Nonparametric Biresponse Penalized Spline Regression for Modeling Stunting and Wasting in Kalimantan

Samsul Arifin; Ardiansyah Abubakar; A. Fahmi Indrayani

doi:10.31764/jtam.v10i3.38418

Nonparametric Biresponse Penalized Spline Regression for Modeling Stunting and Wasting in Kalimantan

Samsul Arifin, Ardiansyah Abubakar, A. Fahmi Indrayani

Abstract

Stunting and wasting remain major nutritional problems in Indonesia, including in Kalimantan, with considerable interregional variation. This condition suggests that the relationships between determinants and indicators of child nutritional status may be nonlinear and interdependent. This study aims to develop and implement a biresponse nonparametric penalized spline regression model to simultaneously model the prevalence of stunting (Y₁) and wasting (Y₂) in Kalimantan. The data used secondary data from the 2024 Indonesian Nutritional Status Survey (SSGI) of the Ministry of Health and official publications from Statistics Indonesia (BPS), with districts/cities in Kalimantan as the unit of analysis. The predictor variables included the percentage of households with access to improved sanitation (X₁), low birth weight (X₂), and the percentage of the population covered by health insurance (X₃). The Pearson correlation test indicated a significant association between stunting and wasting (p-value = 0.012), supporting the application of a biresponse modeling approach. Model selection was conducted simultaneously for the knot points and the smoothing parameter (λ) using the minimum Generalized Cross-Validation (GCV) criterion. The optimal configuration was obtained with one knot for each predictor, namely X₁ = 66, X₂ = 107, and X₃ = 53, with λ = 63.09 and GCV = 20.83. Model performance evaluation yielded MSE = 28.012 and R² = 0.241 for stunting, and MSE = 4.810 and R² = 0.106 for wasting. These results indicate that the biresponse penalized spline model can serve as a flexible approach for simultaneously analyzing stunting and wasting and for capturing heterogeneous, nonlinear relationships between predictors and response variables.

Keywords

Stunting; Wasting; Penalized Spline; Birespon.

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DOI: https://doi.org/10.31764/jtam.v10i3.38418