A unified framework of constrained regression

• DOI: 10.1007/s11222-014-9520-y
• Publication Date: 2014-10-25T02:25:00Z
• Authors: Benjamin Hofner; Thomas Kneib; Torsten Hothorn
• Keywords: FOS: Computer and information sciences; 610 Medicine & health; 10060 Epidemiology, Biostatistics and Prevention Institute (EBPI); Statistics - Applications; 01 natural sciences; Methodology (stat.ME); 03 medical and health sciences; 0302 clinical medicine; Applications (stat.AP); 1804 Statistics, Probability and Uncertainty; 2613 Statistics and Probability; 0101 mathematics; 2614 Theoretical Computer Science; Statistics - Methodology; 1703 Computational Theory and Mathematics

Generalized additive models (GAMs) play an important role in modeling and understanding complex relationships in modern applied statistics. They allow for flexible, data-driven estimation of covariate effects. Yet researchers often have a priori knowledge of certain effects, which might be monotonic or periodic (cyclic) or should fulfill boundary conditions. We propose a unified framework to incorporate these constraints for both univariate and bivariate effect estimates and for varying coefficients. As the framework is based on component-wise boosting methods, variables can be selected intrinsically, and effects can be estimated for a wide range of different distributional assumptions. Bootstrap confidence intervals for the effect estimates are derived to assess the models. We present three case studies from environmental sciences to illustrate the proposed seamless modeling framework. All discussed constrained effect estimates are implemented in the comprehensive R package mboost for model-based boosting.<br/>This is a preliminary version of the manuscript. The final publication is available at http://link.springer.com/article/10.1007/s11222-014-9520-y<br/>