Estimation of Multivariate Adaptive Regression Splines (MARS) Model Parameters by Using Generalized Least Square (GLS) Method - Nurul Azizah Rahmadani Ritonga (JMEA : Journal of Mathematics Education and Application, 2023)
The regression analysis method for estimating the regression curve is divided into 3 (three) categories, namely parametric regression analysis, non-parametric regression analysis, and semi-parametric regression analysis. One form of non-parametric regression model is spline which can be developed into Multivariate Adaptive Regression Splines (MARS). The OLS estimation method will get good estimation results compared to other methods if the classical assumptions are fully met. However, if the classical assumptions cannot be fulfilled, this method is not good enough to use. The GLS method can be used if the classical assumptions required by the OLS method are not met. This study aims to estimate the parameters of the MARS model using the GLS method. The GLS method can be used if the classical assumptions required by the OLS method are not met. An example of a case used in the application of non-parametric estimation of the MARS model is the data on the number of doctors and gross enrollment rates for tertiary institutions in 32 districts/cities in North Sumatra in 2021. The best MARS model obtained in this study was obtained with a knot point of 21.2, 24 .2 and 27.2, with BF=6, MO=3, MI=0 with a GCV value of 6628.965. The best model obtained based on this research is as follows: