Spline Truncated Nonparametric Regression Estimator on the Status of Unmet Need in East Java Province 2023

Abstract

Nonparametric regression has been widely developed for quantitative responses, yet methodological extensions for categorical response data remain relatively limited. In particular, although truncated spline estimators are well known for accommodating changing regression patterns through knot points, their application to categorical outcomes has not been adequately developed in previous studies. This study aimed to develop a truncated spline nonparametric regression estimator for categorical data and to evaluate its performance in modelling the status of unmet need in East Java Province in 2023. The study combined theoretical development with an empirical application using secondary data from 38 regencies/cities and three predictor variables related to demographic and socio-economic conditions. Model performance was assessed using deviance, classification accuracy, sensitivity, specificity, area under the curve (AUC), and Press’s Q statistic. The results show that the proposed truncated spline nonparametric regression outperformed binary logistic regression, yielding a smaller deviance value (15.9745 vs. 30.9507), higher accuracy (86.8421% vs. 76.3158%), and stronger discriminatory ability, as indicated by a higher AUC (86.3077% vs. 72.7692%). The proposed model also produced a larger Press’s Q statistic (20.6316), exceeding the chi-square benchmark and indicating classification performance better than chance. These findings suggest that truncated spline nonparametric regression provides a flexible and effective alternative for modelling categorical outcomes characterized by potentially nonlinear relationships.