title: Quantile regression provides a fuller analysis of speed data.
abstract: Considerable interest already exists in terms of assessing percentiles of speed distributions, for example monitoring the 85th percentile speed is a common feature of the investigation of many road safety interventions. However, unlike the mean, where t-tests and ANOVA can be used to provide evidence of a statistically significant change, inference on these percentiles is much less common. This paper examines the potential role of quantile regression for modelling the 85th percentile, or any other quantile. Given that crash risk may increase disproportionately with increasing relative speed, it may be argued these quantiles are of more interest than the conditional mean. In common with the more usual linear regression, quantile regression admits a simple test as to whether the 85th percentile speed has changed following an intervention in an analogous way to using the t-test to determine if the mean speed has changed by considering the significance of parameters fitted to a design matrix. Having briefly outlined the technique and briefly examined an application with a widely published dataset concerning speed measurements taken around the introduction of signs in Cambridgeshire, this paper will demonstrate the potential for quantile regression modelling by examining recent data from Northamptonshire collected in conjunction with a "community speed watch" programme. Freely available software is used to fit these models and it is hoped that the potential benefits of using quantile regression methods when examining and analysing speed data are demonstrated.
authors.affiliation: School of Mathematics and Statistics, University of Plymouth, Drake Circus, Plymouth PL4 8AA, United Kingdom. paul.hewson@plymouth.ac.uk
authors.forename: Paul
authors.initials: P
authors.lastname: Hewson
mesh_terms: D000063:Accidents, Traffic / Q000517:prevention & control*; D001336:Automobiles / Q000706:statistics & numerical data*; D003625:Data Collection; D006801:Humans; D015233:Models, Statistical; D012044:Regression Analysis; D012449:Safety / Q000706:statistics & numerical data*; D012984:Software; D018709:Statistics, Nonparametric