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Bootstrapping Pseudo - R2 Measures for Binary Response Variable Model

Received: 7 March 2017     Accepted: 16 March 2017     Published: 31 March 2017
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Abstract

Statistical inference is based generally on some estimates that are functions of the data. Bootstrapping procedure offers strategies to estimate or approximate the sampling distribution of a statistic. Logistics regression model with binary response is commonly used. This paper focuses on the behavior of bootstrapping pseudo - R2 measures in logistic regression model. Simulation and real data results also presented. We conclude and suggest to use either R2M or R2D, since they have convergence in there values.

Published in Biomedical Statistics and Informatics (Volume 2, Issue 3)
DOI 10.11648/j.bsi.20170203.13
Page(s) 107-110
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), 2017. Published by Science Publishing Group

Keywords

Logistic Regression, Pseudo - R2, Bootstrap, Logit, Propit

References
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[2] Carroll, R., J., Ruppert, D., Stefanski, L., A., and Crainiceanu, C., M., (2006), "Measurement Error in Nonlinear Models, A Modern Prespective", 2nd ed., Chapman & Hall/CRC, Florida
[3] Chatterjee, S., and Hadi, A., S. (2006), "Regression Analysis by Example", 4th ed., John Wiley and Sons, Inc., USA.
[4] Cragg, J., G. and Uhler, R., (1970), "The Demand for Automobiles", Canadian Journal of Economics, Vol. 3, pp. 386-406.
[5] Efron, B. (1979) “Bootstrap Methods: Another look at Jackknife”, Annals of Statistics, Vol. 7, pp. 1-26.
[6] Efron, B. and Tibshirani, R., (1993), “An introduction to the bootstrap”, Chapman and Hall, New York.
[7] Friedl, H. and Stampfer, E., (2002), “Jackknife Resampling”, Encyclopedia of Environmetrics, 2, pp. 1089-1098.
[8] Harrell, F., E., (2001) "Regression Modeling Strategies: with Applications to Linear Models, Logistic Regression and Survival Analysis", Springer-Velag, Inc., USA
[9] Horowitz, J., L., and Savin, N., E. (2001), "Binary Response Models: Logits, Probits and Semiparametrics", Journal of Economic Perspectives, Vol. 15, No. 4, pp. 43-56.
[10] Hosmer, D., W. and Lemeshow, S., (2000), "Applied Logistic Regression" 2nd ed., John Wiley & Sons, Inc., New York.
[11] Hu, B., Shao, J. and Palta, M. (2006), "Pseudo- in Logistic Regression Model", Statistica Sinica, Vol. 16, pp. 847-860.
[12] Long, S., J. (1997) "Regression Models for Categorical and Limited Dependent Variables", SAGE Publication, USA.
[13] McFadden, D. (1974), "Conditional Logit Analysis of Qualitative Choice Behavior, in P. Zarembka (ed.), Frontiers in Econometrics, New York: Academic Press.
[14] Mittlebick, M., and Heinzl, H., (2003), "Pseudo- Measures for Generalized Linear Models", 1st European Workshop on the Assessment of Diagnostic Performance, pp. 71-80.
[15] Algamal, Z. Y. and Lee, M. H., (2015),” Penalized logistic regression with the adaptive LASSO for gene selection in high-dimensional cancer classification”, Expert Systems with Applications, Vol. 42, pp. 9326–9332.
[16] Algamal, Z., Y. and Lee, M., H., (2015), “Regularized logistic regression with adjusted adaptive elastic net for gene selection in high dimensional cancer classification”, Computers in Biology and Medicine, Vol. 67, pp. 136–145.
[17] Algamal, Z., Y., and Lee, M., H., (2015), “Penalized Poisson Regression Model using adaptive modified Elastic Net Penalty”, Electronic Journal of Applied Statistical Analysis, Vol. 8, No. 2, pp. 236-245.
[18] Algamal, Z., Y., and Lee, M., H., (2015), “Applying Penalized Binary Logistic Regression with Correlation Based Elastic Net for Variables Selection”, Journal of Modern Applied Statistical Methods, Vol. 14, No. 1, pp. 168-179.
[19] Algamal, Z., Y., and Lee, M., H., (2015), “High Dimensional Logistic Regression Model using Adjusted Elastic Net Penalty”, Pakistan Journal of Statistics and Operation Research, Vol. 11, No. 4, pp. 667-676.
Cite This Article
  • APA Style

    Zakariya Yahya Algamal, Haithem Taha Mohammad Ali. (2017). Bootstrapping Pseudo - R2 Measures for Binary Response Variable Model. Biomedical Statistics and Informatics, 2(3), 107-110. https://doi.org/10.11648/j.bsi.20170203.13

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    ACS Style

    Zakariya Yahya Algamal; Haithem Taha Mohammad Ali. Bootstrapping Pseudo - R2 Measures for Binary Response Variable Model. Biomed. Stat. Inform. 2017, 2(3), 107-110. doi: 10.11648/j.bsi.20170203.13

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    AMA Style

    Zakariya Yahya Algamal, Haithem Taha Mohammad Ali. Bootstrapping Pseudo - R2 Measures for Binary Response Variable Model. Biomed Stat Inform. 2017;2(3):107-110. doi: 10.11648/j.bsi.20170203.13

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  • @article{10.11648/j.bsi.20170203.13,
      author = {Zakariya Yahya Algamal and Haithem Taha Mohammad Ali},
      title = {Bootstrapping Pseudo - R2 Measures for Binary Response Variable Model},
      journal = {Biomedical Statistics and Informatics},
      volume = {2},
      number = {3},
      pages = {107-110},
      doi = {10.11648/j.bsi.20170203.13},
      url = {https://doi.org/10.11648/j.bsi.20170203.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20170203.13},
      abstract = {Statistical inference is based generally on some estimates that are functions of the data. Bootstrapping procedure offers strategies to estimate or approximate the sampling distribution of a statistic. Logistics regression model with binary response is commonly used. This paper focuses on the behavior of bootstrapping pseudo - R2 measures in logistic regression model. Simulation and real data results also presented. We conclude and suggest to use either R2M or R2D, since they have convergence in there values.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Bootstrapping Pseudo - R2 Measures for Binary Response Variable Model
    AU  - Zakariya Yahya Algamal
    AU  - Haithem Taha Mohammad Ali
    Y1  - 2017/03/31
    PY  - 2017
    N1  - https://doi.org/10.11648/j.bsi.20170203.13
    DO  - 10.11648/j.bsi.20170203.13
    T2  - Biomedical Statistics and Informatics
    JF  - Biomedical Statistics and Informatics
    JO  - Biomedical Statistics and Informatics
    SP  - 107
    EP  - 110
    PB  - Science Publishing Group
    SN  - 2578-8728
    UR  - https://doi.org/10.11648/j.bsi.20170203.13
    AB  - Statistical inference is based generally on some estimates that are functions of the data. Bootstrapping procedure offers strategies to estimate or approximate the sampling distribution of a statistic. Logistics regression model with binary response is commonly used. This paper focuses on the behavior of bootstrapping pseudo - R2 measures in logistic regression model. Simulation and real data results also presented. We conclude and suggest to use either R2M or R2D, since they have convergence in there values.
    VL  - 2
    IS  - 3
    ER  - 

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Author Information
  • Department of Statistics and Informatics, University of Mosul, Mosul, Iraq

  • College of Computers and Information Technology, Nawroz University, Kurdistan Region, Iraq

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