Poisson Ridge Regression Estimators: A Performance Test

Etaga Harrison Oghenekevwe; Aforka Kenechukwu Florence; Awopeju Kabiru Abidemi; Etaga Njideka Cecilia

doi:doi:10.11648/j.ajtas.20211002.13

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Poisson Ridge Regression Estimators: A Performance Test

Etaga Harrison Oghenekevwe, Aforka Kenechukwu Florence, Awopeju Kabiru Abidemi, Etaga Njideka Cecilia

Published in American Journal of Theoretical and Applied Statistics (Volume 10, Issue 2)

Received: 27 February 2021 Accepted: 15 March 2021 Published: 30 March 2021

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Abstract

In Multiple regression analysis, it is assumed that the independent variables are uncorrelated with one another, when such happen, the problem of multicollinearity occurs. Multicollinearity can create inaccurate estimates of the regression coefficients, inflate the standard errors of the regression coefficients, deflate the partial t-tests for the regression coefficients, give false p-values and degrade the predictability of the model. There are several methods to get rid of this problem and one of the most famous one is the ridge regression. The purpose of this research is to study the performance of some popular ridge regression estimators based on the effects of sample sizes and correlation levels on their Average Mean Square Error (AMSE) for Poisson Regression models in the presence of multicollinearity. As performance criteria, average MSE of k was used. A Monte Carlo simulation study was conducted to compare performance of Fifty (50) k estimators under four experimental conditions namely: correlation, Number of explanatory variables, sample size and intercept. From the results of the analysis as summarized in the Tables, the MSE of the estimators performed better in a lower explanatory variables p and an increased intercept value. It was also observed that some estimators performed better on the average at all correlation levels, sample sizes, intercept values and explanatory variables than others.

Published in	American Journal of Theoretical and Applied Statistics (Volume 10, Issue 2)
DOI	10.11648/j.ajtas.20211002.13
Page(s)	111-121
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

Keywords

Multicollinearity, Ridge, Poisson, Estimators, Maximum Likelihood, Monte-Carlo Simulations, MSE

References

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[2]	Alkahamisi, M. A and Shukur, G. (2008), A Monte Carlo Study of Recent Ridge Parameter, Communications in Statistic-Simulation and Computation, 36, (3), 535-547.
[3]	Algamal ZY, Alanaz MM (2018) Proposed methods in estimating the ridge regression parameter in Poisson regression model. Electron J Appl Stat Anal 11 (2): 506–515.
[4]	Asar, Y. and Gen¸c, A. (2017). A new two-parameter estimator for the poisson regression model. Iranian Journal of Science and Technology, Transactions A: Science.
[5]	Asar Y, Gen ç A (2018) A new two-parameter estimator for the Poisson regression model. Iran J Sci Technol Trans A Sci 42 (2): 793–803
[6]	Hoerl A. E., and Kennard, R. W. (1970a), Ridge Regression: Biased Estimator for Non-orthogonal Problems, Technometrics, 12, 55-67.
[7]	Hoerl A. E., and Kennard, R. W. (1970b), Ridge Regressin: An Applications for Non-orthogonal Problems, Technometriccs, 12, 69-82.
[8]	Kaçıranlar S, Dawoud I (2018) On the performance of the poisson and the negative binomial ridge predictors. Commun Stat Simul Comput 47 (6): 1751–1770.
[9]	Khalaf Ghadban, and Ghazi Shukur (2005), Choosing Ridge Parameter for Regression Problems. Communications in statistics-Theory and Methods, vol. 34, no. 5, 1177-1182.
[10]	Kibria, B. M. G. (2003), Performance of Some New Ridge Regression Estimators, Communications in Statistics-Simulation and computation, 32, (2), 417-435.
[11]	Kibria B. M. G., Kristofer Mansson and Shukur, G. (2015), A Simulation Study of some Biasing Parameter for Ridge Type Estimation of Poisson Regression, Communications in Statistics- Simulation and Computation, 44, 943-957.
[12]	Kibra, B. M. G., Mansson, K., Shukur, G. (2012). Performance of some logistic ridge regression parameters. Computational Economics 40: 401-414.
[13]	Mansson Kristofer and Shukur, G. (2011), A Poisson Ridge Regression Estimator, Economic Modeling, 28, 1475-1481.
[14]	Muniz, G., Kibria, B. M. G. (2009), On Some Ridge Regression Estimators: An Empirical Comparison, Communications in Statistics-Simulations and Computation, 38, 621-630.
[15]	Qasim M, Kibria BMG, Månsson K (2020) A new Poisson Liu regression estimator: method and application. J Appl Stat.; 47 (12): 2258–2271.
[16]	Schaeffer, R. L., Rio, L. D and Wolfe, R. A. (1984), A Ridge Logistic Estimator, Communications in Statistics- Theory and Methods, 13, pp. 99-113.
[17]	Zaldivar Cynthia (2018), on the performance of some Poisson Ridge Regression estimator, FIU Electronic Theses and Dissertations. 3669.

