01024602

Component

This paper describes how there has been considerable research conducted on the development of statistical models for predicting crashes on highway facilities. Despite numerous advancements made for improving the estimation tools of statistical models, the most common probabilistic structure used for modeling motor vehicle crashes remains the traditional Poisson and Poisson-gamma (or Negative Binomial) distribution. When crash data exhibit over-dispersion, the Poisson-gamma model is usually the model of choice most favored by transportation safety modelers. Crash data collected for safety studies often have the unusual attributes of being characterized by low sample mean values. Studies have shown that the goodness-of-fit of statistical models produced from such datasets can be significantly affected. This issue has been defined as the “low mean problem” (LMP). Despite recent developments on methods to circumvent the LMP and test the goodness-of-fit of models developed using such datasets, no work has so far examined how the LMP affects the fixed dispersion parameter of Poisson-gamma models used for modeling motor vehicle crashes. The dispersion parameter plays an important role in many types of safety studies. The primary objective of this research project was to verify whether the LMP affects the estimation of the dispersion parameter and, if it is, to determine the magnitude of the problem. The secondary objective consisted of determining the effects of a mis-specified dispersion parameter on common analyses performed in highway safety studies. To accomplish the objectives of the study, a series of Poisson-gamma distributions were simulated using different values describing the mean, the dispersion parameter, and the sample size. Three estimators commonly used for estimating the dispersion parameter of Poisson-gamma models of motor vehicle crashes were evaluated: the method of moments (MM), the weighted regression (WR) and the Maximum Likelihood method (ML). In an attempt to complement the outcome of the simulation study, Poisson-gamma models were fitted to crash data collected in Toronto, Ont. characterized by a low sample mean and small sample size. The study shows that a low sample mean combined with a small sample size can seriously affect the estimation of the dispersion parameter, no matter which estimator is used within the estimation process. The probability the dispersion parameter becomes mis-specified increases significantly as the sample mean and sample size decrease. