Combating the Multicollinearity in Bell Regression Model: Simulation and Application

Authors

  • G. A. Shewa Department of Mathematical Sciences, Taraba State University, Jalingo/Taraba, Nigeria
  • F. I. Ugwuowo Department of Statistics, University of Nigeria, Nsukka/Enugu, Nigeria

Keywords:

Bell regression, Liu, Multicollinearity, Poisson regression, Ridge

Abstract

Poisson regression model has been popularly used to model count data. However, over-dispersion is a threat to the performance of the Poisson regression model. The Bell Regression Model (BRM) is an alternative means of modelling count data with over-dispersion. Conventionally, the parameters in BRM is popularly estimated using the Method of Maximum Likelihood (MML). Multicollinearity posed challenge on the efficiency of MML. In this study, we developed a new estimator to overcome the problem of multicollinearity. The theoretical, simulation and application results were in favor of this new method.

Dimensions

F. Castellares, S. L. P. Ferrari & A. J. Lemonte, “On the Bell Distribution and its Associated Regression Model for Count Data”, Applied Mathematical Modelling 56 (2017) 172, https://doi.org/10.1016/j.apm.2017.12.014

M. Amin, M. N. Akram, & A. Majid, “On the Estimation of Bell Regression Model Using Ridge Estimator”, Communications in Statistics - Simulation and Computation 2021 (2021),

https://doi.org/10.1080/03610918.2020.1870694

A. Majid, M. Amin, & M. N. Akram, “On the Liu Estimation of Bell Regression Model in the Presence of Multicollinearity”, Journal of Statistical Computation and Simulation 2021 (2021) 21.

https://doi.org/10.1080/00949655.2021.1955886

E. T. Bell, “Exponential Numbers”, The American Mathematical Monthly 41 (1934a) 419.

E. T. Bell, “Exponential Polynomials”, Annals of Mathematics 35 (1934b) 258.

N. T. Longford, “A Fast Scoring Algorithm for Maximum Likelihood Estimation in Unbalanced Mixed Models with Nested Random Effects”, Biometrika, 74 (1987) 817.

B. M. G. Kibria, “Performance of Some New Ridge Regression Estimators”, Communications in Statistics-Simulation and Computation 32 (2003) 419.

A. F. Lukman, B. Aladeitan, K. Ayinde & M. R. Abonazel, “Modified Ridge – Type for the Poisson Regression Model: Simulation and Application”, Journal of Applied Statistics 2021 (2021a),

https://doi.org/10.1080/02664763.2021.1889998

A. F. Lukman, E. Adewuyi, K. Månsson & B. M. G. Kibria, “A New Estimator for the Multicollinear Poisson Regression Model: Simulation and Application, Scientific Reports 11 (2021b) 3732.

https://doi.org/10.1038/s41598-021-82582-w.

A. E. Hoerl & R. W. Kennard “Ridge Regression: Biased Estimation for Nonorthogonal Problems”, Technometrics, 12 (1970) 55.

K. Liu, “A New Class of Biased Estimate in Linear Regression”, Commun Stat. 22 (1993) 393.

A. F. Lukman, K. Ayinde, S. Binuomote & A. C. Onate, “Modified Ridge - Type Estimator to Combat Multicollinearity: Application to Chemical Data”, Journal of Chemometrics 2019 (2019) e3125. https://doi.org/10.1002/cem.3125

R. Farebrother, “Further Results on the Mean Square Error of Ridge Regression”, Journal of the Royal Statistical Society, Series B (Methodological) 38 (1976) 248.

G. Trenkler & H. Toutenburg, “Mean Squared Error Matrix Comparisons between Biased Estimators an Overview of Recent Results”, Statistical Papers 31 (1990) 179.

M. R. Ozkale & S. Kaciranlar, The Restricted and Unrestricted Two-Parameter Estimators” Commun. Statist. Theory, Meth. 36 (2007) 2707.

Stan Development Team, RStan: The R Interface to Stan. R package Version 2.19.3 (2020), https://mc-stan.org

M. Arashi, M. Roozbeh, N. A. Hamzah, & M. Gasparini, “Ridge Regression and its Applications in Genetic Studies” PloS One 16 (2021a) 4, e0245376.

M. Arashi, M. Norouzirad, M. Roozbeh, & N. M. Khan, “A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations”, Mathematics 9 (2021b) 3057, https://doi.org/10.3390/math9233057

Y. M. Bulut, “Performance of the Liu-type Estimator in the Bell Regression Mode”, 9th International Conference on Applied Analysis and Mathematical Modeling (ICAAMM21), Istanbul/TURKEY (2021).

O. G. Obadina, A. F. Adedotuun & O. A. Odusanya, “Ridge Estimation’s

Effectiveness for Multiple Linear Regression with Multicollinearity: An Investigation Using Monte-Carlo Simulations”, Journal of the Nigerian Society of Physical Sciences 3 (2021) 278.

M. Qasim, K. Månsson, P. Sjolander & B. M. G. Kibria, ”A New Class of Efficient and Debiased Two – Step Shrinkage Estimators: Method and Application”, Journal of Applied Statistics 2021 (2021), https://doi.org/10.1080/02664763.2021.1973389

A. K. M. E. Saleh, M. Arashi, & B. M. G. Kibria, Theory of Ridge Regression Estimation with Applications , John Wiley, USA (2019).

M. Suhail, S. Chand & B. M. G. Kibria, “Quantile-Based Robust Ridge M-Estimator for Linear Regression Model in Presence of Multicollinearity and Outliers”, Communications in Statistics Simulation and Computation 50 (2021) 3194.

N. K. Rashad & Z. Y. Algamal, “A New Ridge Estimator for the Poisson Regression Model”, Iranian Journal of Science and Technology, Transactions A: Science, 43 (2019), https://doi.org/10.1007/s40995-019-00769-3

Z. Y. Algamal & Y. Asar, “Liu-Type Estimator for the Gamma Regression Model”, Communications in Statistics-Simulation and Computation 8 (2018) 2035.

B. M. G. Kibria & A. F. Lukman, “A New Ridge – Type Estimator for the Linear Regression Model: Simulations and Applications”, Scientific 2020 (2020) 9758378, https://doi.org/10.1155/2020/9758378

R. H. Myers, D. C. Montgomery, G. G. Vining & T. J. Robinson, Generalized Linear Models: With Applications in Engineering and the Sciences, Wiley, New York (2012) 791.

Published

2022-08-15

How to Cite

Combating the Multicollinearity in Bell Regression Model: Simulation and Application. (2022). Journal of the Nigerian Society of Physical Sciences, 4(3), 713. https://doi.org/10.46481/jnsps.2022.713

Issue

Volume 4, Issue 3, August 2022

Section

Original Research
Copyright & Licensing

Copyright (c) 2022 G. A. Shewa, F. I. Ugwuowo

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Combating the Multicollinearity in Bell Regression Model: Simulation and Application. (2022). Journal of the Nigerian Society of Physical Sciences, 4(3), 713. https://doi.org/10.46481/jnsps.2022.713