Simultaneous inference for empirical best predictors in generalized linear mixed models: A poverty study in West JAVA

Accurate poverty mapping at the district and municipal levels remains challenging due to small sample sizes in household surveys, which often result in unstable direct estimates. To address this issue, this study employs microdata from the 2023 National Socioeconomic Survey (SUSENAS) to estimate household-level poverty proportions across 27 districts and municipalities in West Java Province using a binomial Generalized Linear Mixed Model (GLMM) combined with the Empirical Best Predictor (EBP) and Simultaneous Confidence Intervals (SCI). The GLMM framework captures household characteristics and random area effects to account for spatial heterogeneity. Three SCI approaches—Bonferroni correction, Bootstrap-t, and the Simes procedure—were implemented to evaluate EBP uncertainty while controlling the family-wise error rate. Results reveal substantial disparities, with Tasikmalaya (21.7%), Bandung Barat (15.5%), and Cianjur (12.8%) consistently above the provincial average of (6.8%), while urban areas such as Cimahi, Bekasi, and Depok report poverty rates below 2%. All methods achieved full empirical coverage (ECP = 100%), although interval widths differed: Bonferroni produced the widest intervals (AIW = 44.99), Bootstrap-t yielded the narrowest and most efficient (AIW = 29.16), and Simes provided intermediate but highly consistent results (AIW = 33.24). These findings underscore the methodological importance of integrating GLMM, EBP, and SCI for small area estimation while offering practical insights for evidence-based policy development and poverty reduction strategies in Indonesia.