Advertisement

A Forward Variable Selection Method for Fuzzy Logistic Regression

  • Fatemeh Salmani
  • Seyed Mahmoud TaheriEmail author
  • Alireza Abadi
Article
  • 12 Downloads

Abstract

The logistic regression analysis is a popular method for describing the relation between variables. However, when there are a big number of variables in the regression model, the selection of the best model becomes a major problem. In this condition, the question is which subset of predictors can best predict the response pattern, and which process can be used to achieve such a subset. This article is written to answer this questioning fuzzy logistic regression models. To this end, based on the existing criteria of regression models, three goodness-of-fit criteria, namely MSEF, AICF, and \(C_{p}^{\text{F}}\), are proposed. These criteria are helpful to select the best-fitted model among all possible fuzzy logistic regression models with fuzzy covariates and responses. In addition, based on the concepts of efficiency level and MSEF, a forward model selection method for fuzzy logistic regression is proposed. The proposed method is justified by some simulation studies, indicating the good performance and efficiency of the method. In addition, we applied the presented methods in a clinical trial study.

Keywords

Fuzzy logistic regression Fuzzy predictor Forward method Goodness-of-fit criteria 

References

  1. 1.
    Taheri, S.M., Mirzaei Yeganeh, S.: Logistic regression with non-precise response. In: Proceedings of the 57th ISI Conference, Durban (South Africa), pp. 98–101 (2009)Google Scholar
  2. 2.
    Pourahmad, S., Ayatollahi, S.M.T., Taheri, S.M.: Fuzzy logistic regression: a new possibilistic model and its application in clinical vague status. Iran. J. Fuzzy Syst. 8(1), 1–17 (2011)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Atalik, G., Senturk, S.: A new approach for parameter estimation in fuzzy regression. Iran. J. Fuzzy Syst. 15(1), 91–102 (2018)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Pourahmad, S., Ayatollahi, S.M.T., Taheri, S.M., Agahi, Z.H.: Fuzzy logistic regression based on the least squares approach with application in clinical studies. Comput. Math Appl. 62(9), 3353–3365 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Namdari, M., Yoon, J.H., Abadi, A., Taheri, S.M., Choi, S.H.: Fuzzy logistic regression with least absolute deviations estimators. Soft. Comput. 19(4), 909–917 (2015)CrossRefGoogle Scholar
  6. 6.
    Salmani, F., Taheri, S.M., Yoon, J.H., Abadi, A., Majd, H.A., Abbaszadeh, A.: Logistic regression for fuzzy covariates: modeling, inference, and applications. Int. J. Fuzzy Syst. 15(5), 1635–1644 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gao, Y., Lu, Q.: A fuzzy logistic regression model based on the least squares estimation. Comput. Appl. Math. 37(3), 3562–3579 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Mustafa, S., Asghar, S., Hanif, M.: Fuzzy logistic regression based on least square approach and trapezoidal membership function. Iran. J. Fuzzy Syst. 15(6), 97–106 (2018)zbMATHGoogle Scholar
  9. 9.
    Kim, I.K., Lee, W.-J., Yoon, J.H., Choi, S.H.: Fuzzy regression model using trapezoidal fuzzy numbers for re-auction data. Int. J. Fuzzy Log. Intell. Syst. 16(1), 72–80 (2016)CrossRefGoogle Scholar
  10. 10.
    Agresti, A.: Categorical Data Analysis. Wiley, Hoboken (2003)zbMATHGoogle Scholar
  11. 11.
    Wang, H.F., Tsaur, R.C.: Bicriteria variable selection in a fuzzy regression equation. Comput. Math Appl. 40(6–7), 877–883 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    D’Urso, P., Santoro, A.: Goodness of fit and variable selection in the fuzzy multiple linear regression. Fuzzy Sets Syst. 157(19), 2627–2647 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Kao, C., Chyu, C.-L.: A fuzzy linear regression model with better explanatory power. Fuzzy Sets Syst. 126(3), 401–409 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gładysz, B., Kuchta, D.: A method of variable selection for fuzzy regression-the possibility approach. Oper. Res. Decis. 21(2), 5–15 (2011)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Chen, L.H., Chang, C.J.: Approaches to select suitable subset of explanatory variables for establishing fuzzy regression models. J. Intell. Fuzzy Syst. 34(1), 437–457 (2018)CrossRefGoogle Scholar
  16. 16.
    Kim, B., Bishu, R.R.: Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets Syst. 100(1–3), 343–352 (1998)CrossRefGoogle Scholar
  17. 17.
    Hosseinzadeh, E., Hassanpour, H., Arefi, M., Aman, M.: A weighted goal programming approach to fuzzy linear regression with quasi type-2 fuzzy input-output data. TWMS J. Appl. Eng. Math. 6(2), 193–212 (2016)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Campobasso, F., Fanizzi, A.: Goodness of fit measures and model selection in a fuzzy least squares regression analysis. In: Madani, K., et al. (eds.) Studies in Computational Intelligence, vol. 465, pp. 241–257. Springer, Berlin (2013)CrossRefGoogle Scholar
  19. 19.
    Zimmermann, H.-J.: Fuzzy Set Theory and Its Applications, 3rd edn. Dordrecht, Kluwer (1996)CrossRefzbMATHGoogle Scholar
  20. 20.
    Xu, R., Li, C.: Multidimensional least-squares fitting with a fuzzy model. Fuzzy Sets Syst. 119(2), 215–223 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Mallows, C.L.: Some comments on C P. Technometrics 15(4), 661–675 (1973)zbMATHGoogle Scholar
  23. 23.
    Abdalla, H.A., El-Sayed, A.A., Hamed, R.: Fuzzy multinomial logistic regression analysis: a multi-objective programming approach. In: AIP Conference Proceedings (2017)Google Scholar
  24. 24.
    Sheikh Asadi, H.: Effects of Distraction on Pain Relief with a Loved One’s Voice While Pulling a Chest Tube After Open Heart Surgery. Shahid Beheshti University of Medical Sciences, Tehran (2013)Google Scholar
  25. 25.
    Taheri, S.M., Salmani, F., Abadi, A., Majd, H.A.: A transition model for fuzzy correlated longitudinal responses. J. Intell. Fuzzy Syst. 30(3), 1265–1273 (2016)CrossRefzbMATHGoogle Scholar
  26. 26.
    Taheri, S.M., Kelkinnama, M.: Fuzzy linear regression based on least absolutes deviations. Iran. J. Fuzzy Syst. 9, 121–140 (2012)MathSciNetzbMATHGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association 2019

Authors and Affiliations

  • Fatemeh Salmani
    • 1
  • Seyed Mahmoud Taheri
    • 2
    Email author
  • Alireza Abadi
    • 3
  1. 1.Department of Epidemiology and Biostatistics, Faculty of HealthBirjand University of Medical ScienceBirjandIran
  2. 2.School of Engineering Science, College of EngineeringUniversity of TehranTehranIran
  3. 3.Department of Community Medicine, Faculty of MedicineShahid Beheshti University of Medical SciencesTehranIran

Personalised recommendations