Modeling longitudinal data based on Fourier regression

Abstract

Regression analysis is an analysis in statistics for modeling the relationship between predictor variables and response variable. Regression analysis can be performed by two approaches; parametric and non-parametric models. Some commonly used estimators of nonparametric approaches are spline, local polynomial, kernel, wavelet, and Fourier. Fourier nonparametric regression is a regression based on Fourier series with cosine and sinus patterns. Regression analysis can be explored, not only for cross section data but also for longitudinal data. Longitudinal data is an observed data of some uncorrelated subjects, and each subject was observed for some periods. This research developed a nonparametric regression approach for longitudinal data by using Fourier series. One of the advantages of Fourier series is it combines additive that is able to overcome the data with recurrent and high fluctuations. The research use data with 3 subjects and 128 observations. The Fourier model by combining additive linear functions and cosine functions is more suitable for modeling repeated data that has an element of trend, as the 2nd sector.