Assessing the Application of Spline Regression Models in Capturing Nonlinear Trends and Smooth Functional Relationships

Posted: Feb 24, 2017

• Alexander Green
• Alexander Hill
• Alexander Martin

Abstract

The challenge of accurately modeling nonlinear relationships in data represents one of the most persistent problems in statistical analysis and machine learning. Traditional parametric approaches, while computationally efficient and easily interpretable, often fail to capture the complex functional forms that characterize real-world phenomena across scientific disciplines. This research addresses critical gaps in the current literature by developing and validating an adaptive knot selection methodology that optimizes spline performance across diverse application domains. Our approach integrates information-theoretic criteria with cross-validation techniques to determine both the number and placement of knots, creating a more data-driven framework for spline modeling. We investigate the performance of various spline types—including B-splines, natural splines, and smoothing splines—across multiple real-world domains.