For modeling count data, the Poisson regression model is widely used in which the response variable takes non-negative integer values. However, the presence of strong correlation between the explanatory variables causes the problem of multicollinearity. Due to multicollinearity, the variance of the maximum likelihood estimator (MLE) will be inflated causing the parameters estimation to become unstable. Multicollinearity can be tackled by using biased estimators such as the ridge estimator in order to minimize the estimated variance of the regression coefficients. An alternative approach is to specify exact linear restrictions on the parameters in addition to regression model. In this paper, the restricted Poisson ridge regression estimator (RPRRE) is suggested to handle multicollinearity in Poisson regression model with exact linear restrictions on the parameters. In addition, the conditions of superiority of the suggested estimator in comparison to some existing estimators are discussed based on the mean squared error (MSE) matrix criterion. Moreover, a simulation study and a real data application are provided to illustrate the theoretical results. The results indicate that the suggested estimator, RPRRE, outperforms the other existing estimators in terms of scalar mean squared error (SMSE). Therefore, it is recommended to use the RPRRE for the Poisson regression model when the problem of multicollinearity is present.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 4) |
| DOI | 10.11648/j.sjams.20210904.12 |
| Page(s) | 106-112 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Poisson Regression, Multicollinearity, Ridge Regression Estimator, Restricted Maximum Likelihood Estimator, Restricted Ridge Regression Estimator
| [1] | Alanaz, M. M., & Algamal, Z. Y. (2018). Proposed methods in estimating the ridge regression parameter in Poisson regression model. Electronic Journal of Applied Statistical Analysis, 11 (2): 506-515. |
| [2] | Algamal, Z. Y. (2018). Biased estimators in Poisson regression model in the presence of multicollinearity: A subject review. Al-Qadisiyah Journal for Administrative and Economic Sciences, 20 (1): 36-43. |
| [3] | Alkhateeb, A. N., & Algamal, Z. Y. (2020). Jackknifed Liu-type estimator in Poisson regression model. Journal of the Iranian Statistical Society, 19 (1): 21-37. |
| [4] | Asar, Y. (2015). Some new methods to solve multicollinearity in logistic regression. Communications in Statistics-Simulation and Computation, 46 (4): 2576-2586. |
| [5] | Asar, Y., Erişoglu, M., & Arashi, M. (2017). Developing a restricted two-parameter Liu-type estimator: A comparison of restricted estimators in the binary logistic regression model. Communications in Statistics-Theory and Methods, 46 (14): 6864-6873. |
| [6] | Asar, Y., & Genç, A. (2018). A new two-parameter estimator for the Poisson regression model. Iranian Journal of Science and Technology, Transactions A: Science, 42 (2): 793-803. |
| [7] | Batah, F. S. M., Ramanathan, T. V., & Gore, S. D. (2008). The efficiency of modified Jackknife and ridge type regression estimators: A comparison. Surveys in Mathematics and its Applications, 3: 111-122. |
| [8] | Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. John Wiley & Sons, New York, Inc. |
| [9] | Duffy, D. E., & Santner, T. J. (1989). On the small sample properties of norm-restricted maximum likelihood estimators for logistic regression models. Communications in Statistics-Theory and Methods, 18 (3): 959-980. |
| [10] | Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12 (1): 55-67. |
| [11] | Inan, D., & Erdogan, B. E. (2013). Liu-type logistic estimator. Communications in Statistics-Simulation and Computation, 42 (7): 1578-1586. |
| [12] | Kibria, B. M. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics-Simulation and Computation, 32 (2): 419-435. |
| [13] | Kibria, B. M. G., Månsson, K., & Shukur, G. (2012). Performance of some logistic ridge regression estimators. Computational Economics, 40 (4): 401-414. |
| [14] | Kibria, B. M. G., Månsson, K., & Shukur, G. (2015). A simulation study of some biasing parameters for the ridge type estimation of Poisson regression. Communications in Statistics-Simulation and Computation, 44 (4): 943-957. |
| [15] | Liu, K. (1993). A new class of biased estimate in linear regression. Communications in Statistics-Theory and Methods, 22 (2): 393-402. |
| [16] | Liu, K. (2003). Using Liu-type estimator to combat collinearity. Communications in Statistics-Theory and Methods, 32 (5): 1009-1020. |
| [17] | Månsson, K., & Kibria, B. M. G. (2021). Estimating the unrestricted and restricted Liu estimators for the Poisson regression model: Method and application. Computational Economics, 58: 311-326. |
| [18] | Månsson, K., Kibria, B. M. G., & Shukur, G. (2016). A restricted Liu estimator for binary regression models and its application to an applied demand system. Journal of Applied Statistics, 43 (6): 1119-1127. |
| [19] | Månsson, K., Kibria, B. M. G., Sjӧlander, P., & Shukur, G. (2012). Improved Liu estimators for the Poisson regression model. International Journal of Statistics and Probability, 1 (1): 2-6. |
| [20] | Månsson, K., & Shukur, G. (2011). A Poisson ridge regression estimator. Economic Modelling, 28 (4): 1475-1481. |
| [21] | McDonald, G. C., & Galarneau, D. I. (1975). A Monte Carlo evaluation of some ridge-type estimators. Journal of the American Statistical Association, 70 (350): 407-416. |
| [22] | Muniz, G., & Kibria, B. M. G. (2009). On some ridge regression estimators: An empirical comparisons. Communications in Statistics-Simulation and Computation, 38 (3): 621-630. |
