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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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