Nonparametric truncated spline regression on modelling mean years schooling of regencies in Java

Abstract

Education is widely accepted to be a fundamental resource, both for individuals and societies. Mean Years of Schooling (MYS) is one of the two education indicators in UNDP's Human Development Index (HDI) and can reflect important aspects related to the degree of education in some countries or regencies. The results of the preliminary identification show that the relationship patterned between MYS as response and all predictor variables does not follow particular pattern (linear or a certain degree polynomial). Therefore the analysis of nonparametric regression should be performed. The scatter plot between response and predictors variables shows patterns that change at certain sub-intervals so the suitable method used is the nonparametric regression with truncated spline estimation. Truncated polynomial spline regression is used because it has an advantage which the model tends to find its own estimate of the data pattern wherever it moves. In this regard, the objective of this research is to get estimator of nonparametric truncated spline regression and investigate the significant factors affecting mean years of schooling of 119 regencies across Java in 2017. The numbers of knot points used are one, two, three, and combination of knot points. The method of selecting optimum knots uses minimum Generalized Cross Validation (GCV) and the best model is obtained with combination knots with a coefficient of determination 87.99 percent. Based on the result of a statistical significance test, the factors that significantly affect MYS are population density, student-teacher ratio, per capita gross regional domestic products, and student-school ratio. The results of this study are expected to be the input for the government to regulate policy in order to improve the overall national mean years of schooling.