Modelling beyond regression functions: An application of multimodal regression to speed-flow data

Einbeck, Jochen; Tutz, Gerhard

Abstract

For speed–flow data, which are intensively discussed in transportation science, common nonparametric regression models of the type y=m(x)+noise turn out to be inadequate since simple functional models cannot capture the essential relationship between the predictor and response. Instead a more general setting is required, allowing for multifunctions rather than functions. The tool proposed is conditional modes estimation which, in the form of local modes, yields several branches that correspond to the local modes. A simple algorithm for computing the branches is derived. This is based on a conditional mean shift algorithm and is shown to work well in the application that is considered.

Citation

Einbeck, J., & Tutz, G. (2006). Modelling beyond regression functions: An application of multimodal regression to speed-flow data. Journal of the Royal Statistical Society: Series C, 55(4), 461-475. https://doi.org/10.1111/j.1467-9876.2006.00547.x

• Journal Article Type: Article
• Publication Date: Aug 1, 2006
• Deposit Date: Feb 29, 2008
• Publicly Available Date: May 9, 2016
• Journal: Journal of the Royal Statistical Society: Series C
• Print ISSN: 0035-9254
• Electronic ISSN: 1467-9876
• Publisher: Royal Statistical Society
• Peer Reviewed: Peer Reviewed
• Volume: 55
• Issue: 4
• Pages: 461-475
• DOI: https://doi.org/10.1111/j.1467-9876.2006.00547.x
• Keywords: Conditional density, Multi-valued regression, Smoothing, Speed-flow curves.
• Public URL: https://durham-repository.worktribe.com/output/1580665
• Publisher URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2006.00547.x