Modeling Traffic Crash-Flow Relationships for Intersections: Dispersion Parameter, Functional Form, and Bayes Versus Empirical Bayes Methods

Abstract

Statistical relationships between traffic crashes and traffic flows at roadway intersections have been extensively modeled and evaluated in recent years. The underlying assumptions adopted in the popular models for intersections are challenged. First, the assumption that the dispersion parameter is a fixed parameter across sites and time periods is challenged. Second, the mathematical limitations of some functional forms used in these models, particularly their properties at the boundaries, are examined. It is also demonstrated that, for a given data set, a large number of plausible functional forms with almost the same overall statistical goodness of fit (GOF) is possible, and an alternative class of logical formulations that may enable a richer interpretation of the data is introduced. A comparison of site estimates from the empirical Bayes and full Bayes methods is also presented. All discussions and comparisons are illustrated with a set of data collected for an urban fourlegged signalized intersection in Toronto, Ontario, Canada, from 1990 to 1995. In discussing functional forms, the need for some goodness-oflogic measures, in addition to the GOF measure, is emphasized and demonstrated. Finally, analysts are advised to be mindful of the underlying assumptions adopted in the popular models, especially the assumption that the dispersion parameter is a fixed parameter, and the limitations of the functional forms used. Promising directions in which this study may be extended are also discussed.

On the nature of over-dispersion in motor vehicle crash prediction models

“…Relatively early work on this topic is reported by Chapman (1972), Satterthwaite (1981), and Hauer et al (1988). Further development and continuation of the previous crash modeling research is reported by Bonneson and McCoy (1993), Belanger (1994), Maher and Summersgill (1996), Persaud and Nguyen (1998), Lord and Persaud (2000), Wang and Nihan (2004), Persaud et al (2002), and Miaou and Lord (2003). A main focus of prior studies has been to identify a defensible statistical relationship between crash counts and exposure.…”

“…While modeling urban intersection crashes using this func tional form for variance structure, Miaou and Lord (2003) found an improvement in model estimation. In addition they mentioned that treatment of dispersion parameter as a fixed parameter can seriously undermine the goodness of the estimate for individ ual sites by up to about 35%.…”

“…While model ing traffic crash-flow relationship for intersections, Miaou and Lord (2003) also challenged the assumption of fixed dispersion parameter. Due to complexity and interaction of traffic flow in and around intersections, they suspected that the unmodeled heterogeneity of the mean of crash counts would be spatially structured.…”

Bias properties of Bayesian statistics in finite mixture of negative binomial regression models in crash data analysis

“…This is by far the most common prior within the standard NB model (e.g., Miaou and Lord, 2003). This prior has a spike near zero with a mean=1 and a large variance of 100.…”

“…Over-dispersion caused by unobserved heterogeneity in crash data is a serious problem and has been addressed in a variety of ways within the negative binomial (NB) modeling framework (Hauer, 2001;Heydecker and Wu, 2001;Miaou and Lord, 2003;Geedipally et al, 2009;Anastasopoulos and Mannering, 2009). However, the true factors that affect heterogeneity are often unknown to researchers and failure to accommodate such heterogeneity in the model can undermine the validity of the empirical results.…”