Advertisement

A New Ridge Estimator for the Poisson Regression Model

  • Nadwa K. Rashad
  • Zakariya Yahya AlgamalEmail author
Research Paper
  • 30 Downloads
Part of the following topical collections:
  1. Mathematics

Abstract

The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The Poisson regression model is a well-known model in application when the response variable is count data. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the Poisson regression coefficients. To address this problem, a Poisson ridge regression model has been proposed by numerous researchers. In this paper, a new Poisson ridge estimator (NPRRM) is proposed and derived. The idea behind the NPRRM is to get diagonal matrix with small values of diagonal elements that leading to decrease the shrinkage parameter, and therefore, the resultant estimator can be better with small amount of bias. Our Monte Carlo simulation results suggest that the NPRRM estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the NPRRM estimator outperforms both Poisson ridge regression and maximum likelihood estimators in terms of predictive performance.

Keywords

Multicollinearity Ridge estimator Poisson regression model Shrinkage Monte Carlo simulation 

References

  1. Algamal ZY (2012) Diagnostic in poisson regression models. Electron J Appl Stat Anal 5:178–186MathSciNetGoogle Scholar
  2. Algamal ZY (2018a) A new method for choosing the biasing parameter in ridge estimator for generalized linear model. Chemom Intell Lab Syst 183:96–101CrossRefGoogle Scholar
  3. Algamal ZY (2018b) Shrinkage parameter selection via modified cross-validation approach for ridge regression model. Commun Stat Simul Comput.  https://doi.org/10.1080/03610918.2018.1508704 CrossRefGoogle Scholar
  4. Algamal ZY, Alanaz MM (2018) Proposed methods in estimating the ridge regression parameter in Poisson regression model. Electron J Appl Stat Anal 11:506–515MathSciNetGoogle Scholar
  5. Algamal ZY, Lee MH (2015a) Adjusted adaptive lasso in high-dimensional poisson regression model. Mod Appl Sci 9:170–177.  https://doi.org/10.5539/mas.v9n4p170 CrossRefGoogle Scholar
  6. Algamal ZY, Lee MH (2015b) Applying penalized binary logistic regression with correlation based elastic net for variables selection. J Mod Appl Stat Method 14:15CrossRefGoogle Scholar
  7. Algamal ZY, Lee MH (2015c) High dimensional logistic regression model using adjusted elastic net penalty. Pak J Stat Oper Res 11:667–676MathSciNetCrossRefGoogle Scholar
  8. Algamal ZY, Lee MH (2015d) Penalized poisson regression model using adaptive modified elastic net penalty. Electron J Appl Stat Anal 8:236–245MathSciNetGoogle Scholar
  9. Algamal ZY, Lee MH, Al-Fakih AM, Aziz M (2017) High-dimensional QSAR classification model for anti-hepatitis C virus activity of thiourea derivatives based on the sparse logistic regression model with a bridge penalty. J Chemom 31:e2889CrossRefGoogle Scholar
  10. Asar Y, Genç A (2015) New shrinkage parameters for the Liu-type logistic estimators. Commun Stat Simul Comput 45:1094–1103.  https://doi.org/10.1080/03610918.2014.995815 MathSciNetCrossRefzbMATHGoogle Scholar
  11. Asar Y, Genç A (2017) A new two-parameter estimator for the poisson regression model. Iran J Sci Technol Trans A Sci.  https://doi.org/10.1007/s40995-017-0174-4 CrossRefzbMATHGoogle Scholar
  12. Batah FSM, Ramanathan TV, Gore SD (2008) The efficiency of modified jackknife and ridge type regression estimators—a comparison. Surv Math Appl 3:111–122MathSciNetzbMATHGoogle Scholar
  13. Cameron AC, Trivedi PK (2013) Regression analysis of count data, vol 53. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  14. De Jong P, Heller GZ (2008) Generalized linear models for insurance data, vol 10. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  15. Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12:55–67CrossRefGoogle Scholar
  16. KaÇiranlar S, Dawoud I (2017) On the performance of the Poisson and the negative binomial ridge predictors. Commun Stat Simul Comput.  https://doi.org/10.1080/03610918.2017.1324978 CrossRefzbMATHGoogle Scholar
  17. Khurana M, Chaubey YP, Chandra S (2014) Jackknifing the ridge regression estimator: a revisit. Commun Stat Theory Method 43:5249–5262MathSciNetCrossRefGoogle Scholar
  18. Kibria BMG (2003) Performance of some new ridge regression estimators. Commun Stat Simul Comput 32:419–435.  https://doi.org/10.1081/SAC-120017499 MathSciNetCrossRefzbMATHGoogle Scholar
  19. Kibria BMG, Banik S (2016) Some ridge regression estimators and their performances. J Mod Appl Stat Method 15:12–24CrossRefGoogle Scholar
  20. Kibria BMG, Månsson K, Shukur G (2015) A simulation study of some biasing parameters for the ridge type estimation of poisson regression. Commun Stat Simul Comput 44:943–957.  https://doi.org/10.1080/03610918.2013.796981 MathSciNetCrossRefzbMATHGoogle Scholar
  21. Månsson K, Shukur G (2011) A poisson ridge regression estimator. Econ Model 28:1475–1481.  https://doi.org/10.1016/j.econmod.2011.02.030 CrossRefzbMATHGoogle Scholar
  22. Montgomery DC, Peck EA, Vining GG (2015) Introduction to linear regression analysis. Wiley, New YorkzbMATHGoogle Scholar
  23. Nyquist H (1988) Applications of the jackknife procedure in ridge regression. Comput Stat Data Anal 6:177–183MathSciNetCrossRefGoogle Scholar
  24. Özkale MR (2008) A jackknifed ridge estimator in the linear regression model with heteroscedastic or correlated errors. Stat Probab Lett 78:3159–3169.  https://doi.org/10.1016/j.spl.2008.05.039 MathSciNetCrossRefzbMATHGoogle Scholar
  25. Singh B, Chaubey Y, Dwivedi T (1986) An almost unbiased ridge estimator. Sank Indian J Stat Ser B 13:342–346MathSciNetzbMATHGoogle Scholar
  26. Türkan S, Özel G (2015) A new modified jackknifed estimator for the poisson regression model. J Appl Stat 43:1892–1905.  https://doi.org/10.1080/02664763.2015.1125861 MathSciNetCrossRefGoogle Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of Management Information SystemsUniversity of MosulMosulIraq
  2. 2.Department of Statistics and InformaticsUniversity of MosulMosulIraq

Personalised recommendations