Comparing of Car-Bym, Generalized Poisson, and Negative Binomial Models on Tuberculosis Data in Banyumas Districs
Pembandingan Model Car-Bym, Generalized Poisson, dan Binomial Negatif pada Data Tuberkolosis di Kabupaten Banyumas
In 2019 the number of people with TB (Tuberculosis) in Banyumas, Central Java, is high (1,910 people have been detected with TB). The number of people infected Tuberculosis (TB) in Banyumas is the count data and it is also the area data. In modeling, the parameter estimation and characteristic of the data need to be considered. Here, we studied comparing Generalized Poisson (GP), negative binomial (NB), and Poisson and CAR.BYM model for TB cases in Banyumas. Here, we use two methods for parameter estimation, maximum likelihood estimation (MLE) and Bayes. The MLE is used for GP and NB models, whereas Bayes is used for Poisson and CAR-BYM. The results showed that Poisson model detected overdispersion where deviance value is 67.38 for 22 degrees of freedom. Therefore, ratio of deviance to degrees of freedom is 3.06 (>1). This indicates that there was overdispersion. The folowing GP, NB, Poisson-Bayes and CAR-BYM are used to modeling TB data in Banyumas and we compare their RMSE. With refer to RMES criteria, we found that CAR-BYM is the best model for modeling TB in Banyumas because its RMSE is smallest.
Aswi, A., Cramb, S., Duncan, E., & Mengersen, K. (2020). Evaluating the impact of a small number of areas on spatial estimation. International Journal of Health Geographics, 19(1), 1–14.
Banerjee, S., Carlin, B. P., & Gelfand, A. E. (2014). Hierarchical modeling and analysis for spatial data. CRC press.
Besag, J., & Kooperberg, C. (1995). On conditional and intrinsic autoregressions. Biometrika, 82(4), 733–746.
Cressie, N. A. (1993). Statistics for spatial data. John Willy and Sons. Inc., New York.
De Oliveira, V. (2012). Bayesian analysis of conditional autoregressive models. Annals of the Institute of Statistical Mathematics, 64(1), 107–133.
Gaetan, C., & Guyon, X. (2010). Spatial statistics and modeling (Vol. 90). Springer.
Han, X., & Lee, L. (2013). Bayesian estimation and model selection for spatial Durbin error model with finite distributed lags. Regional Science and Urban Economics, 43(5), 816–837.
Hendricks, J., & Neumann, C. (2020). A Bayesian approach for the analysis of error rate studies in forensic science. Forensic Science International, 306, 110047.
Ibrahim, J., Chen, M., & Sinha, D. (2001). Bayesian Survival Analysis Springer Series in Statistics. New York, NY: Springer. Doi, 10, 978–1.
Iddrisu, A.-K., & Amoako, Y. A. (2016). Spatial Modeling and Mapping of Tuberculosis Using Bayesian Hierarchical Approaches. Open Journal of Statistics, 6(3), 482–513.
Kyung, M., & Ghosh, S. (2014). Maximum likelihood estimation for generalized conditionally autoregressive models of spatial data. Journal of the Korean Statistical Society, 43, 339–353.
MacNab, Y. C., Farrell, P. J., Gustafson, P., & Wen, S. (2004). Estimation in Bayesian disease mapping. Biometrics, 60(4), 865–873.
McCullagh, P., & Nelder, J. A. (1989). Generalized Linear Models (Vol. 37). CRC Press.
Obaromi, D. (2019). Spatial Modelling of Some Conditional Autoregressive Priors in A Disease Mapping Model: The Bayesian Approach. Biomedical Journal of Scientific & Technical Research, 14(3).
Srinivasan, R., & Venkatesan, P. (2014). Bayesian random effects model for disease mapping of relative risks. Ann Biol Res, 5(1), 23–31.
Stern, H. S., & Cressie, N. (2000). Posterior predictive model checks for disease mapping models. Statistics in Medicine, 19(17‐18), 2377–2397