Penalized Spline Regression Modeling on the Human and Cultural Development Index (IPMK) for 2022

Abstract

Human and cultural development is a multidimensional phenomenon whose relationship with socioeconomic factors is often complex and nonlinear, making it challenging to model with conventional parametric approaches. This study aims to model the influence of socioeconomic variables on the Human and Cultural Development Index (IPMK) across 34 provinces in Indonesia in 2022 using the nonparametric Penalized Spline (P-spline) regression method within a Generalized Additive Model (GAM) framework. Secondary data from the Central Statistics Agency (BPS) were used, with predictor variables including School Participation Rate (APS), percentage of access to safe drinking water, Gini Ratio, per capita expenditure, average years of schooling (RLS), and open unemployment rate (TPT). Initial data exploration via scatterplots confirmed nonlinear relationship patterns between the predictor variables and IPMK. The best model was obtained using a first-order cubic spline with 10 knot points, selected based on the minimum Generalized Cross Validation (GCV) criterion. The modeling results demonstrated excellent performance, with an Adjusted R² value of 0.842 and a Deviance Explained of 92.3%. Significance analysis indicated that access to safe drinking water, per capita expenditure, average years of schooling, and the open unemployment rate significantly influence IPMK. Visual interpretation of the significant spline curves revealed informative relationship patterns, such as the diminishing returns effect of per capita expenditure. This study concludes that the P-spline approach is effective and interpretable for modeling complex nonlinear relationships in development data, providing a richer evidence base for policy formulation.