Spline estimator for bi-responses nonparametric regression model for longitudinal data

Regression analysis is a method used to determine the relationship between the predictor variables with the response variables. One of the uses of regression analysis is in the analysis of longitudinal data, and using bi-responses. Nonparametric regression approach is used when the shape of the curve regression is unknown, so we called the model of bi-responses nonparametric regression model for longitudinal data. The purposes of this study are to obtain the function form of the nonparametric bi-responses regression on longitudinal data, to obtain the spline estimator in estimating the nonparametric bi-responses regression curve on longitudinal data, and to apply the spline estimator in estimating the curve of nonparametric bi-responses regression on longitudinal data on simulated data. bi-responses nonparametric regression model on longitudinal data on the equation y_kit= f_ki(x_it) +ε_kithas a function form f(x) = Td + Vc. Bi-responses nonparametric regression of the spline estimator on longitudinal data which meet the criteria of minimizing Penalized Weighted Least Square (PWLS) is f_αA* (λ) y, with A* (λ) = T*(T*M^-1WT*)^-1T*M^-1W + V* M^-1W[I-T*(T*M^-1WT*)^-1T*M^-1W] The simulation results show that the spline estimator can be applied to the generation of data with m = 4 (cubic spline) which gives the value of R²of 94.63%.