| [23] | Najarian, S., Arashi, M., & Kibria, B. M. G. (2013). A simulation study on some restricted ridge regression estimators. Communications in Statistics-Simulation and Computation, 42 (4): 871-890. |
| [24] | Özkale, M. R., & Kaçiranlar, S. (2007). The restricted and unrestricted two-parameter estimators. Communications in Statistics-Theory and Methods, 36 (15): 2707-2725. |
| [25] | Qasim, M., Kibria, B. M. G., Månsson, K., & Sjӧlander, P. (2020). A new Poisson Liu regression estimator: Method and application. Journal of Applied Statistics, 47 (12): 2258-2271. |
| [26] | Rao, C. R., & Toutenburg, H. (1995). Linear models: Least squares and alternatives, 2nd edition, Springer-Verlag, New York, Inc. |
| [27] | Rao, C. R., Toutenburg, H., Shalabh, & Heumann, C. (2008). Linear models and generalizations, Springer, Berlin. |
| [28] | Saleh, A. M. E., & Kibria, B. M. G. (2013). Improved ridge regression estimators for the logistic regression model. Computational Statistics, 28 (6): 2519-2558. |
| [29] | Şiray, G. Ü., Toker, S., & Kaçiranlar, S. (2015). On the restricted Liu estimator in the logistic regression model. Communications in Statistics-Simulation and Computation, 44 (1): 217-232. |
| [30] | Türkan, S., & Özel, G. (2016). A new modified Jackknifed estimator for the Poisson regression model. Journal of Applied Statistics, 43 (10): 1892-1905. |
APA Style
Enas Gawdat Yehia. (2021). On the Restricted Poisson Ridge Regression Estimator. Science Journal of Applied Mathematics and Statistics, 9(4), 106-112. https://doi.org/10.11648/j.sjams.20210904.12
ACS Style
Enas Gawdat Yehia. On the Restricted Poisson Ridge Regression Estimator. Sci. J. Appl. Math. Stat. 2021, 9(4), 106-112. doi: 10.11648/j.sjams.20210904.12
AMA Style
Enas Gawdat Yehia. On the Restricted Poisson Ridge Regression Estimator. Sci J Appl Math Stat. 2021;9(4):106-112. doi: 10.11648/j.sjams.20210904.12
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.sjams.20210904.12,
author = {Enas Gawdat Yehia},
title = {On the Restricted Poisson Ridge Regression Estimator},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {9},
number = {4},
pages = {106-112},
doi = {10.11648/j.sjams.20210904.12},
url = {https://doi.org/10.11648/j.sjams.20210904.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210904.12},
abstract = {For modeling count data, the Poisson regression model is widely used in which the response variable takes non-negative integer values. However, the presence of strong correlation between the explanatory variables causes the problem of multicollinearity. Due to multicollinearity, the variance of the maximum likelihood estimator (MLE) will be inflated causing the parameters estimation to become unstable. Multicollinearity can be tackled by using biased estimators such as the ridge estimator in order to minimize the estimated variance of the regression coefficients. An alternative approach is to specify exact linear restrictions on the parameters in addition to regression model. In this paper, the restricted Poisson ridge regression estimator (RPRRE) is suggested to handle multicollinearity in Poisson regression model with exact linear restrictions on the parameters. In addition, the conditions of superiority of the suggested estimator in comparison to some existing estimators are discussed based on the mean squared error (MSE) matrix criterion. Moreover, a simulation study and a real data application are provided to illustrate the theoretical results. The results indicate that the suggested estimator, RPRRE, outperforms the other existing estimators in terms of scalar mean squared error (SMSE). Therefore, it is recommended to use the RPRRE for the Poisson regression model when the problem of multicollinearity is present.},
year = {2021}
}
TY - JOUR T1 - On the Restricted Poisson Ridge Regression Estimator AU - Enas Gawdat Yehia Y1 - 2021/08/26 PY - 2021 N1 - https://doi.org/10.11648/j.sjams.20210904.12 DO - 10.11648/j.sjams.20210904.12 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 106 EP - 112 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20210904.12 AB - For modeling count data, the Poisson regression model is widely used in which the response variable takes non-negative integer values. However, the presence of strong correlation between the explanatory variables causes the problem of multicollinearity. Due to multicollinearity, the variance of the maximum likelihood estimator (MLE) will be inflated causing the parameters estimation to become unstable. Multicollinearity can be tackled by using biased estimators such as the ridge estimator in order to minimize the estimated variance of the regression coefficients. An alternative approach is to specify exact linear restrictions on the parameters in addition to regression model. In this paper, the restricted Poisson ridge regression estimator (RPRRE) is suggested to handle multicollinearity in Poisson regression model with exact linear restrictions on the parameters. In addition, the conditions of superiority of the suggested estimator in comparison to some existing estimators are discussed based on the mean squared error (MSE) matrix criterion. Moreover, a simulation study and a real data application are provided to illustrate the theoretical results. The results indicate that the suggested estimator, RPRRE, outperforms the other existing estimators in terms of scalar mean squared error (SMSE). Therefore, it is recommended to use the RPRRE for the Poisson regression model when the problem of multicollinearity is present. VL - 9 IS - 4 ER -
Email: