Relation of Flow, Speed, and Density of Urban Freeways to Functional Form of a Safety Performance Function

Constructive discussion of the appropriate choice for the functional form of safety performance functions (SPFs) is generally absent from research literature on road safety. Among researchers who develop SPFs, there appears to be a consensus that the underlying randomness in accident counts is well described by the negative binomial (NB) distribution. The underlying phenomenon itself, however, is not well understood and is rarely discussed. The choice of the regression equation is usually not explained or documented. Researchers most commonly use the power function, possibly because most generalized linear modeling (GLM) statistical packages can accommodate the power function with little effort. The modeling process, however statistically rigorous, at times seems disconnected from the physical phenomenon that it is trying to describe. The disconnect, however, has attracted only limited interest from researchers to date. Accidents on an urban freeway are a by-product of traffic flow; therefore, changes in the flow parameters may give clues about the probability of accident occurrence and changes in accident frequency. This study related traffic flow parameters, such as speed and density, to the choice of the functional form of the SPF. It compared SPF models for urban freeways developed with sigmoid and exponential functional forms with the use of data from Colorado and California and contrasted the cumulative residual (CURE) plots of the models. SPFs developed around a sigmoid functional form through the use of neural network (NN) methodology suggested underlying relationships between safety and traffic flow characteristics. CURE plots for NN-generated SPFs generally showed a better-quality model tit when compared with power-function SPFs, which were developed in the GLM framework with an NB error structure.