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

Year 2021, Volume: 26 Issue: 2, 94 - 101, 31.08.2021

Asuman Yılmaz H.eray Çelik

https://doi.org/10.53433/yyufbed.837533

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

• 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
• 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
• 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
• 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.
• 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.
• 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.
• Geyer, C. J. (1992). Practical markov chain montecarlo. Statistical Science, 10, 473-483.
• 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
• 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.
• 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
• Hair, F. T., William, C. B., Babin, B. T., & Anderson E. R. (2006). Overview of Multivariate Methods. Oxford, UK: Wiley & Sons.
• Huggins, J. H., Campbell, T., & Broderick, T. (2016). Coresets for scalable bayesian logistic regression. arXiv preprint arXiv:1605.06423.
• Lukman, P. A., Abdullah, S., & Rachman, A. (2021). Bayesian logistic regression and its application for hypothyroid prediction in post-radiation nasopharyngeal cancer patients. In Journal of Physics: Conference Series, 1725(1), 012010. doi:10.1088/1742-6596/1725/1/012010
• Rashwan, N. I., & El Dereny, M. (2012). The comparison between result of application Bayesian and maximum likelihood approaches on logistic regression model for prostate cancer data. Applied Mathematical Scienses, 6, 1143-1158.
• Suleiman, M., Demirhan, H., Boyd, L., Girosi, F., & Aksakalli, V. (2019). Bayesian logistic regression approaches to predict incorrect DRG assignment. Health care management science, 22(2), 364-375. doi: 10.1007/s10729-018-9444-8.
• Spyroglou, I. I., Spöck, G., Chatzimichail, E. A., Rigas, A., & Paraskakis, E. (2018). A Bayesian logistic regression approach in asthma persistence prediction. Epidemiology, Biostatistics and Public Health, 15(1). doi:10.2427/12777.
• Tektaş, D., & Günay, S. (2008). Bayesian approach to parameter estimation in binary logit models. Hacettepe Journal of Mathematics and Statistics, 37, 167-176.
• Zellner, A., & Rossi, P.E. (1984). Bayesian analysis of dichotomous quantal response models. Journal of Econometrics, 25, 365-393.