Robust Logistic Regression in Application to Divorce Data

  • Sanizah AhmadEmail author
  • Rosa Shafiqa Azureen Mohamad Rosni
Conference paper


In logistic regression, the parameters are commonly estimated by using maximum likelihood estimator (MLE). However, MLE is easily affected when outliers appear in the data. The objective of this study is to compare the performance between the MLE and four robust methods namely the Mallows-type, Conditionally Unbiased Bounded Influence (CUBIF), Bianco and Yohai (BY), and Weighted Bianco and Yohai (WBY) which are available in R by applying to a sample of real dataset on potential divorce which contains outliers. The performance of the parameter estimators is determined by using the chi-square arcsine transformation with the best estimator having the smallest value. The result in this study found that the WBY method proved to be best robust method in estimating the parameters of potential divorce data.


Outliers Divorce Robust Maximum likelihood Logistic regression 



The authors wish to thank Universiti Teknologi MARA (UiTM) Shah Alam for providing the internal grant (600-IRMI/MyRA 5/3/LESTARI(0129/2016) and Syariah Lower Court for providing the data.


  1. 1.
    Syaiba, B.A., Habshah, H.: The performance of classical and robust logistic regression estimators in the presence of outliers. Pertanika J. Sci. Technol. 20(2), 313–325 (2012)Google Scholar
  2. 2.
    Bellio, R., Ventura, L.: An introduction to robust estimation with R functions. In: Proceedings of 1st International Work, pp. 1–57 (2005)Google Scholar
  3. 3.
    Sarkar, S.K., Midi, H., Rana, M.: Detection of outliers and influential observations in binary logistic regression: an empirical study. J. Appl. Sci. 11(1), 26–35 (2011)CrossRefGoogle Scholar
  4. 4.
    Sanizah, A., Habshah, M., Norazan, M.R.: Robust estimators in logistic regression: a comparative simulation study. J. Mod. Appl. Stat. Methods 9(2), 502–511 (2010)CrossRefGoogle Scholar
  5. 5.
    Kunsch, H.R., Stefanski, L.A., Carroll, R.J.: Conditionally unbiased bounded influence estimation in general regression models, with applications to generalized linear models. J. Am. Stat. Assoc. 84, 460–466 (1989)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Carroll, R.J., Pederson, S.: On robust estimation in the logistic regression model. J. Roy. Stat. Soc. B 55, 693–706 (1993)zbMATHGoogle Scholar
  7. 7.
    Kordzakhia, N., Mishra, G.D., Reiersølmoen, L.: Robust estimation in the logistic regression model. J. Stat. Plan. Inference 98(1), 211–223 (2001)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Croux, C., Haesbroeck, G.: Implementing the bianco and yohai estimator for logistic re gression. Comput. Stat. Data Anal. J. 44, 273–279 (2003)CrossRefGoogle Scholar
  9. 9.
    Sanizah, A., Hasfariza, F., Norin Rahayu, S., Nur Niswah Naslina, A.: Determinants of marital dissolution: a survival analysis approach. Int. J. Econ. Stat. 2, 348–354 (2014)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Sanizah Ahmad
    • 1
    Email author
  • Rosa Shafiqa Azureen Mohamad Rosni
    • 1
  1. 1.Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARAShah AlamMalaysia

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