A Truncated Spline Nonparametric Logistic Regression: Simultaneous Testing and Model Comparison

Abstract

Regression is widely used in statistical analysis. For binary response variables, Logistic Regression has been widely applied due to its interpretability. However, conventional Binary Logistic Regression (BLR) generally assumes a linear relationship between predictors and the response, which may limit its ability to capture complex data patterns. To address this limitation, this study examines a Truncated Spline Nonparametric Logistic Regression (TSNLR) model that provides greater flexibility in modeling nonlinear relationships through the use of knot points. Statistical inference of the proposed model is examined using simultaneous hypothesis testing to assess the significance of predictor variables. The TSNLR model is applied to Human Development Index (HDI) data of cities/districts in Indonesia, which are classified into high and low HDI categories. Model performance is evaluated and compared with BLR using classification performance metrics. These findings suggest that TSNLR is an effective alternative for modeling binary response data with complex predictor relationships and can offer improved interpretability in applied statistical analysis.