Comparison of Optimal Knots Point Selection Method With Cross Validation and Generalized Cross Validation in Nonparametric Regression Truncated Spline Biresponse

The nonparametric regression that has been widely used in recent years is a spline. Spline has a very good statistical interpretation and visual interpretation. Several studies that have been developed by researchers are uniresponse spline truncated models. This model is very good in terms of modeling smooth data but it has not been able to solve modeling problems that contain more than one response. Therefore, the researchers began to develop a bi-response spline truncated. Three things need to be considered in the use of the spline, namely determining the number of the order, the number of the knots, and the location of the knots. Cross-Validation (CV) and Generalized Cross-Validation (GCV) has developed to select the optimal knot points. However, until now there has been no research that concludes the best method between CV and GCV. This study will compare the CV and GCV methods in selecting the optimal knot point on the poverty percentage and poverty severity index in East Java using the spline truncated bi-response model. The criteria for the selected model are based on the coefficient of determination (R²). The results of the analysis show that by using the CV method, there are 3 optimal knots with R² value of 94.71%. Meanwhile, using the GCV method, there are 3 optimal knots with R² of 95.76%. From these results, it can be said that GCV is the best method for choosing the optimal knot point compared to the CV method.