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APA Style

Etaga Harrison Oghenekevwe, Aforka Kenechukwu Florence, Awopeju Kabiru Abidemi, Etaga Njideka Cecilia. (2021). Poisson Ridge Regression Estimators: A Performance Test. American Journal of Theoretical and Applied Statistics, 10(2), 111-121. https://doi.org/10.11648/j.ajtas.20211002.13

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ACS Style

Etaga Harrison Oghenekevwe; Aforka Kenechukwu Florence; Awopeju Kabiru Abidemi; Etaga Njideka Cecilia. Poisson Ridge Regression Estimators: A Performance Test. Am. J. Theor. Appl. Stat. 2021, 10(2), 111-121. doi: 10.11648/j.ajtas.20211002.13

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AMA Style

Etaga Harrison Oghenekevwe, Aforka Kenechukwu Florence, Awopeju Kabiru Abidemi, Etaga Njideka Cecilia. Poisson Ridge Regression Estimators: A Performance Test. Am J Theor Appl Stat. 2021;10(2):111-121. doi: 10.11648/j.ajtas.20211002.13

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@article{10.11648/j.ajtas.20211002.13,
  author = {Etaga Harrison Oghenekevwe and Aforka Kenechukwu Florence and Awopeju Kabiru Abidemi and Etaga Njideka Cecilia},
  title = {Poisson Ridge Regression Estimators: A Performance Test},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {2},
  pages = {111-121},
  doi = {10.11648/j.ajtas.20211002.13},
  url = {https://doi.org/10.11648/j.ajtas.20211002.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211002.13},
  abstract = {In Multiple regression analysis, it is assumed that the independent variables are uncorrelated with one another, when such happen, the problem of multicollinearity occurs. Multicollinearity can create inaccurate estimates of the regression coefficients, inflate the standard errors of the regression coefficients, deflate the partial t-tests for the regression coefficients, give false p-values and degrade the predictability of the model. There are several methods to get rid of this problem and one of the most famous one is the ridge regression. The purpose of this research is to study the performance of some popular ridge regression estimators based on the effects of sample sizes and correlation levels on their Average Mean Square Error (AMSE) for Poisson Regression models in the presence of multicollinearity. As performance criteria, average MSE of k was used. A Monte Carlo simulation study was conducted to compare performance of Fifty (50) k estimators under four experimental conditions namely: correlation, Number of explanatory variables, sample size and intercept. From the results of the analysis as summarized in the Tables, the MSE of the estimators performed better in a lower explanatory variables p and an increased intercept value. It was also observed that some estimators performed better on the average at all correlation levels, sample sizes, intercept values and explanatory variables than others.},
 year = {2021}
}

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TY  - JOUR
T1  - Poisson Ridge Regression Estimators: A Performance Test
AU  - Etaga Harrison Oghenekevwe
AU  - Aforka Kenechukwu Florence
AU  - Awopeju Kabiru Abidemi
AU  - Etaga Njideka Cecilia
Y1  - 2021/03/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211002.13
DO  - 10.11648/j.ajtas.20211002.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 111
EP  - 121
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211002.13
AB  - In Multiple regression analysis, it is assumed that the independent variables are uncorrelated with one another, when such happen, the problem of multicollinearity occurs. Multicollinearity can create inaccurate estimates of the regression coefficients, inflate the standard errors of the regression coefficients, deflate the partial t-tests for the regression coefficients, give false p-values and degrade the predictability of the model. There are several methods to get rid of this problem and one of the most famous one is the ridge regression. The purpose of this research is to study the performance of some popular ridge regression estimators based on the effects of sample sizes and correlation levels on their Average Mean Square Error (AMSE) for Poisson Regression models in the presence of multicollinearity. As performance criteria, average MSE of k was used. A Monte Carlo simulation study was conducted to compare performance of Fifty (50) k estimators under four experimental conditions namely: correlation, Number of explanatory variables, sample size and intercept. From the results of the analysis as summarized in the Tables, the MSE of the estimators performed better in a lower explanatory variables p and an increased intercept value. It was also observed that some estimators performed better on the average at all correlation levels, sample sizes, intercept values and explanatory variables than others.
VL  - 10
IS  - 2
ER  -

