Modeling Air Quality Index in Indonesia Using Smoothing Splines and Truncated Splines Regression
Keywords: air quality index (AQI), nonparametric regression, smoothing splines, truncated splines, generalized cross validation (GCV)
Abstract
The Air Quality Index (AQI) is a composite indicator that reflects regional air quality conditions and is influenced by multiple determinants with complex and nonlinear relationships. In such circumstances, parametric regression may be restrictive because it requires a predetermined functional form. This study applies spline based nonparametric regression using smoothing splines and truncated splines to model AQI in Indonesia and to compare the performance of both approaches. AQI is treated as the response variable, while population density, land cover area within and outside forest areas, and the number of motor vehicles are considered as predictor variables. For smoothing splines, the optimal smoothing parameter is selected using Generalized Cross Validation, whereas truncated splines are estimated using Ordinary Least Squares under various knot configurations and selected based on the minimum Generalized Cross Validation value. Model performance is evaluated using Generalized Cross Validation, Mean Squared Error, and Adjusted R squared. The study aims to identify the most appropriate model and to determine key factors influencing AQI variation in Indonesia, thereby providing empirical support for environmental policy making. The results show that the smoothing spline model provides better performance than the truncated spline model, with a lower Mean Squared Error (MSE) of 0.0716 and a higher Adjusted R² of 0.794. These results indicate that smoothing splines are more effective in capturing the nonlinear relationships influencing AQI variation in Indonesia.
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