Research Article
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Year 2020, Issue: 33, 76 - 84, 31.12.2020

Emre Dünder , Mehmet Ali Cengiz

Abstract

References

  • D. M. Sakate, D. N. Kashid, D.T. Shirke, Subset Selection in Poisson Regression. Journal of Statistical Theory and Practice, 5(2) (2011) 207-219.
  • V. Calcagno, and C. de Mazancourt, glmulti: An R Package for Easy Automated Model Selection with (generalized) Linear Models, Journal of Statistical Software, 34(12) (2010) 1-29.
  • H. H. Örkcü, Subset Selection in Multiple Linear Regression Models: A Hybrid of Genetic and Simulated Annealing Algorithms, Applied Mathematics and Computation, 219(23) (2013) 11018-11028.
  • A. Unler, A. Murat, A Discrete Particle Swarm Optimization Method for Feature Selection in Binary Classification Problems, European Journal of Operational Research, 206(3) (2010) 528-539.
  • H. Akaike, Maximum Likelihood Identification of Gaussian Autoregressive Moving Average Models, Biometrika, 60(2) (1973) 255-265.
  • G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics, 6(2) (1978) 461–464.
  • H. Bozdogan, Model Selection and Akaike's Information Criterion (AIC): The General Theory and Its Analytical Extensions, Psychometrika, 52(3) (1987) 345-370.
  • C. M Hurvich, C. L. Tsai, Regression and Time Series Model Selection in Small Samples, Biometrika, 76(2) (1989) 297-307.
  • H. Bozdogan, Statistical Data Mining and Knowledge Discovery, CRC Press, 15-56 (2004) Boca Raton.
  • F. Cribari-Neto, A. Zeileis, Beta Regression in R, Journal of Statistical Software, 34(2) (2010) 1-24.
  • K. M. Mullen, D. Ardia, D. L. Gil, D. Windover and J. Cline, DEoptim: An R Package for Global Optimization by Differential Evolution. Journal of Statistical Software, 40(6) (2011) 1-26.
  • S. Ferrari, F. Cribari-Neto, Beta Regression for Modelling Rates and Proportions. Journal of Applied Statistics, 31(7) (2004) 799-815.
  • W. Zhao, R. Lv, Y. Zhang, J. Liu, Variable Selection for Varying Dispersion Beta Regression Model, Journal of Applied Statistics, 41(1) (2014) 95-108.
  • T. C. M. Dias and C. A. R. Diniz, The Use of Several Link Functions on a Beta Regression Model: a Bayesian Approach, In AIP Conference Proceedings, 1073(1) (2008) 144-149, American Institute of Physics.
  • D. Karaboğa, Yapay Zeka Optimizasyon Algoritmaları, Nobel Yayınevi, (2011) 201-221, İstanbul.
  • H. Bozdogan, Akaike's Information Criterion and Recent Developments in Information Complexity, Journal of Mathematical Psychology, 44(1) (2000) 62-91.
  • E. Pamukçu, H. Bozdogan, H. and S. Çalık, A Novel Hybrid Dimension Reduction Technique for Undersized High Dimensional Gene Expression Data Sets Using Information Complexity Criterion for Cancer Classification. Computational and Mathematical Methods in Medicine (2015) doi:10.1155/2015/370640.
  • K. A. Bollen, S. Ray, J. Zavisca and J. J. Harden, A Comparison of Bayes Factor Approximation Methods Including Two New Methods, Sociological Methods & Research, 41(2) (2012) 294-324.
  • H. Bozdogan, A New Class of Information Complexity (ICOMP) Criteria with an Application to Customer Profiling and Segmentation, Istanbul University Journal of the School of Business, 39(2) (2010) 370-398.
  • E. Dünder, Model Selection in Beta Regression Analysis Using Heuristic Optimization Algorithms, PhD Dissertation, Ondokuz Mayıs University (2017) Samsun, Turkey.
  • A. Zeileis, F. Cribari-Neto, B. Gruen, I. Kosmidis, A. B. Simas, A. V. Rocha, M. A. Zeileis, (2016). Package 'betareg'.
  • D. Ardia, K.M. Mullen, B. G. Peterson and J. Ulrich, 'DEoptim': Differential Evolution in 'R'. (2016) version 2.2-4.
  • E. K. Koc, H. Bozdogan, Model Selection in Multivariate Adaptive Regression Splines (MARS) Using Information Complexity as the Fitness Function, Machine Learning, 101(1-3) (2015) 35-58.
  • J. Verzani, Using R: Data Sets, Etc. for the Text "Using R for Introductory Statistics", Second Edition. R package version 2.0-5, (2015) https://CRAN.R-project.org/package=UsingR
  • P. Rossi, PERregress: Regression Functions and Datasets R Package Version 1.0-8, (2013) https://CRAN.R-project.org/package=PERregress.
  • E. Deniz, O. Akbilgic, J. A. Howe, Model Selection Using Information Criteria Under a New Estimation Method: Least Squares Ratio, Journal of Applied Statistics, 38(9) (2011) 2043-2050.

Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization

Year 2020, Issue: 33, 76 - 84, 31.12.2020

Emre Dünder , Mehmet Ali Cengiz

Abstract

In the context of generalized linear modelling (GLM), the beta regression analysis is used to estimate regression models when the dependent variable lies between (0,1). In this paper, we carried out a model selection process using several information criteria with heuristic optimization. We employed the differential evolution algorithm as a heuristic optimization method to select the best model for beta regression analysis. The results show that the alternative-type information criteria provide competitive results during the model selection process in beta regression analysis.

Keywords

Beta regression differential evolution algorithm information criteria model selection

References

  • D. M. Sakate, D. N. Kashid, D.T. Shirke, Subset Selection in Poisson Regression. Journal of Statistical Theory and Practice, 5(2) (2011) 207-219.
  • V. Calcagno, and C. de Mazancourt, glmulti: An R Package for Easy Automated Model Selection with (generalized) Linear Models, Journal of Statistical Software, 34(12) (2010) 1-29.
  • H. H. Örkcü, Subset Selection in Multiple Linear Regression Models: A Hybrid of Genetic and Simulated Annealing Algorithms, Applied Mathematics and Computation, 219(23) (2013) 11018-11028.
  • A. Unler, A. Murat, A Discrete Particle Swarm Optimization Method for Feature Selection in Binary Classification Problems, European Journal of Operational Research, 206(3) (2010) 528-539.
  • H. Akaike, Maximum Likelihood Identification of Gaussian Autoregressive Moving Average Models, Biometrika, 60(2) (1973) 255-265.
  • G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics, 6(2) (1978) 461–464.
  • H. Bozdogan, Model Selection and Akaike's Information Criterion (AIC): The General Theory and Its Analytical Extensions, Psychometrika, 52(3) (1987) 345-370.
  • C. M Hurvich, C. L. Tsai, Regression and Time Series Model Selection in Small Samples, Biometrika, 76(2) (1989) 297-307.
  • H. Bozdogan, Statistical Data Mining and Knowledge Discovery, CRC Press, 15-56 (2004) Boca Raton.
  • F. Cribari-Neto, A. Zeileis, Beta Regression in R, Journal of Statistical Software, 34(2) (2010) 1-24.
  • K. M. Mullen, D. Ardia, D. L. Gil, D. Windover and J. Cline, DEoptim: An R Package for Global Optimization by Differential Evolution. Journal of Statistical Software, 40(6) (2011) 1-26.
  • S. Ferrari, F. Cribari-Neto, Beta Regression for Modelling Rates and Proportions. Journal of Applied Statistics, 31(7) (2004) 799-815.
  • W. Zhao, R. Lv, Y. Zhang, J. Liu, Variable Selection for Varying Dispersion Beta Regression Model, Journal of Applied Statistics, 41(1) (2014) 95-108.
  • T. C. M. Dias and C. A. R. Diniz, The Use of Several Link Functions on a Beta Regression Model: a Bayesian Approach, In AIP Conference Proceedings, 1073(1) (2008) 144-149, American Institute of Physics.
  • D. Karaboğa, Yapay Zeka Optimizasyon Algoritmaları, Nobel Yayınevi, (2011) 201-221, İstanbul.
  • H. Bozdogan, Akaike's Information Criterion and Recent Developments in Information Complexity, Journal of Mathematical Psychology, 44(1) (2000) 62-91.
