Polynomial spline regression: Theory and Application

TL;DR

This paper explores polynomial spline regression models, comparing their theoretical properties and practical performance, and finds P-spline models to be the most effective for prediction tasks.

Contribution

It provides a comprehensive comparison of Polynomial Spline models, including Truncated Power, B-spline, and P-spline, with a focus on prediction accuracy using cross-validation.

Findings

P-spline outperforms other spline models in prediction accuracy

Cross-validation is effective for model selection in spline regression

Theoretical insights into spline model properties are discussed

Abstract

To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more efficient to use flexible regression techniques that can automatically handle nonlinear behavior. One such method is the Polynomial Spline (PS) regression. Because the number of possible spline regression models is many, efficient strategies for choosing the best one are required. This study investigates the different spline regression models (Polynomial Spline based on Truncated Power, B-spline, and P-Spline) in theoretical and practical ways. We focus on the fundamental concepts as the spline regression is theoretically rich. In particular, we focus on the prediction using cross-validation (CV) rather than interpretation, as polynomial splines are challenging to interpret. We compare different PS models based on a real data set and conclude that the P-spline model is the best.