Methodology for fitting and updating predictive accident models with trend

Abstract

Reliable predictive accident models (PAMs) have a variety of important uses in traffic safety research and practice. They are used to help identify sites in need of remedial treatment, in the design of transport schemes to assess safety implications, and to estimate the effectiveness of remedial treatments. The PAMs currently in use in the UK are now quite old; the data used in their development was gathered up to 30 years ago. Many changes have occurred over that period in road and vehicle design, in road safety campaigns and legislation, and the national accident rate has fallen substantially. It seems unlikely that these aging models can be relied upon to provide accurate and reliable predictions of accident frequencies on the roads today. This paper addresses a number of methodological issues that arise in seeking practical and efficient ways to update PAMs. Models for accidents on rural single carriageway roads have been chosen to illustrate these issues, including the choice of distributional assumption for overdispersion, the choice of goodness of fit measures, questions of independence between observations in different years, and between links on the same scheme, the estimation of trends in the models, the uncertainty of predictions, as well as considerations about the most efficient and convenient ways to fit the required models, given the considerable advances that have been seen in statistical computing software in recent years.

Updating outdated predictive accident models

“…In the lower left-hand plot, the mean of the observed values in each bin is plotted against the mean of the predictions, and in the lower right-hand plot the mean of the residuals is plotted against the mean of the predictions. By aggregating the data, a lot of the variability is removed and this permits a more informative view of the data and any systematic variations (Connors et al, 2012). These lower panels show that there are no systematic variations across the data.…”

“…There is no unique, best way of determining the scaling factor as all of the goodness-of-fit criteria are sensible and desirable. These issues are discussed in more detail in Connors et al (2012). We chose to estimate the scaling factor as ∑ ∑ = j j y sf µ which minimises the absolute value of the mean error as this is simple, intuitive and minimises bias.…”

“…In an earlier paper, the authors addressed the principal methodological issues that arise in seeking practical and efficient ways to update PAMs (Connors et al, 2012). These issues were illustrated by application to a basic model for rural single carriageway roads, and include: the choice of distributional assumption for overdispersion; the choice of goodness of fit measures; questions of independence between observations at the same site in different years, and between links on the same scheme; the estimation of trends in the models; the uncertainty of predictions; the most efficient and convenient ways to fit the required models, given the considerable advances that have been seen in statistical computing software in recent years.…”

“…These models had the same independent variables, factors and form as those given by TRL. Connors et al (2012) tested assumptions about the distributional form of the model and recommended a method in which the model was considered in two linked parts. In the first part the aggregated data across all years (2005)(2006)(2007)(2008)(2009)) was used to estimate the model parameters using a Poisson distribution for the accident distribution at each site and a Variable Shaped Gamma (VS-G) distribution for the overdispersion (i.e.…”

“…There is now a general recognition of the need to allow for overdispersion in accident modelling and the assumption of a negative binomial error structure is commonly used (see, for example, Maher and Summersgill, 1996). However, this is primarily for mathematical convenience, with recent research suggesting that alternative forms of error structure are now not only feasible but may also be more appropriate (Maher and Mountain, 2009, Lord and Mannering, 2010, Connors et al, 2012. Perhaps the most serious difficulty arises, however, because, over time, there will inevitably be changes in road, vehicle and driver characteristics such that the relationship between the dependent and independent variables may also tend to change.…”