A Truncated Spline and Local Linear Mixed Estimator in Nonparametric Regression for Longitudinal Data and Its Application

Abstract

Longitudinal data modeling is widely carried out using parametric methods. However, when the parametric model is misspecified, the obtained estimator might be severely biased and lead to erroneous conclusions. In this study, we propose a new estimation method for longitudinal data modeling using a mixed estimator in nonparametric regression. The objective of this study was to estimate the nonparametric regression curve for longitudinal data using two combined estimators: truncated spline and local linear. The weighted least square method with a two-stage estimation procedure was used to obtain the regression curve estimation of the proposed model. To account for within-subject correlations in the longitudinal data, a symmetric weight matrix was given in the regression curve estimation. The best model was determined by minimizing the generalized cross-validation value. Furthermore, an application to a longitudinal dataset of the poverty gap index in Bengkulu Province, Indonesia, was conducted to illustrate the performance of the proposed mixed estimator. Compared to the single estimator, the truncated spline and local linear mixed estimator had better performance in longitudinal data modeling based on the GCV value. Additionally, the empirical results of the best model indicated that the proposed model could explain the data variation exceptionally well.

Keywords

• local linear
• longitudinal data
• mixed estimator
• nonparametric regression
• poverty gap index
• truncated spline