Estimation of Stunting and Wasting Prevalence in Southern Part of Sumatra Using Nadaraya-Watson Kernel and Penalized Spline

Cinta Rizki Oktarina; Sigit Nugroho; Idhia Sriliana

doi:10.31764/jtam.v10i2.36177

Estimation of Stunting and Wasting Prevalence in Southern Part of Sumatra Using Nadaraya-Watson Kernel and Penalized Spline

Cinta Rizki Oktarina, Sigit Nugroho, Idhia Sriliana

Abstract

This study aims to estimate the prevalence of stunting and wasting in the southern region of Sumatra using a bivariate nonparametric regression framework based on the Nadaraya-Watson Kernel and Penalized Spline estimators with Penalized Weighted Least Squares (PWLS). The analysis utilizes data from the 2023 Indonesian Toddler Nutrition Survey, comprising 60 regencies and cities across five provinces, namely Bengkulu, South Sumatra, Lampung, Jambi, and Bangka Belitung. By jointly modeling stunting and wasting as correlated response variables, this study seeks not only to compare methodological performance, but also to provide empirical insights into the nonlinear patterns underlying child nutritional outcomes influenced by maternal-child health and socioeconomic conditions. Model performance was evaluated using the Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and the coefficient of determination (R²). The empirical results indicate that the Nadaraya-Watson Kernel estimator outperforms the Penalized Spline approach, yielding a substantially lower prediction error (MSE = 0.0008), high goodness-of-fit values (R² of 99.98% for stunting and 99.95% for wasting), and relatively small RMSE values of 0.038 and 0.017, respectively. These findings suggest that the kernel-based estimator provides stable and accurate predictions within the data structure considered, particularly in capturing complex nonlinear relationships between predictors and nutritional outcomes. Furthermore, the results reveal that the effects of health-related and socioeconomic factors vary across different prevalence levels, underscoring the importance of nonparametric methods in accommodating heterogeneous and nonlinear response patterns. In line with previous evidence emphasizing integrated, multisectoral approaches to child nutrition improvement, the findings highlight the relevance of combining health interventions with broader social protection strategies. Nevertheless, the interpretation of results is subject to methodological caution, given the limited sample size and the aggregated nature of the data. Overall, this study demonstrates the potential of bivariate nonparametric regression as a complementary analytical tool for health data analysis and evidence-based policy formulation related to stunting and wasting reduction.

Keywords

Bivariate Nonparametric Regression; Kernel Nadaraya Watson; Penalized Spline; Stunting; Wasting.

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DOI: https://doi.org/10.31764/jtam.v10i2.36177