Estimation of a Bi-Response Truncated Spline Nonparametric Regression Model on Life Expectancy and Prevalence of Underweight Children in Indonesia

Abstract

Researchers use the nonparametric regression method because it provides excellent flexibility in the modeling process. Nonparametric regression procedures can be used if the relationship pattern between the predictor and response variables is unknown. The truncated spline method is one of the most frequently used nonparametric regression methods. A truncated spline is a polynomial slice with continuous segmented properties, and the resulting curve is relatively smooth. The advantage of truncated splines is that they can be used on data that experience behavior changes at specific intervals. The nonparametric spline truncated bi-response regression approach is used when one or more predictor variables affect the two response variables with the assumption that there is a correlation between the response variables. This study aimed to obtain the best spline truncated bi-response nonparametric regression model on life expectancy data and the prevalence of underweight children in Indonesia in 2021. The data used comes from the Central Bureau of Statistics and the Indonesian Ministry of Health. The optimal knot point selection method uses the Generalized Cross Validation (GCV) method. The results showed that the best model formed was obtained using three-knot points based on a minimum GCV value of 22.77 and a coefficient of determination of 99.58%.