Comparison of Kernel and Spline Nonparametric Regression (Case Study: Food Security Index of Jambi Province 2023)

Food security is one of the issues that plays an important role in national development, especially in regions with varying levels of economic welfare such as Jambi Province. One of the main factors affecting food security is food expenditure, which reflects the economic capacity of households to access food. The complex and non-linear relationship between Food Security Index (FSI) and Food Expenditure requires a flexible modeling approach in the analysis. This study aims to compare the performance of nonparametric regression Kernel ans Spline regression methods, namely the Nadaraya-Watson Estimator (NWE) and Local Polynomial Estimator (LPE) for Kernel Regression as well as Smoothing Spline and B-Spline for Spline Regression. The analysis was conducted using secondary data obtained from the Food Security and Vulnerability Map (FSVA) of 2023, with a total of 141 subdistricts in Jambi Province. The response variable is the Food Security Index (FSI), while the predictor variable is Food Expenditure. Model evaluation was conducted using the Mean Squared Error (MSE) and the coefficient of determination (R²). The results showed that the NWE method had the best performance with the smallest MSE value of 24.47690 and the highest R² value of 0.3332, meaning that approximately 33.32% of the variation in FSI could be explained by Food Expenditure. The LPE method showed nearly comparable performance, while Smoothing Spline and B-Spline exhibited higher prediction error rates. Therefore, the NWE method can be recommended as an effective nonparametric regression approach for modeling the relationship between food expenditure and food security.