Anna Islamiyati, Fatmawati and Nur Chamidah

DOI: 10.14456/sjst-psu.2020.115

pp. 897 - 909

Abstract

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.

Keywords

• penalized spline estimator
• multi-smoothing parameters
• longitudinal data
• blood glucose levels
• type 2 diabetes
  patients