The purpose of this research are: (1) to obtain spline function estimation in nonparametric regression for longitudinal data with and without considering the autocorrelation between data of observation within subject, (2) to develop the algorithm that generates simulation data with certain autocorrelation level based on size of sample (N) and error variance ( EV), (3) to establish shape of spline estimator in nonparametric regression for longitudinal data to simulation with various level of

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... correlation, as well as compare DM and TM approaches in predicting spline estimator in the data simulation with different of autocorrelation observational data on within subject. The results of the application as follows: (a) Implementation of smoothing spline with PWLS approach with or without consideration of autocorrelation in general (in all sizes and all Downloaded by [University of Virginia, Charlottesville] at 10:55 09 October 2017 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 2 error variances levels) provides significantly different spline estimator when the autocorrelation level > 0.8. (b) spline estimator in nonparametric regression smoothing spline with PWLS approach with or without consideration of autocorrelation in all sizes observations showed significantly different results when the autocorrelation level > 0.8, whereas the size of a small observation when the level of autocorrelation > 0.7, the size of the observation was and the size of a large observation when the level of autocorrelation> 0.8. (c) spline estimator in nonparametric regression smoothing spline with PWLS approach with or without consideration of autocorrelation in all the error variance give significantly different results when the autocorrelation level> 0.8, whereas the small variance error when autocorrelation level> 0.7, error variance was and the error variance is greater when the level of autocorrelation of 0.8.