Fast Grid Search Algorithms for Multi-phase Regression Models

Abstract

This thesis focuses on a special case of threshold models called continuous multi-phase regression models, which are characterized by the presence of multiple threshold parameters. This type of methods provides a flexible and interpretable way to model nonlinear relationships with multiple phase changes. We develop a fast grid search algorithm for fitting multi-phase regression models with particular attention to three-phase linear models. The proposed algorithm is shown to have significantly greater computational efficiency compared to the brute force grid search procedure. In addition, the finite sample performance of the three-phase model estimators is investigated through two series of Monte Carlo experiments.