DOI: https://doi.org/10.14710/medstat.14.2.194-205

A STUDY OF GENERALIZED LINEAR MIXED MODEL FOR COUNT DATA USING HIERARCHICAL BAYES METHOD

*Etis Sunandi scopus  -  Department of Mathematics, Bengkulu University, Indonesia
Khairil Anwar Notodiputro scopus  -  Department of Statistics, IPB University, Indonesia
Bagus Sartono scopus  -  Department of Statistics, IPB University, Indonesia
Open Access Copyright (c) 2021 MEDIA STATISTIKA under http://creativecommons.org/licenses/by-nc-sa/4.0.

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Abstract
Poisson Log-Normal Model is one of the hierarchical mixed models that can be used for count data. Several estimation methods can be used to estimate the model parameters. The first objective of this study was to examine the performance of the parameter estimator and model built using the Hierarchical Bayes method via Markov Chain Monte Carlo (MCMC) with simulation. The second objective was applied the Poisson Log-Normal model to the West Java illiteracy Cases data which is sourced from the Susenas data on March 2019. In 2019, the incidence of illiteracy is a very rare occurrence in West Java Province. So that, it is suitable as an application case in this study. The simulation results showed that the Hierarchical Bayes parameter estimator through MCMC has the smallest Root Mean Squared Error of Prediction (RMSEP) value and the absolute bias is relatively mostly similar when compared to the Maximum Likelihood (ML) and Penalized Quasi-Likelihood (PQL) methods. Meanwhile, the empirical results showed that the fixed variable is the number of respondents who have a maximum education of elementary school have the greatest risk of illiteracy. Also, the diversity of census blocks significantly affects illiteracy cases in West Java 2019.
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Keywords: Absolute bias; GLMM; illiteracy; MCMC; Poisson Log-Normal

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  1. Astuti, N. K., Purhadi, P., & Andari, S. (2017). Pemodelan Angka Buta Huruf di Kabupaten/Kota se-Jawa Timur dengan Metode Geographically Weighted t Regression. Jurnal Sains Dan Seni ITS, 6(2), 224–228. https://doi.org/10.12962/j23373520.v6i2.25005
  2. Berliana, S. M., Purhadi, Sutikno, & Rahayu, S. P. (2019). Multivariate generalized Poisson regression model with exposure and correlation as a function of covariates: Parameter estimation and hypothesis testing. AIP Conference Proceedings 2192, 090001, 1–10. https://doi.org/10.1063/1.5139171
  3. Bermúdez, L., Karlis, D., & Morillo, I. (2020). Modelling unobserved heterogeneity in claim counts using finite mixture models. Risks, 8(10), 1–13. https://doi.org/10.3390/risks8010010
  4. Bolker, B. M., Brooks, M. E., Clark, C. J., Geange, S. W., Poulsen, J. R., Stevens, M. H. H., & White, J. S. S. (2009). Generalized linear mixed models: a practical guide for ecology and evolution. In Trends in Ecology and Evolution (Vol. 24, Issue 3, pp. 127–135). https://doi.org/10.1016/j.tree.2008.10.008
  5. BPS. (2020). Badan Pusat Statistik Provinsi Jawa Barat. https://jabar.bps.go.id/Istilah/index?Istilah%5Bberawalan%5D=B
  6. Breslow, N. E., & Clayton, D. G. (1993). Approximate Inference in Generalized Linear Mixed Models. Journal of the American Statistical Association, 88(421), 9–25. https://doi.org/10.2307/2290687
  7. Brostrom, G. (2020). Package ‘ glmmML ’: Generalized linear models with clustering. In Cran. http://cran.r-project.org/web/packages/glmmML/index.html
  8. Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis, third edition. In Bayesian Data Analysis, Third Edition. Chapman and Hall/CRC
  9. Hadfield, J. (2012). MCMCglmm: MCMC generalised linear mixed models
  10. Hadfield, J. D. (2015). MCMCglmm Course Notes. Notes, 1443
  11. Jiang, J. (2007). Linear and Generalized Linear Mixed Models and Their Applications. In Linear and Generalized Linear Mixed Models and Their Applications. Springer. https://doi.org/10.1007/978-0-387-47946-0
  12. Kemdikbud. (2020). Kementerian Pendidikan dan Kebudayaan » Republik Indonesia. https://www.kemdikbud.go.id/main/blog/2020/09/pemerintah-terus-berkomitmen-dalam-mengentaskan-buta-aksara
  13. Mallya, S., Sander, B., Roy-Gagnon, M. H., Taljaard, M., Jolly, A., & Kulkarni, M. A. (2018). Factors associated with human West Nile virus infection in Ontario: A generalized linear mixed modelling approach. BMC Infectious Diseases, 18(1), 1–9. https://doi.org/10.1186/s12879-018-3052-6
  14. Mariyono. (2016). Strategi Pemberantasan Buta Aksara Melalui Penggunaan Teknik Metastasis Berbasis Keluarga. Pancaran, 5(1), 55–66
  15. Maulina, R. F., Djuraidah, A., & Kurnia, A. (2019). Pemodelan Kemiskinan Di Jawa Menggunakan Bayesian Spasial Probit Pendekatan Integrated Nested Laplace Approximation (INLA). MEDIA STATISTIKA, 12(2), 140–151. https://doi.org/10.14710/medstat.12.2.140-151
  16. McCullagh, P., & Nelder, J. A. (1989). Generalized Linear Models, Second Edition, Chapman & Hall/CRC, Boca Raton, FL. In Chapman and Hall
  17. McCulloh, C. E., & Searle, S. R. (2001). Generalized, Linear, and Mixed Models (1st ed.). John Wiley & Sons, Inc
  18. Pinheiro, J. (2020). Title Linear and Nonlinear Mixed Effects Models. https://bugs.r-project.org
  19. Rao, J. N. K., & Molina, I. (2015). Small Area Estimation: Second Edition. In Small Area Estimation: Second Edition. John Wiley & Sons, Inc. https://doi.org/10.1002/9781118735855
  20. Rohmani Nur Indah. (2017). Gangguan Berbahasa: Kajian Pengantar. In UIN-Maliki Press
  21. Stroup, W. W. (2013). Generalized Linear Mixed Models - Modern Concepts, Methods and Applications. In International Statistical Review (Vol. 81, Issue 3)
  22. Sunandi, E., Notodoputro, K. A., & Sartono, B. (2021). A study on group lasso for grouped variable selection in regression model. IOP Conference Series: Materials Science and Engineering, 1115(1). https://doi.org/10.1088/1757-899x/1115/1/012089
  23. Wahyuni, S., Machfudz, M., & Badrih, M. (2017). Pemberdayaan Masyrakat Perempuan Melalui Pemberantasan Buta Aksara Guna Menumbuhkembangkan Usaha Kreatif Berbasis Literasi dan Potensi Lokal. Jurnal Inovasi Pendidikan, 1(2), 48–71
  24. Yanuar, F., Sari, P. T., & Asdi, Y. (2020). Identification Of Rainfall Distribution In West Sumatera And Assessment Of Its Parameters Using Bayes Method. MEDIA STATISTIKA, 13(2), 161–169. https://doi.org/10.14710/medstat.13.2.161-169

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