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), 2021. Published by Science Publishing Group |
Poisson Regression, Multicollinearity, Ridge Regression Estimator, Restricted Maximum Likelihood Estimator, Restricted Ridge Regression Estimator
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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
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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 -
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