The data model that is often used to determine the pattern of the relationship between the response variables and predictors is the regression model. There are three methods for estimating the regression curve, such as parametric, nonparametric, and semiparametric regression. The combination of parametric regression and nonparametric regression is semiparametric regression. Parametric regression assumes that the regression model is known based on the relationship between the response variable and the predictor variable. Nonparametric regression is assumed to be unknown in the shape of the curve because the estimated shape of the regression curve is not influenced by the subjectivity factor of the researcher. Some estimator for nonparametric regression and semiparametric regression curves include local polynomial, spline, local linear, kernel and Fourier series . Most of these estimators work cross section data case. Based on the development of data analysis in regression modeling, there are also other types of data, there are longitudinal data.
Longitudinal data is data that is observed repeatedly for each subject in several subjects taken. Longitudinal data assumes that each subject does not depend on each other but between observations in the same subject are interdependent so that there is a correlation. Longitudinal data have the advantage of being in the same number of subjects, the results of error measurements produce an estimator of the effect of a more efficient treatment because longitudinal data are estimated for each observation and are more powerful even if only using fewer subjects.
There are several approaches to estimating semiparametric regression curves, one of which is using a Fourier series estimator. One of the advantages of the Fourier series estimator is that it is able to overcome data patterns that have a trigonometric function, in this case the sine function and the cosines function. Fourier series estimators can be obtained by optimizing WLS while to estimate the optimal bandwidth parameters using the GCV method. This research discussed about weighted matrix selection is used Fourier series estimator in semiparametric regression modeling for longitudinal data.
In this study it provides a representation of the longitudinal data structure in accordance with the Fourier series estimator in semiparametric regression. The data pattern is assumed to be smooth when approached by the Fourier series estimator by determining the optimal smoothing parameters based on GCV optimization. Repeated observations of data for each independent subject are part of the longitudinal data. The relationship between subjects in the longitudinal data model is assumed to be independent from one subject to another, so there is a correlation if observations between subjects are interdependent. Studying how the observed subject changes over time is the main objective of the longitudinal data model. The combination of cross section data and time series data will become longitudinal data.
Penulis: Kuzairi
Detailed information from this research can be seen in our writing at:
https://iopscience.iop.org/article/10.1088/1742-6596/1836/1/012038
Kuzairi, Miswanto and M F F Mardianto
Published under licence by IOP Publishing Ltd
Journal of Physics: Conference Series, Volume 1836, The 4th International Conference on Combinatorics, Graph Theory, and Network Topology (ICCGANT) 2020 22-23 August 2020, East Java, Indonesia Citation Kuzairi et al 2021 J. Phys.: Conf. Ser. 1836 012038
