A statistical inference framework for FSNBLR: Modeling underdeveloped regional status in Eastern Indonesia

Persistent regional disparities in Indonesia, particularly in Eastern provinces, necessitate advanced modeling to understand underdevelopment determinants. This study enhances the Fourier Series Nonparametric Binary Logistic Regression (FSNBLR) model by introducing a statistical inference framework comprising simultaneous and partial hypothesis testing using the Likelihood Ratio Test (LRT). Applying the model to data from 232 regencies in Eastern Indonesia (2021) identifies infrastructure quality and local fiscal capacity as significant predictors of underdevelopment. Compared with the conventional Binary Logistic Regression (BLR), the FSNBLR with significant parameters demonstrates superior classification accuracy and lower AIC values, effectively capturing nonlinear relationships among predictors. The proposed framework strengthens the inferential foundation of FSNBLR and broadens its applicability to complex binary response analyses in socioeconomic studies. The highlights of this study are: Developed inferential hypothesis testing for the FSNBLR model. Implemented LRT for simultaneous and partial inference. The FSNBLR model outperforms BLR model in capturing nonlinearities.