Spline Estimator for Bi-Responses and Multi-Predictors Nonparametric Regression Model in Case of Longitudinal Data

Abstract

Nonparametric regression approach is used when the shape of the curve regression is unknown. The spline estimator approach for longitudinal data can accommodate the correlation between observations within the same subject, which is not found in the cross-section data, so that the autocorrelation assumption problem can be resolved. On the other hand, with bi-responses approach, it will accommodate any correlation between each response variables. The purposes of this study are (1) to obtain the function form of the nonparametric bi-responses and multipredictorsregression on longitudinal data, (2) to obtain the spline estimator in estimating the nonparametric bi-responses and multipredictorsregression curve on longitudinal data and (3) to apply the spline estimator in estimating the curve of nonparametric bi-responses and multi-predictorsregression on longitudinal data. Bi-responses and multipredictors nonparametric regression of the spline estimator on longitudinal data which meet the criteria of minimizing Penalized Weighted Least Square (PWLS). Application of data set (Patient in Pulmonary Tuberculosis) result shows that the spline estimator can be applied which gives the value of R 2 of 97.77%.

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Comparison of spline estimator at various levels of autocorrelation in smoothing spline non parametric regression for longitudinal data

“…is assumed NT-variat normal distribution, with mean E (  ) = (NT-vector) and the variancecovariance matrix Var (  ) = Σ (matrix measuring NT × NT) as follows ( [8], [9], 8], [11]):…”

“…Spline approach generally specify i f in equation ( 1) in the form of regression curve shape is unknown, but i f it's assumed smooth, in the sense of space is contained in a particular function, especially Sobolev spaces or written ( [8], [9], 8], [11]),…”

“…Considering the equation that is function f d c  TV , then the nonparametric regression model ( 1) can be stated as [8]:…”