Analysis Spatial Heterogeneity of the Human Development Index in Central Java Using Bayesian Intrinsic Conditional Autoregressive Multinomial Logistic Regression
Keywords:
Human Development Index, Spatial Bayesian, ICAR, Multinomial Logistic RegressionAbstract
The Human Development Index (HDI) is an important indicator used to measure human development achievements in terms of health, education, and standard of living. Disparities in HDI values across districts/cities in Central Java Province indicate the presence of spatial dependence, thus requiring an analytical approach that can accommodate spatial structure. This study aims to model HDI categories using a spatial Bayesian multinomial logistic regression (MLR) with an intrinsic conditional autoregressive (ICAR) prior. Spatial autocorrelation is tested using Moran’s Index, while parameter estimation is conducted using the markov chain monte carlo (MCMC) method with the no-u-turn sampler (NUTS) algorithm. The model is evaluated using smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). The results show the presence of positive spatial autocorrelation in the HDI distribution and spatial effect variation across regions, reflecting geographical relationships. Most predictor variables do not show significant effects as their 95% credible intervals still include zero; however, the direction of the coefficients indicates relationships between socio-economic factors and HDI categories. The spatial Bayesian MLR ICAR model is able to capture spatial dependence in the HDI data and demonstrates stable predictive performance. These findings provide important insights into understanding human development patterns and can serve as a basis for more targeted development policy formulation.
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