Enhancing Beta Regression for Bounded Response Modeling Using Spline-Based Mean and Precision Functions

Abstract

Beta regression is widely used for modeling continuous outcomes constrained to the unit interval (0,1). Classical beta regression often assumes linear relationships between predictors and the mean or precision parameter, potentially limiting flexibility for complex data patterns. We propose a spline-enhanced beta regression framework that models both the mean and precision parameters using natural cubic splines. We benchmark this method against Transformed Gaussian regression, Quantile regression, using three diverse test functions: Trigonometric, Polynomial, and Exponential-Log. Extensive simulations over multiple sample sizes demonstrate that the spline-based beta regression consistently improves predictive accuracy while maintaining model interpretability. Our results suggest that spline-based extensions provide a robust and flexible alternative for bounded response modeling