Spline estimation method in nonparametric regression using truncated spline approach

Abstract

A parametric regression approach is used when the shape of the regression curve is known, and the nonparametric approach is used when the shape of the regression curve is unknown, the parametric regression model is still forced as a model of data patterns, it will cause inaccurate conclusions if the form of the function is not known. The truncated spline approach can be used to estimate curves in nonparametric regression models using a knot basis. The curve estimation method used is Weighted Least Square (WLS) for the truncated spline approach. In this study, the nonparametric regression model was implemented on fertilizer subsidy data in East Java. This study aims to examine comprehensively the factors that influence the satisfaction of the farming community. The response variable used in this study is the Courage of Field Extension Officers (Y), while the predictor variables include: Farmers National Culture (X1), Financial Reward for Field Extension Officers (X2), and Leadership Role (X3). The novelty of this research is trying to do regression modeling in which the whole relationship between the response variable and the predictor variable is non-linear. The results of the linearity assumption test show that all predictor variables show a non-linear relationship to the response variable, so it needs to be solved by nonparametric regression. The coefficient of determination shows that the variability of Courage of Field Extension Officers can be explained by 87,65% in the model, while the remaining 12,35% is explained by factors that are not included in the model.