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Author Information

Etaga Harrison Oghenekevwe

Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria
Aforka Kenechukwu Florence

Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria
Awopeju Kabiru Abidemi

Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria
Etaga Njideka Cecilia

Department of Educational Foundations, Faculty of Education, Nnamdi Azikiwe University, Awka, Nigeria

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Plain Text BibTeX RIS

APA Style

Etaga Harrison Oghenekevwe, Aforka Kenechukwu Florence, Awopeju Kabiru Abidemi, Etaga Njideka Cecilia. (2021). Poisson Ridge Regression Estimators: A Performance Test. American Journal of Theoretical and Applied Statistics, 10(2), 111-121. https://doi.org/10.11648/j.ajtas.20211002.13

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ACS Style

Etaga Harrison Oghenekevwe; Aforka Kenechukwu Florence; Awopeju Kabiru Abidemi; Etaga Njideka Cecilia. Poisson Ridge Regression Estimators: A Performance Test. Am. J. Theor. Appl. Stat. 2021, 10(2), 111-121. doi: 10.11648/j.ajtas.20211002.13

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AMA Style

Etaga Harrison Oghenekevwe, Aforka Kenechukwu Florence, Awopeju Kabiru Abidemi, Etaga Njideka Cecilia. Poisson Ridge Regression Estimators: A Performance Test. Am J Theor Appl Stat. 2021;10(2):111-121. doi: 10.11648/j.ajtas.20211002.13

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@article{10.11648/j.ajtas.20211002.13,
  author = {Etaga Harrison Oghenekevwe and Aforka Kenechukwu Florence and Awopeju Kabiru Abidemi and Etaga Njideka Cecilia},
  title = {Poisson Ridge Regression Estimators: A Performance Test},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {2},
  pages = {111-121},
  doi = {10.11648/j.ajtas.20211002.13},
  url = {https://doi.org/10.11648/j.ajtas.20211002.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211002.13},
  abstract = {In Multiple regression analysis, it is assumed that the independent variables are uncorrelated with one another, when such happen, the problem of multicollinearity occurs. Multicollinearity can create inaccurate estimates of the regression coefficients, inflate the standard errors of the regression coefficients, deflate the partial t-tests for the regression coefficients, give false p-values and degrade the predictability of the model. There are several methods to get rid of this problem and one of the most famous one is the ridge regression. The purpose of this research is to study the performance of some popular ridge regression estimators based on the effects of sample sizes and correlation levels on their Average Mean Square Error (AMSE) for Poisson Regression models in the presence of multicollinearity. As performance criteria, average MSE of k was used. A Monte Carlo simulation study was conducted to compare performance of Fifty (50) k estimators under four experimental conditions namely: correlation, Number of explanatory variables, sample size and intercept. From the results of the analysis as summarized in the Tables, the MSE of the estimators performed better in a lower explanatory variables p and an increased intercept value. It was also observed that some estimators performed better on the average at all correlation levels, sample sizes, intercept values and explanatory variables than others.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Poisson Ridge Regression Estimators: A Performance Test
AU  - Etaga Harrison Oghenekevwe
AU  - Aforka Kenechukwu Florence
AU  - Awopeju Kabiru Abidemi
AU  - Etaga Njideka Cecilia
Y1  - 2021/03/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211002.13
DO  - 10.11648/j.ajtas.20211002.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 111
EP  - 121
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211002.13
AB  - In Multiple regression analysis, it is assumed that the independent variables are uncorrelated with one another, when such happen, the problem of multicollinearity occurs. Multicollinearity can create inaccurate estimates of the regression coefficients, inflate the standard errors of the regression coefficients, deflate the partial t-tests for the regression coefficients, give false p-values and degrade the predictability of the model. There are several methods to get rid of this problem and one of the most famous one is the ridge regression. The purpose of this research is to study the performance of some popular ridge regression estimators based on the effects of sample sizes and correlation levels on their Average Mean Square Error (AMSE) for Poisson Regression models in the presence of multicollinearity. As performance criteria, average MSE of k was used. A Monte Carlo simulation study was conducted to compare performance of Fifty (50) k estimators under four experimental conditions namely: correlation, Number of explanatory variables, sample size and intercept. From the results of the analysis as summarized in the Tables, the MSE of the estimators performed better in a lower explanatory variables p and an increased intercept value. It was also observed that some estimators performed better on the average at all correlation levels, sample sizes, intercept values and explanatory variables than others.
VL  - 10
IS  - 2
ER  -

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