Liu-type Estimator in the Bell Regression Model

Abstract

This study proposes a new estimator used in the case of multicollinearity problems in the Bell regression model that is an alternative model for the Poisson
regression model. The Bell regression model is used to solve the overdispersion problem. Generally, the maximum likelihood estimation (MLE) method is used to
estimate the parameters of the Bell regression model. But, the performance of the MLE decreases when the multicollinearity problem occurs. Therefore, the Bell liutype
estimator is proposed. Monte Carlo simulation study is conducted to compare the performance of the proposed estimator with Bell Ridge and Bell Liu estimators.
Additionally, the real data example is given to support the simulation study.

Keywords

• Bell regression
• Count Data
• Overdispersion
• Multicollinearity
• Liu type estimator

Bell Regresyon Modelinde Liu tipi Tahmin Edici

Abstract

Bu çalışmada, sayım verilerini modellemek için kullanılan Poisson regresyon
modeline alternatif olarak tanımlanan Bell regresyon modelinde çoklu iç ilişki
olması durumunda kullanılan yanlı tahmin edicilere alternatif bir tahmin edici
önerilmiştir. Bell regresyon modeli aşırı yayılım probleminin çözümü için kullanılan
bir modeldir. Bell regresyon modelinin parametreleri genellikle en çok olabilirlik
(EÇO) tahmin edicisi kullanılarak tahmin edilmektedir. Fakat, çoklu iç ilişki
problemi olması durumunda EÇO tahmin edicisinin performansı düşmektedir. Bu
sebeple, Bell Liu-tipi tahmin edicisi önerilmiştir. Önerilen Bell Liu tipi tahmin
edicinin performansı Bell Ridge ve Bell Liu tahmin edicileri ile Monte Carlo
simülasyon çalışması yardımıyla karşılaştırılmıştır. Ayrıca, simülasyon çalışmasına
desteklemek için gerçek veri örneği verilmiştir.

Keywords

• Bell Regresyon
• Sayım verileri
• Aşırı yayılım
• Çoklu İç İlişki
• Liu Tipi Tahmin Edici
• Bell regression
• Count Data
• Overdispersion
• Multicollinearity
• Liu type estimator

References

1. [1] Lemonte, A., Moreno-Arenas, G., & Castellares, F. 2020. Zero-inflated Bell regression models for count data. Journal of Applied Statistics, 47(2), 265-286.
2. [2] Castellares, F., Ferrari, S., Lemonte, A. 2018. On the Bell distribution and its associated regression model for count data. Applied Mathematical Modelling, 56, 172-185.
3. [3] Asar, Y., Genç, A. 2016. New shrinkage parameters for the Liu-type logistic estimator . Communications in Statistics - Simulation and Computation, 45(3), 1094-1103.
4. [4] Farrar, D. E., Glauber, R. R. 1967. Multicollinearity in Regression Analysis: The Problem Revisited, The Review of Economics and Statistics, 49 (1), 92-107.
5. [5] Silvey S. 1969. Multicollinearity and Imprecise Estimation. Journal of the Royal Statistical Society: Series B (Methodological), 31 (3), 539-552.
6. [6] Lipovetsky S., Conklin, W. M. 2001. Multiobjective Regression Modifications for Collinearity. Computers and Operations Research, 28, 1333-1345.
7. [7] Hoerl, A., Kennard, R. 1970. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 42(1), 80-86.
8. [8] Månsson, K., Shukur, G. 2011. A Poisson ridge regression estimator. Econ. Model. 28, 1475-1481.

9. [9] Månsson, K. 2012. On ridge estimators for the negative binomial regression model. Economic Modelling, 29, 178-184.
10. [10] Amin, M., Akram, M., Majid, A. 2021. On the estimation of Bell regression model using ridge estimator. Communications in Statistics-Simulation and Computation.
11. [11] Liu, K. 1993. A new class of blased estimate in linear regression. Communications in Statistics - Theory and Methods, 22(2), 393-402.
12. [12] Akdeniz, F., Kaçıranlar, S. 1995. On the almost unbiased generalized Liu estimator and unbiased estimation of the bias and MSE. Communications in Statistics-Theory and Methods, 24(7), 1789-1797.
13. [13] Urgan N., Tez M. 2008. Liu estimator in logistic regression when the data are collinear. The 20th international conference, EURO mini conference, Continuous Optimization and Knowladge-based Technologies, 323-327.
14. [14] Kurtoğlu F., Özkale M. 2016. Liu estimation in generalized linear models: application on gamma distributed response variable. Statistical Papers, 57(4), 911-928.
15. [15] Qasim, M., Amin, M., Amanullah, M. 2018. On the performance of some new liu parameters for the gamma regression model. Journal of Statistical Computation and Simulation, 88(16), 3065-3080.
16. [16] Qasim, M., Kibria, B., Månsson, K., Sjölander, P. 2019. A new Poisson Liu Regression Estimator: method and application. Journal of Applied Statistics.
17. [17] Majid, A., Amin, M., Akram, M. N. 2021. On the Liu estimation of Bell regression model in the presence of multicollinearity, Journal of Statistical Computation and Simulation.
18. [18] Liu, K. 2003. Using Liu-type Estimator to Combat Collinearity. Communications in Statistics- Theory and Methods, 32(5), 1009-1020
19. [19] Asar, Y., Karaibrahimoğlu, A., Başbozkurt, H. Genç, A. 2015. Developing a Liu-type estimator for the Poisson Regression. 9th International Statistics Congress, Antalya.
20. [20] Asar, Y. 2018. Liu-Type Negative Binomial Regression: A Comparison of Recent Estimators and Applications. In Trends and Perspectives in Linear Statistical Inference, 23–39. Cham: Springer.
21. [21] Bell, E. 1934. Exponential numbers. The American Mathematical Monthly, 41(7), 411-419.
22. [22] Ertaş, H., Kaçıranlar, S., Güler, H. 2017. Robust Liu type estimator for regression based on M-estimator. Communication in Statistics – Simulation and Computation, 46(5), 3907-3932.
23. [23] McDonald, G., Galarneau, D. 1975. A monte carlo evaluation of some ridge-type estimators. Journal of the American Statistical Association, 70(350), 407-416.
24. [24] Newhouse, J., Oman, S. (1971). An evaluation of ridge estimators. Rand Corporation (p-716-PR), Santa Monica., 1-16.
25. [25] Team, R. C. (tarih yok). R: Alanguage and environment for statistical computing. Vienna, Austria: http://www.R-project.org.
26. [26] Myers, R., Montgomery, D., Vining, G., Robinson, T. 2012. Generalized Linear Models with Applications in Engineering and the Sciences. Second Edition, Wiley, A John Wiley&Sons, Inc., Publication.