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Modified Ridge Estimator for Poisson Regression

Year 2024, Volume: 45 Issue: 4, 811 - 822, 30.12.2024

Shuaib Mursal Ibrahim , Aydın Karakoca

https://doi.org/10.17776/csj.1372265

Abstract

Poisson regression is a statistical model used to model the relationship between a count-valued-dependent variable and one or more independent variables. A frequently encountered problem when modeling such relationships is multicollinearity, which occurs when the independent variables are highly correlated with each other. Multicollinearity can affect the maximum likelihood (ML) estimates of unknown model parameters, making them unstable and inaccurate. In this study, we propose a modified ridge parameter estimator to combat multicollinearity in Poisson regression. We conducted extensive simulations to evaluate the performance of our proposed estimator using the mean squared error (MSE). We also apply our estimator to real data. The results show that our proposed estimator outperforms the ML estimator in both simulations and real data applications.

Keywords

Poisson regression Multicollinearity Ridge estimator Monte Carlo simulations Maximum likelihood estimation

References

  • [1] Agresti, An Introduction To Categorical Data Analysis, Third Edition. Wiley, 2019. [Online]. Available: http://www.wiley.com/go/wsps
  • [2] Belsey D. A., Kuh E., Welsch R. E., Regression Diagnostics. Wiley, 2005.
  • [3] Menard S., Applied Logistic Regression Analysis, 3rd ed. Sage, (2001).
  • [4] Hoerl E., Kennard R. W., Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics, 12(1) (1970) 55–67.
  • [5] Tibshiranit R., Regression Shrinkage and Selection via the Lasso, J. R. Statist. Soc. B, 58(1) (1996) 267–288.
  • [6] Kibria M. G., Performance of some New Ridge regression estimators, Communications in Statistics Part B: Simulation and Computation, 32(2) (2003) 419–435.
  • [7] Shukur G., Choosing ridge parameter for regression problems, Commun Stat Theory Methods, 34(5) 1177–1182
  • [8] Alkhamisi M., Khalaf G., Shukur G., Some modifications for choosing ridge parameters, Commun. Stat. Theory Methods, 35(11) (2006) 2005–2020.
  • [9] Muniz G., Kibria B. M. G., On some ridge regression estimators: An empirical comparisons, Commun. Stat. Simul. Comput., 38(3) (2009) 621–630
  • [10] Kibria M. G., Månsson K., Shukur G., Performance of Some Logistic Ridge Regression Estimators, Comput. Econ., 40(4) (2012) 401–414.
  • [11] Asar Y., Genç A., A New Two-Parameter Estimator for the Poisson Regression Model, Iran J. Sci. Technol. Trans. A Sci., 42(2) (2018) 793–803.
  • [12] Lukman F., Arashi M., Prokaj V., Robust biased estimators for Poisson regression model: Simulation and applications, Concurr. Comput., 35(7) (2023) 7594.
  • [13] Lukman F., Adewuyi E., Månsson K., Kibria B. M. G., A new estimator for the multicollinear Poisson regression model: simulation and application, Sci. Rep., 11(1) (2021) s41598-021-82582-w.
  • [14] Rashad N. K., Algamal Z. Y., A New Ridge Estimator for the Poisson Regression Model, Iran J. Sci. Technol. Trans. A Sci., 43(6) (2019) 2921–2928.
  • [15] Myers R. H., Montgomery D. C., Vining G. G., Robinson T. J., Generalized Linear Models with Application in Engineering and the Sciences, Second edition. Wiley, 2012.
  • [16] K. Månsson and G. Shukur, A Poisson ridge regression estimator, Econ Model, 28(4) (2011) 1475–1481.
  • [17] Asar Y., Genç A., A note on some new modifications of ridge estimators, Kuwait J. Sci, 44(3) (2017) 75–82.
  • [18] Khalaf G., A proposed ridge parameter to improve the least squares estimator, Journal of Modern Applied Statistical Methods, 11(2) (2012) 443–449.
  • [19] Dorugade V., New ridge parameters for ridge regression, (2014) University of Bahrain.
  • [20] Lawless J.F., Wang P., A Simulation Study Of Ridge And Other Regression Estimators, Commun. Stat. Theory Methods, 5(4) (1976) 307–323.
  • [21] Hocking R. R., Speed F. M., Lynn M. J., A Class of Biased Estimators in Linear Regression, Technometrics, 18(4) (1976) 425–437.
  • [22] V. Dorugade, On Comparison of Some Ridge Parameters in Ridge Regression, Sri Lankan J. Appl. Stat., 15(1) (2014) 31–46.
  • [23] Asar Y., Karaibrahimoğlu A., Genç A., Modified ridge regression parameters: A comparative Monte Carlo study, Hacettepe Journal of Mathematics and Statistics, 43(5) (2014) 827–841.

