Poverty Gap Index Modeling in Bengkulu Province using Truncated Spline Regression for Longitudinal Data

This study utilized nonparametric truncated spline regression on longitudinal data to model the poverty gap index in Bengkulu Province. The poverty gap index (PGI-P1) is an essential indicator generated by BPS for poverty measurement. Bengkulu is one of the provinces in Indonesia with a significant poverty rate. The PGI-P1 data observed in several regions over multiple time periods constitutes a longitudinal observation. Longitudinal data modeling is widely carried out by employing parametric methods. Sometimes, the obtained estimators might be severely biased when the parametric model is miss-specified and lead to erroneous conclusions. In this study, the researcher proposed a nonparametric regression method for longitudinal data employing truncated spline estimator which is more flexible and is able to enhance estimation robustness. The best spline model was selected by using the generalized cross validation (GCV) method in determining the optimum knot point. In accordance with the analysis result, the best model for modeling PGI-P1 in Bengkulu is a linear truncated spline regression model with two knots which possesses a minimum GCV value 1.569 × 10^-4, this model provides R-square equal to 99.89% and MSE equal to 1.089 × 10^-8. These empirical findings imply that modeling the case with truncated spline nonparametric regression for longitudinal data is appropriate. Furthermore, the model can make good estimations based on the obtained data visually.