Modelling beyond regression functions: an application of multimodal regression to speed–flow data

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.