Comparative Analysis of Parametric and Nonparametric Methods in Modeling Under-Five Malnutrition Prevalence Across Indonesia

Abstract

Malnutrition prevalence among children under five in Indonesia varied widely across provinces in 2024, ranging from 8.70% to 37.00%. Addressing this issue supports the global Sustainable Development Goals (SDGs) agenda, particularly SDG 2 (Zero Hunger) and SDG 3 (Good Health and Well-being). While most studies rely on multiple linear regression, its strict assumption of linearity is often violated in practice. This study conducts a comparative analysis between multiple linear regression and nonparametric penalized spline regression to model the effects of professional-assisted deliveries, safe sanitation access, complete basic immunization, and households at risk of stunting across 36 Indonesian provinces. Cross-sectional data for 2024 from the Central Bureau of Statistics (BPS) were analyzed, using MSE, R², and GCV for model comparison. The multiple linear regression model yielded an MSE of 18.812 and an R²  of 53.03%. Conversely, the penalized spline model (second-order polynomial, three knot points, λ = 0.0004) achieved a substantially lower MSE of 2.653 and a higher R² of 92.31%, demonstrating its superior capability in capturing nonlinear patterns. Regarding predictor significance, both models consistently identified safe sanitation, complete basic immunization, and households at risk of stunting as influential factors. However, professional assisted deliveries showed no significant effect in the nonparametric model. These findings confirm that the penalized spline approach provides more accurate estimates and is better suited for modeling provincial level malnutrition determinants.