. Simul. Comput., 45(3)(2015) 1094-1103. https://doi.org/10.1080/03610918.2014.995815
[4] F. S. M. Batah, T. V. Ramanathan and S. D. Gore, The efficiency of modefied jackknife and ridge type regression estimators - A comparison, Surv. Math. Appl., 3 (2008) 111 – 122.
[5] L. Firinguettia, B. M. G. Kibria and R. Araya, Study of Partial Least Squares and Ridge Regression Methods, Commun Stat. Simul. . Comput., 46(8) (2017) 6631-6644.
[6] A. E. Hoerl and R. W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Technometrics, 12(1)(1970) 55-67.
[7] I. J. Kang, L. W. Wang, S. J. Hsu, C. C. Lee, Y. C. Lee , Y. S. Wu, . . . and J. H. Chern, Design and efficient synthesis of novel arylthiourea derivatives as potent hepatitis C virus inhibitors , Bioorg. Med. Chem. Lett.,19(21)(2009) 6063-6068, https://doi.org/10.1016/j.bmcl.2009.09.037.
[8] F. S. M. Batah, T. V. Ramanathan and S. D. Gore, The efficiency of modefied jackknife and ridge type regression estimators - A comparison, Surv. Math. Appl., 3 (2008) 111 – 122.
[9] L. Firinguettia, B. M. G. Kibria and R. Araya, Study of Partial Least Squares and Ridge Regression Methods, Commun, Stat. Simul. and Comput., 46(8)(2017) 6631-6644.
[10] A. E. Hoerl and R. W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Technometrics, 12(1) (1970) 55-67.
[11] I. J. Kang, L. W. Wang, S. J. Hsu, C. C. Lee, Y. C. Lee, Y. S. Wu, . . . and J. H. Chern, Design and efficient synthesis of novel arylthiourea derivatives as potent hepatitis C virus inhibitors, Bioorg. Med. Chem. Lett, 19(21)(2009) 6063-6068, https://doi.org/10.1016/j.bmcl.2009.09.037.
[12] I. J. Kang, L. W. Wang, C. C. Lee, Y. C. Lee, Chao, Y. S. Hsu, T. A. Hsu and J. H. Chern, Design, synthesis, and anti-HCV activity of thiourea compounds, Bioorg. Med. Chem. Lett. , 19(7) (2009) 1950-1955. https://doi. org/10.1016/j.bmcl.2009.02.048
[13] I. J. Kang, L. W. Wang, T. K. Yeh , C. C. Lee, Y. C. Lee, S. J. Hsu, . . . and J. H. Chern, Synthesis, activity, and pharmacokinetic properties of a series of conformationally-restricted thiourea analogs as novel hepatitis C virus inhibitors, Bioorg. Med. Chem., 18(17) (2010) 6414-6421. https://doi.org/10.1016/j.bmc.2010.07.002
[14] N. Khatri, V. Lather and A. K. Madan, Diverse classification models for anti-hepatitis C virus activity of thiourea derivatives, Chemom. Intell. Lab. Syst. , 140(2015) 13-21. https://doi.org/10.1016/j.chemolab.2014.10.007
[15] M. Khurana, Y. P. Chaubey and S. Chandra, Jackknifing the ridge regression estimator: A revisit, Communications in Statistics-Theory and Methods, 43(24)(2014) 5249-5262.
[16] B. M. G. Kibria, Performance of some new ridge regression estimators, Commun. Stat. Simul. Comput., 32(2)(2003) 419-435. https://doi.org/10.1081/SAC-120017499
[17] B. M. G. Kibria, K. M˚ansson and G. Shukur, A Simulation Study of Some Biasing Parameters for the Ridge Type Estimation of Poisson Regression, Commun. Stat. Simul. Comput., 44(4)(2015) 943-957, https://doi.org/10. 1080/03610918.2013.796981.
[18] S. Le Cessie and J. C. Van Houwelingen , Ridge estimators in logistic regression, J. R. Stat. Soc.: Ser. C (Applied Statistics), 41(1)(1992) 191-201.
[19] A. Lee and M. Silvapulle , Ridge estimation in logistic regression, Commun. Stat. Simul. Comput., 17(4)(1988) 1231-1257.
[20] K. M˚ansson and G. Shukur, A Poisson ridge regression estimator, Econ. Modell., 28(4)(2011) 1475-1481. https: //doi.org/10.1016/j.econmod.2011.02.030.
[21] D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to linear regression analysis, New York: John Wiley & Sons, 2015.
[22] H. Nyquist, Applications of the jackknife procedure in ridge regression, Comput. Stat. . Data Anal., 6(2)(1988), 177-183.
[23] M. R. Ozkale, ckkniA ja ¨ fed ridge estimator in the linear regression model with heteroscedastic or correlated errors, Stat. Probab. Lett., 78(18)(2008) 3159-3169, https://doi.org/10.1016/j.spl.2008.05.039.
[24] N. K. Rashad and Z. Y. Algamal, A New Ridge Estimator for the Poisson Regression Model, Iran. J. Sci. Technol., Trans. A: Sci., https://doi.org/10.1007/s40995-019-00769-3.
[25] A. K. M. E. Saleh, M. Arashi and B. M. G. Kibria , Theory of Ridge Regression Estimation with Applications, New York: Wiley, 2019 .[26] A. K. M. E. Saleh and B. M. G. Kibria , Improved ridge regression estimators for the logistic regression model, Comput. Stat., 28(6)(2012) , 2519-2558.
[27] B. Singh, Y. P. Chaubey and T. D. Dwivedi An almost unbiased ridge estimator, Sankhy¯a: Indian J. Stat. Ser. B, (1986) 342-346.
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Volume 13, Issue 1
March 2022Pages 2127-2135
- Receive Date: 05 May 2021
- Accept Date: 14 October 2021