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Modelling beyond regression functions: an application of multimodal regression to speed–flow data
Author(s) -
Einbeck Jochen,
Tutz Gerhard
Publication year - 2006
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2006.00547.x
Subject(s) - nonparametric regression , simple (philosophy) , conditional expectation , regression , nonparametric statistics , regression analysis , computer science , flow (mathematics) , noise (video) , algorithm , local regression , mathematics , simple linear regression , statistics , artificial intelligence , machine learning , polynomial regression , philosophy , geometry , epistemology , image (mathematics)
Summary. 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.