  • E. Pamukçu, H. Bozdogan, H. and S. Çalık, A Novel Hybrid Dimension Reduction Technique for Undersized High Dimensional Gene Expression Data Sets Using Information Complexity Criterion for Cancer Classification. Computational and Mathematical Methods in Medicine (2015) doi:10.1155/2015/370640.
  • K. A. Bollen, S. Ray, J. Zavisca and J. J. Harden, A Comparison of Bayes Factor Approximation Methods Including Two New Methods, Sociological Methods & Research, 41(2) (2012) 294-324.
  • H. Bozdogan, A New Class of Information Complexity (ICOMP) Criteria with an Application to Customer Profiling and Segmentation, Istanbul University Journal of the School of Business, 39(2) (2010) 370-398.
  • E. Dünder, Model Selection in Beta Regression Analysis Using Heuristic Optimization Algorithms, PhD Dissertation, Ondokuz Mayıs University (2017) Samsun, Turkey.
  • A. Zeileis, F. Cribari-Neto, B. Gruen, I. Kosmidis, A. B. Simas, A. V. Rocha, M. A. Zeileis, (2016). Package 'betareg'.
  • D. Ardia, K.M. Mullen, B. G. Peterson and J. Ulrich, 'DEoptim': Differential Evolution in 'R'. (2016) version 2.2-4.
  • E. K. Koc, H. Bozdogan, Model Selection in Multivariate Adaptive Regression Splines (MARS) Using Information Complexity as the Fitness Function, Machine Learning, 101(1-3) (2015) 35-58.
  • J. Verzani, Using R: Data Sets, Etc. for the Text "Using R for Introductory Statistics", Second Edition. R package version 2.0-5, (2015) https://CRAN.R-project.org/package=UsingR
  • P. Rossi, PERregress: Regression Functions and Datasets R Package Version 1.0-8, (2013) https://CRAN.R-project.org/package=PERregress.
  • E. Deniz, O. Akbilgic, J. A. Howe, Model Selection Using Information Criteria Under a New Estimation Method: Least Squares Ratio, Journal of Applied Statistics, 38(9) (2011) 2043-2050.
There are 26 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Article
Authors

Emre Dünder 0000-0003-0230-8968

Mehmet Ali Cengiz 0000-0002-1271-2588

Publication Date December 31, 2020
Submission Date December 7, 2020
Published in Issue Year 2020 Issue: 33

Cite

APA Dünder, E., & Cengiz, M. A. (2020). Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization. Journal of New Theory(33), 76-84.
AMA Dünder E, Cengiz MA. Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization. JNT. December 2020;(33):76-84.
Chicago Dünder, Emre, and Mehmet Ali Cengiz. “Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization”. Journal of New Theory, no. 33 (December 2020): 76-84.
EndNote Dünder E, Cengiz MA (December 1, 2020) Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization. Journal of New Theory 33 76–84.
IEEE E. Dünder and M. A. Cengiz, “Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization”, JNT, no. 33, pp. 76–84, December 2020.
ISNAD Dünder, Emre - Cengiz, Mehmet Ali. “Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization”. Journal of New Theory 33 (December 2020), 76-84.
JAMA Dünder E, Cengiz MA. Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization. JNT. 2020;:76–84.
MLA Dünder, Emre and Mehmet Ali Cengiz. “Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization”. Journal of New Theory, no. 33, 2020, pp. 76-84.
Vancouver Dünder E, Cengiz MA. Model Selection in Beta Regression Analysis Using Several Information Criteria and Heuristic Optimization. JNT. 2020(33):76-84.
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