Comparing between mGCV and aGCV Methods to Choose The Optimal Knot Points in Semiparametric Regression with Spline Truncated Using Longitudinal Data

Abstract

Semiparametric regression is a combination of parametric and nonparametric components. The estimation of the semiparametric regression function uses a parametric approach and a nonparametric approach. This study uses longitudinal data. The estimation technique in this study uses Spline truncated which has very special, excellent statistical interpretation and visual interpretation. The estimation technique in longitudinal semiparametric regression uses the weighted least square (WLS). The choice of knots in semiparametric spline truncated regression is very important because the number of knot points and locations of each knot will affect the regression estimation form. The method of selecting knots in this study uses a Modification of Generalized Cross-Validation (mGCV) and aGCV. This study uses cases of life expectancy in East Java Province 2001-2015. Comparison of the two methods based on the R-square value and the value of Mean Square Error (MSE). The results show that the R-square value of mGCV is greater than aGCV and the MSE value of mGCV is smaller than aGCV. So, it can be concluded that the mGCV method is better than the aGCV method for optimal selection of knot points in the case of life expectancy in East Java Province.