Parameter Estimation of Partial Spline Regression Using Weighted Least Squares with Moving Average Approach

Abstract

Regression analysis is a statistical method used to model the relationship between predictor variables and a response variable. In analyzing stunting prevalence, conventional parametric approaches are often limited in capturing complex and nonlinear patterns in the data. Therefore, a semiparametric regression approach is used, as it combines parametric and nonparametric components, providing greater flexibility in modeling relationships between variables. The truncated spline method is applied to accommodate nonlinear patterns, particularly in the variable of access to proper sanitation. This study aims to model the prevalence of stunting in Indonesia using a truncated spline semiparametric regression approach, with the percentage of poor population as the parametric component and access to proper sanitation as the nonparametric component. Parameter estimation is conducted using Ordinary Least Squares (OLS) and improved using Weighted Least Squares (WLS) with a moving average approach to address heteroscedasticity. The optimal model is selected based on the minimum Generalized Cross Validation (GCV) value. The results show that the best model is obtained with order 1 and one knot point at 93.884, producing the minimum GCV value of 25.19599. The WLS approach improves the model performance, increasing the coefficient of determination (R²) from 53.25% to 74.40%, and successfully overcomes heteroscedasticity issues. The analysis also indicates that the percentage of poor population has a positive effect on stunting prevalence, while access to proper sanitation has a negative and nonlinear effect, with a stronger impact after exceeding the knot point. These findings indicate that the truncated spline semiparametric regression model with WLS estimation provides a better and more reliable approach in modeling stunting prevalence.