An Empirical Study on Unmet Need: A Statistical Inference Framework for Truncated Spline Nonparametric Binary Logistic Regression (TSNLBR)

Nonparametric regression offers a flexible approach to uncover complex relationships without relying on rigid functional form assumptions. Among the available techniques, truncated spline regression serves as a powerful tool for approximating nonlinear effects. This study introduces the Truncated Spline Nonparametric Binary Logistic Regression (TSNBLR) model, specifically designed to accommodate binary response data, with a particular emphasis on developing a rigorous hypothesis testing framework. Model parameters are estimated using the Maximum Likelihood Estimation (MLE) method, while inference and evaluation are conducted through the Likelihood Ratio Test (LRT) and the Wald test. The proposed methodology is applied to unmet need data from East Java, Indonesia, where the response variable reflects the achievement of family planning targets. Empirical findings demonstrate that the truncated spline regression model not only provides a superior fit but also achieves higher classification accuracy compared to conventional Binary Logistic Regression (BLR). These results shows the effectiveness of TSNBLR in capturing nonlinear structures and enhancing the reliability of hypothesis testing in binary response modeling.