Modeling of Human Development Index Using Bayesian Spatial Autoregressive Approach
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Keywords:
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HDI, Spatial Autoregressive, Bayesian Spatial Autoregressive, Maximum Likelihood Estimation
Abstract
Spatial regression analysis is a technique employed to examine the relationship between independent and dependent variables in datasets that exhibit regional neighborhood influences or spatial effects. When a spatial effect exists for the independent variable, the Spatial Autoregressive (SAR) regression can be utilized. The Maximum Likelihood Estimation (MLE) is a commonly used parameter estimator for SAR. However, due to the limitations of MLE, the Bayesian method provides an alternative approach for parameter estimation. This study compares the results of SAR estimations using both MLE and Bayesian methods to determine the most accurate estimation model. Both methods were implemented in this research to model the factors affecting the Human Development Index (HDI) in East Java Province for the year 2022. The findings indicate that the Bayesian SAR offers a superior proposed model compared to the MLE SAR. The factors influencing the HDI in East Java Province in 2022 include poverty, per capita expenditure, and the presence of an upper middle-class manufacturing industry.
References
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Zhang, Y., J. Jiang, and Y. Feng (2021b). Penalized Quantile Regression for Spatial Panel Data with Fixed Effects. Communications in Statistics - Theory and Methods; 1–13.
Anselin, L. (2009). Spatial Regression. In A. S. Fotheringham and P. A. Regerson, editors, The Sage Handbook of Spatial Analysis. SAGE Publications Ltd, pages 225–276.
Badan Pusat Statistik Provinsi Jawa Timur (2023). Indeks Pembangunan Manusia Provinsi Jawa Timur 2022. Badan Pusat Statistik Provinsi Jawa Timur.
Caniago, M. A. I. and M. G. Wibowo (2024). Determinants of Human Development Index in Indonesia with Maqashid Sharia Approach. Jurnal Ilmiah Ekonomi Islam, 10(1); 200.
Dai, X. and L. Jin (2021). Minimum Distance Quantile Regression for Spatial Autoregressive Panel Data Models with Fixed Effects. PLoS One, 16(12); e0261144.
Dai, X., Z. Yan, M. Tian, and M. Tang (2020). Quantile Regression for General Spatial Panel Data Models with Fixed Effects. Journal of Applied Statistics, 47(1); 45–60.
Hepple, L. W. (1995). Bayesian Techniques in Spatial and Network Econometrics: 2. Computational Methods and Algorithms. Environment and Planning A: Economy and Space, 27(4); 615–644.
Jaya, I. G. N. M., T. Toharudin, and A. S. Abdullah (2018). A Bayesian Spatial Autoregressive Model with k-NN Optimization for Modeling the Learning Outcome of the Junior High Schools in West Java. Model Assisted Statistics and Applications, 13(3); 207–219.
Jin, L., X. Dai, A. Shi, and L. Shi (2016). Detection of Outliers in Mixed Regressive-Spatial Autoregressive Models. Communications in Statistics - Theory and Methods, 45(17); 5179–5192.
Kakamu, K. and H. Wago (2008). Small-Sample Properties of Panel Spatial Autoregressive Models: Comparison of the Bayesian and Maximum Likelihood Methods. Spatial Economic Analysis, 3(3); 305–319.
Lesage, J. P. (1997). Bayesian Estimation of Spatial Autoregressive Models. International Regional Science Review, 20(1-2); 113–129.
Lesage, J. P. (1999). The Theory and Practice of Spatial Econometrics. Department of Economics, University of Toledo.
LeSage, J. P. and R. K. Pace (2009). Introduction to Spatial Econometrics. Chapman & Hall/CRC.
Ntzoufras, I. (2009). Bayesian Modeling Using WinBUGS. John Wiley and Sons.
Ogujiuba, K., L. Maponya, and N. Stiegler (2024). Determinants of Human Development Index in South Africa: A Comparative Analysis of Different Time Periods. World, 5(3); 527–550.
Oliveira, V. D. and J. J. Song (2008). Bayesian Analysis of Simultaneous Autoregressive Models. Sankhya: The Indian Journal of Statistics, Series B (2008-), 70(2); 323–350.
Parent, O. and J. P. Lesage (2008). Using the Variance Structure of the Conditional Autoregressive Spatial Specification to Model Knowledge Spillovers. Journal of Applied Econometrics, 23(2); 235–256.
Tyas, D. P. P. and N. M. Sukartini (2022). Determinants of the Human Development Index (HDI) in Indonesia, 2014–2021. Media Trend, 17(2); 481–495.
Ver Hoef, J. M., E. E. Peterson, M. B. Hooten, E. M. Hanks, and M.-J. Fortin (2018). Spatial Autoregressive Models for Statistical Inference from Ecological Data. Ecological Monographs, 88(1); 36–59.
Yanuar, F., T. Abrari, and I. R. Hg (2023a). The Construction of Unemployment Rate Model Using SAR, Quantile Regression, and SARQR Model. Pakistan Journal of Statistics and Operation Research, 19(3); 447–458.
Yanuar, F., T. Abrari, I. Rahmi HG, and A. Zetra (2023b). Spatial Autoregressive Quantile Regression with Application on Open Unemployment Data. Science and Technology Indonesia, 8(2); 321–329.
Yasin, H., A. R. Hakim, and B. Warsito (2020). Development Life Expectancy Model in Central Java Using Robust Spatial Regression with M-Estimators. Communications in Mathematical Biology and Neuroscience, 69; 1–16.
Yasin, H., B. Warsito, A. R. Hakim, and R. N. Azizah (2022). Life Expectancy Modeling Using Modified Spatial Autoregressive Model. Media Statistika, 15(1); 72–82.
Yu, T., F. Gao, X. Liu, and J. Tang (2022). A Spatial Autoregressive Quantile Regression to Examine Quantile Effects of Regional Factors on Crash Rates. Sensors, 22(5); 1–15.
Zhang, J., Q. Lu, L. Guan, and X. Wang (2021a). Analysis of Factors Influencing Energy Efficiency Based on Spatial Quantile Autoregression: Evidence from the Panel Data in China. Energies, 14(2); 504.
Zhang, Y., J. Jiang, and Y. Feng (2021b). Penalized Quantile Regression for Spatial Panel Data with Fixed Effects. Communications in Statistics - Theory and Methods; 1–13.
Authors
Yanuar, F., Wulandari, S., Asdi, Y., Zetra, A., & Haripamyu. (2025). Modeling of Human Development Index Using Bayesian Spatial Autoregressive Approach. Science and Technology Indonesia, 10(1), 72–79. https://doi.org/10.26554/sti.2025.10.1.72-79
This work is licensed under a Creative Commons Attribution 4.0 International License.