Year 2024, Volume: 45 Issue: 4, 811 - 822, 30.12.2024

Shuaib Mursal Ibrahim , Aydın Karakoca

https://doi.org/10.17776/csj.1372265

Abstract

References

  • [1] Agresti, An Introduction To Categorical Data Analysis, Third Edition. Wiley, 2019. [Online]. Available: http://www.wiley.com/go/wsps
  • [2] Belsey D. A., Kuh E., Welsch R. E., Regression Diagnostics. Wiley, 2005.
  • [3] Menard S., Applied Logistic Regression Analysis, 3rd ed. Sage, (2001).
  • [4] Hoerl E., Kennard R. W., Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics, 12(1) (1970) 55–67.
  • [5] Tibshiranit R., Regression Shrinkage and Selection via the Lasso, J. R. Statist. Soc. B, 58(1) (1996) 267–288.
  • [6] Kibria M. G., Performance of some New Ridge regression estimators, Communications in Statistics Part B: Simulation and Computation, 32(2) (2003) 419–435.
  • [7] Shukur G., Choosing ridge parameter for regression problems, Commun Stat Theory Methods, 34(5) 1177–1182
  • [8] Alkhamisi M., Khalaf G., Shukur G., Some modifications for choosing ridge parameters, Commun. Stat. Theory Methods, 35(11) (2006) 2005–2020.
  • [9] Muniz G., Kibria B. M. G., On some ridge regression estimators: An empirical comparisons, Commun. Stat. Simul. Comput., 38(3) (2009) 621–630
  • [10] Kibria M. G., Månsson K., Shukur G., Performance of Some Logistic Ridge Regression Estimators, Comput. Econ., 40(4) (2012) 401–414.
  • [11] Asar Y., Genç A., A New Two-Parameter Estimator for the Poisson Regression Model, Iran J. Sci. Technol. Trans. A Sci., 42(2) (2018) 793–803.
  • [12] Lukman F., Arashi M., Prokaj V., Robust biased estimators for Poisson regression model: Simulation and applications, Concurr. Comput., 35(7) (2023) 7594.
  • [13] Lukman F., Adewuyi E., Månsson K., Kibria B. M. G., A new estimator for the multicollinear Poisson regression model: simulation and application, Sci. Rep., 11(1) (2021) s41598-021-82582-w.
  • [14] Rashad N. K., Algamal Z. Y., A New Ridge Estimator for the Poisson Regression Model, Iran J. Sci. Technol. Trans. A Sci., 43(6) (2019) 2921–2928.
  • [15] Myers R. H., Montgomery D. C., Vining G. G., Robinson T. J., Generalized Linear Models with Application in Engineering and the Sciences, Second edition. Wiley, 2012.
  • [16] K. Månsson and G. Shukur, A Poisson ridge regression estimator, Econ Model, 28(4) (2011) 1475–1481.
  • [17] Asar Y., Genç A., A note on some new modifications of ridge estimators, Kuwait J. Sci, 44(3) (2017) 75–82.
  • [18] Khalaf G., A proposed ridge parameter to improve the least squares estimator, Journal of Modern Applied Statistical Methods, 11(2) (2012) 443–449.
  • [19] Dorugade V., New ridge parameters for ridge regression, (2014) University of Bahrain.
  • [20] Lawless J.F., Wang P., A Simulation Study Of Ridge And Other Regression Estimators, Commun. Stat. Theory Methods, 5(4) (1976) 307–323.
  • [21] Hocking R. R., Speed F. M., Lynn M. J., A Class of Biased Estimators in Linear Regression, Technometrics, 18(4) (1976) 425–437.
  • [22] V. Dorugade, On Comparison of Some Ridge Parameters in Ridge Regression, Sri Lankan J. Appl. Stat., 15(1) (2014) 31–46.
  • [23] Asar Y., Karaibrahimoğlu A., Genç A., Modified ridge regression parameters: A comparative Monte Carlo study, Hacettepe Journal of Mathematics and Statistics, 43(5) (2014) 827–841.
There are 23 citations in total.

Details

Primary Language English
Subjects Applied Statistics
Journal Section Natural Sciences
Authors

Shuaib Mursal Ibrahim 0000-0002-0258-034X

Aydın Karakoca 0000-0001-6503-3872

Publication Date December 30, 2024
Submission Date October 6, 2023
Acceptance Date November 18, 2024
Published in Issue Year 2024Volume: 45 Issue: 4

Cite

APA Ibrahim, S. M., & Karakoca, A. (2024). Modified Ridge Estimator for Poisson Regression. Cumhuriyet Science Journal, 45(4), 811-822. https://doi.org/10.17776/csj.1372265
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