Extending geographically weighted regression from points to flows: a rail-based case study

• Published in: Proceedings of the Institution of Mechanical Engineers. Part F, Journal of rail and rapid transit Journal of rail and rapid transit, 2013-11, Vol.227 (6), p.724-734
• Main Authors: Blainey, Simon P, Preston, John M
• Format: Article
• Language: English
• Subjects: Approximation; Calibration; Comparative analysis; Demand; Railway networks; Regression analysis
• ISSN: 0954-4097; 2041-3017
• DOI: 10.1177/0954409713496987

At present in the UK an elasticity-based approach is used to forecast changes in rail passenger demand resulting from changes in both the rail service offer and external conditions, with uplift factors calculated based on the proportional change in the level of explanatory variables over time. Changes in these explanatory variables may have differing effects on rail demand in different areas. This is currently controlled for via a limited segmentation of the market with different elasticities estimated for each segment, which inevitably limits the complexity of the variations which can be captured. This paper describes the use of geographically weighted regression (GWR) to enhance the modelling of such spatial variation. First, conventional cross-sectional demand models were calibrated covering major rail flows across the Great Britain. These models were then recalibrated using GWR to allow assessment of spatial variations in rail demand elasticities. Previous applications of GWR have almost exclusively focused on spatial data which have a single point location. This is not the case for rail flows, and this paper compares the results given by several different methods for defining point locations for flows. It also assesses different methods for approximating GWR results to simplify their application in real-life forecasting situations. The results show that the use of GWR can give a significant improvement in the fit of flow-based rail demand models, and that it is possible to spatially segment the UK passenger rail market based on the results from these models. In order to integrate such segmentations with the standard UK rail demand forecasting methodology it would, however, be necessary to extend the GWR methodology further to allow the calibration of GWR models on panel data.