Penalized spline estimator with multi smoothing parameters in bi-response multi-predictor nonparametric regression model for longitudinal data

Penalized spline estimators that depend on a smoothing parameter is one type of estimator used in the estimation regression curve in nonparametric regression. The smoothing parameter is one of the most important components in the penalized spline estimator because it is related to the smoothness of the regression curve. In this paper, we determine the optimum number of smoothing parameters in a bi-response multi-predictor nonparametric regression model. Based on the result of the simulation study, we find that the optimum number of smoothing parameters corresponds to the number of predictor variables in each response. We also apply the estimated model to case of blood glucose levels in type 2 diabetes patients. The results of study show that there are different patterns of changes in blood glucose levels, both day and night, based on the length of care, the calorie diet, and the carbohydrate diet.