Biresponse nonparametric regression model in principal component analysis with truncated spline estimator

Objectives: This study aims to model data that contain two correlated responses, multicollinearity in pre- dictors, and has a pattern that does not follow a parametric form.
Methods: We propose the use of principal component analysis of truncated splines in a biresponse model. The use of principal components to overcome correlations between predictors, and biresponse to over- come correlations between responses by involving weighted estimates from the covariance matrix. In the PCA spline contains the optimal knot points which control the accuracy of the regression curve. The knot point chosen is the point which has the smallest GCV value among all knot points. In addition, we also consider the value of MSE in showing the model’s ability.
Results: We demonstrated the ability of this method through simulation studies and obtained smaller GCV and MSE values compared to parametric regression and PCA. Furthermore, the data for type 2 dia- betes mellitus, obtained two main components with different patterns of change. Based on the analysis, it was found that LDL cholesterol, total cholesterol, and triglycerides had a greater effect on changes in the pattern of fasting blood sugar and HbA1C.
Conclusions: The small errors of the simulation data indicate the accurate capabilities of the biresponse spline PCA model. The diabetes data analysis, it shows that patients need to pay attention to their choles- terol and triglyceride levels within normal limits.