Parameter Interval Estimation of Semiparametric Spline Truncated Regression Model for Longitudinal Data

Abstract

Regression analysis is one method in statistics that is used to determine the pattern of functional relationships between response variables with predictor variables. Semiparametric regression approach is a combination of parametric regression and nonparametric regression. The most popular estimator for nonparametric regression or semiparametric regression is spline truncated estimator. Spline is the estimation method that is most often used because it has excellent statistical interpretation and visual interpretation compared to other methods. Regression modelling using longitudinal data is often found in everyday life, where observations are carried out for each subject over a period of time. Interval estimation is often examined by nonparametric regression and semiparametric regression; this estimation aims to determine predictor variables that have a significant influence on the response variable. One indicator used in poverty analysis is the poverty line. Based on Indonesia’s macro poverty analysis calculations, in the period March 2016 to March 2017, the poverty line increased by 5.67 percent, with increases in urban and rural areas at 5.79 percent and 5.19 percent respectively. Modelling using semiparametric spline truncated regression for longitudinal data on data on the percentage of poor people in Indonesia produces the best model using W1 weighting and one point knot. Based on the results of the study with a significance level of 0.05, it was found that the percentage of poor people was influenced by the human development index (HDI) and the unemployment rate. This semiparametric regression model has a minimum GCV value of 1.677, MSE of 5.477 × 10−2 and R2 value of 98.67%.