Research Article

A Bayesian Approach to Binary Logistic Regression Model with Application to OECD Data

Volume: 26 Number: 2 August 31, 2021
EN TR

A Bayesian Approach to Binary Logistic Regression Model with Application to OECD Data

Abstract

In spite of being a common method for estimating the model parameters, Maximum Likelihood (ML) method may give bias results for small sample sizes. To overcome this problem, Bayesian method is usually utilized to obtain the estimates of the model parameters as an alternative to the ML method. In this study, a real data set was analyzed by using the binary logistic regression model. Parameters of the binary logistic regression model were estimated by using ML and Bayesian methods. Modeling performance of the binary logistics regression model based on the Bayesian estimates was compared with the model based on the ML estimates. Well-known information criteria such as AIC and BIC were used in this comparison.

Keywords

Binary-Logistic regression, Maximum likelihood, Bayesian method

References

  1. Acquah, H. D. (2013). Bayesian logistic regression modelling via Markov chain Monte Carlo algorithm. Journal of Social and Development Sciences, 4, 193-197. doi: 10.22610/jsds.v4i4.751
  2. Agresti, A., & Hitchcock, D. B. (2005). Bayesian inference for categorical data analysis. Statistical Methodsand Applications, 14(3), 297-330. doi:10.1007/s10260-005-0121-y
  3. Albert, J. H., & Chib. S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669-679. doi:10.2307/2290350
  4. Cowles, M. K., & Carlin, B. P. (1996). Markov chain Monte Carlo convergence diagnostics: a comparative review. Journal of the American Statistical Association, 91, 883-904.
  5. Dagliati, A., Malovini, A., Decata, P., Cogni, G., Teliti, M., Sacchi, L., & Bellazzi, R. (2016). Hierarchical Bayesian Logistic Regression to forecast metabolic control in type 2 DM patients. In AMIA Annual Symposium Proceedings,2016, 470-479.
  6. Dos Santos, M. A., Moala, F. A., & Tachibana, V. M. (2009). Approximate Bayesian methods for logistic regression model. Revista Brasileira de Biometria, 27, 288-300.
  7. Geyer, C. J. (1992). Practical markov chain montecarlo. Statistical Science, 10, 473-483.
  8. Ghosh, J., Li, Y., & Mitra, R. (2018). On the use of Cauchy prior distributions for Bayesian logistic regression. Bayesian Analysis, 13, 359-383. doi:10.1214/17-BA1051
  9. Griffiths, D. A. (1973). Maximum likelihood estimation for the beta-binomial distribution and an application to the household distribution of the total number of cases of a disease, Biometrics, 7,637-648.
  10. Groenewald, P. C., & Mokgatlhe, L. (2005). Bayesian computation for logistic regression. Computational Statistics & Data Analysis, 48, 857-868. doi:10.1016/j.csda.2004.04.009
APA
Yılmaz, A., & Çelik, H. (2021). A Bayesian Approach to Binary Logistic Regression Model with Application to OECD Data. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 26(2), 94-101. https://doi.org/10.53433/yyufbed.837533
AMA
1.Yılmaz A, Çelik H. A Bayesian Approach to Binary Logistic Regression Model with Application to OECD Data. YYU JINAS. 2021;26(2):94-101. doi:10.53433/yyufbed.837533
Chicago
Yılmaz, Asuman, and H.eray Çelik. 2021. “A Bayesian Approach to Binary Logistic Regression Model With Application to OECD Data”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 26 (2): 94-101. https://doi.org/10.53433/yyufbed.837533.
EndNote
Yılmaz A, Çelik H (August 1, 2021) A Bayesian Approach to Binary Logistic Regression Model with Application to OECD Data. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 26 2 94–101.
IEEE
[1]A. Yılmaz and H. Çelik, “A Bayesian Approach to Binary Logistic Regression Model with Application to OECD Data”, YYU JINAS, vol. 26, no. 2, pp. 94–101, Aug. 2021, doi: 10.53433/yyufbed.837533.
ISNAD
Yılmaz, Asuman - Çelik, H.eray. “A Bayesian Approach to Binary Logistic Regression Model With Application to OECD Data”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 26/2 (August 1, 2021): 94-101. https://doi.org/10.53433/yyufbed.837533.
JAMA
1.Yılmaz A, Çelik H. A Bayesian Approach to Binary Logistic Regression Model with Application to OECD Data. YYU JINAS. 2021;26:94–101.
MLA
Yılmaz, Asuman, and H.eray Çelik. “A Bayesian Approach to Binary Logistic Regression Model With Application to OECD Data”. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 26, no. 2, Aug. 2021, pp. 94-101, doi:10.53433/yyufbed.837533.
Vancouver
1.Asuman Yılmaz, H.eray Çelik. A Bayesian Approach to Binary Logistic Regression Model with Application to OECD Data. YYU JINAS. 2021 Aug. 1;26(2):94-101. doi:10.53433/yyufbed.837533