Abstract
The logistic regression model (LRM) is used when the response variable is in a binary form. In the presence of multicollinearity, the variances and standard errors of the maximum likelihood estimator (MLE) become high. As a remedy caused by multicollinearity, we introduce a new estimator called Dawoud–Kibria (DK) estimator for the LRM and compared its effectiveness with some traditional biased estimators, i.e., ridge and Liu estimators. For investigating the performance of the new estimator, we conduct a Monte Carlo simulation study with different evaluated conditions. Findings proved that the performance of our proposed DK estimator is quite better as compared to the traditional MLE, ridge and Liu estimators. At the end, an empirical application is being considered. Both simulation and application results clearly demonstrate that the proposed DK estimator is a robust and reliable option as compared to the other considered estimators.
Similar content being viewed by others
References
Aguilera AM, Escabias M, Valderrama MJ (2006) Using principal components for estimating logistic regression with high-dimensional multicollinear data. Comput Stati Data Anal 50(8):1905–1924
Akram MN, Amin M, Qasim M (2020) A new Liu-type estimator for the inverse Gaussian regression model. J Stat Comput Sim 90:1153–1172
Akram MN, Amin M, Amanullah M (2021) James Stein estimator for the inverse Gaussian regression model. Iran J Sci Technol Trans A 45(2):1389–1403
Algamal ZY (2018a) Developing a ridge estimator for the gamma regression model. J Chemo 32(10):e3054–e3112. https://doi.org/10.1002/cem.3054
Algamal ZY (2018b) Shrinkage estimators for gamma regression model. Electr J App Stat Anal 11(1):253–268
Amin M, Qasim M, Amanullah M, Afzal S (2020) Performance of some ridge estimators for the gamma regression model. Stat Pap 61:997–1026
Amin M, Akram MN, Kibria BMG (2021a) A new adjusted Liu estimator for the Poisson regression model. Concurr Comput Pract Exp 33:e6340
Amin M, Akram MN, Majid A (2021b) On the estimation of Bell regression model using ridge estimator. Commun Stat Simul Comput. https://doi.org/10.1080/03610918.2020.1870694
Dawoud I, Kibria BMG (2020) A new biased estimator to combat the multicollinearity of the Gaussian linear regression model. Stat 3(4):526–541
Dawoud I, Abonazel MR (2021) Robust Dawoud–Kibria estimator for handling multicollinearity and outliers in the linear regression model. J Stat Comput Simul 91(17):3678–3692
Farebrother RW (1976) Further results on the mean square error of ridge regression. J R Stat Soc 38(3):248–250
Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1):55–67
Khalaf G, Månsson K, Sjölander P, Shukur G (2014) A Tobit ridge regression estimator. Commun Stat-Theory Methods 43(1):131–140
Kibria BMG (2003) Performance of some new ridge regression estimators. Commun Stat-Simul Comput 32:419–435
Kibria BMG, Månsson K, Shukur G (2012) Performance of some logistic ridge regression estimators. Comput Econ 40(4):401–414
Liu K (1993) A new class of biased estimate in linear regression. Commun Stat Theory Methods 22(2):393–402
Lukman AF, Algamal ZY, Kibria BMG, Ayinde K (2021) The KL estimator for the inverse Gaussian regression model. Concurr Comput Pract Exp 33(13):e6222
Mahmoudi A, Belaghi RA, Mandal S (2020) A comparison of preliminary test, Stein-type and penalty estimators in gamma regression model. J Stat Comput Simul 90(17):3051–3079. https://doi.org/10.1080/00949655.2020.1795174
Majid A, Amin M, Akram MN (2022) On the Liu estimation of bell regression model in the presence of multicollinearity. J Stat Comput Simul 92(2):262–282
Månsson K (2012) On ridge estimators for the negative binomial regression model. Econ Model 29(2):178–184
Månsson K, Shukur G (2011) A Poisson ridge regression estimator. Econ Model 28(4):1475–1481
Månsson K, Kibria BMG, Sjolander P, Shukur G, Sweden V (2011) New Liu Estimators for the Poisson Regression Model: Method and Application (No. 51). Stockholm, Sweden: HUI Research
Månsson K (2013) Developing a Liu estimator for the negative binomial regression model: method and application. J Stat Comput Simul 83:1773–1780
Månsson K, Kibria BMG, Shukur G (2012) On Liu estimators for the logit regression model. Econ Model 29(4):1483–1488
McDonald GC, Galarneau DI (1975) A Monte Carlo evaluation of some ridge-type estimators. J Am Stat Assoc 70(350):407–416
Nelder JA, Wedderburn RW (1972) Generalized linear models. J R Stat Soc Ser A (gen) 135(3):370–384
Naveed K, Amin M, Afzal S, Qasim M (2022) New shrinkage parameters for the inverse Gaussian Liu regression. Commun Stat Theory Methods 51(10):3216–3236
Qasim M, Amin M, Amanullah M (2018) On the performance of some new Liu parameters for the gamma regression model. J Stat Comput Simul 88(16):3065–3080
Qasim M, Kibria BMG, Månsson K, Sjölander P (2020) A new Poisson Liu regression estimator: method and application. J App Stat 47(12):2258–2271
Qasim M, Månsson K, Kibria BMG (2021) On some beta ridge regression estimators: method, simulation and application. J Stat Comput Simul 91(9):1699–1712. https://doi.org/10.1080/00949655.2020.1867549
Saleh AME, Kibria BMG (2013) Improved ridge regression estimators for the logistic regression model. Comput Stat 28(6):2519–2558. https://doi.org/10.1007/s00180-013-0417-6
Schaefer RL, Roi LD, Wolfe RA (1984) A ridge logistic estimator. Commun Stat Theory Methods 13(1):99–113
Schaefer RL (1986) Alternative estimators in logistic regression when the data are collinear. J Stat Comput Simul 25(1–2):75–91
Segerstedt B (1992) On ordinary ridge regression in generalized linear models. Commun Stat Theory Methods 21(8):2227–2246
Trenkler G, Toutenburg H (1990) Mean squared error matrix comparisons between biased estimators- an overview of recent results. Stat Pap 31(1):165
Funding
No funding resource is available for this study.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Afzal, N., Amanullah, M. Dawoud–Kibria Estimator for the Logistic Regression Model: Method, Simulation and Application. Iran J Sci Technol Trans Sci 46, 1483–1493 (2022). https://doi.org/10.1007/s40995-022-01354-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40995-022-01354-x