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

Einbeck, Jochen; Tutz, Gerhard

doi:10.1111/j.1467-9876.2006.00547.x

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

Einbeck, Jochen; Tutz, Gerhard

Authors

Professor Jochen Einbeck jochen.einbeck@durham.ac.uk
Professor

Gerhard Tutz

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.
Publisher URL	http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2006.00547.x

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Copyright Statement
This is the accepted version of the following article: Einbeck, J. and Tutz, G. (2006), Modelling beyond regression functions: an application of multimodal regression to speed–flow data. Journal of the Royal Statistical Society: Series C (Applied Statistics), 55(4): 461-475, which has been published in final form at http://dx.doi.org/10.1111/j.1467-9876.2006.00547.x. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.