Penalized Multivariate Adaptive Regression Splines with Generalized Cross Validation for Modeling Health Insurance Ownership in East Java - Deby Victoria; Addina Nurkamila; Yanuar Ibnu Ridho; Rafly Tawekal; Dita Amelia (Inferensi, 2026)
The average programmatic health insurance coverage is a key indicator of public welfare and the effectiveness of healthcare policies. This study proposes the use of Penalized Multivariate Adaptive Regression Splines (PMARS) with Generalized Cross Validation (GCV) to model the determinants of this average coverage rate across 38 regencies and cities in East Java Province, using secondary data from the 2025 BPS East Java publication. Several PMARS specifications are evaluated by varying polynomial degrees, numbers of basis functions, and penalty values to identify the optimal model structure. The PMARS approach effectively captures nonlinear relationships, interaction effects, and variable importance within a flexible regression framework. The optimal model is a quadratic specification consisting of 16 basis functions, a maximum interaction of two, and an optimal penalty parameter, explaining 94.46% of the variability in the average health insurance coverage with a minimum GCV value of 5.49654. Access to improved sanitation, clean water, and health complaints are identified as the most influential determinants, all exhibiting positive associations that drive the need for formal financial protection. These results demonstrate the effectiveness of the GCV-PMARS methodology for modeling complex socio-health data and provide empirical insights to support policies aimed at strengthening universal health coverage, ensuring equitable programmatic utilization, and advancing Sustainable Development Goal 3 on Good Health and Well-Being.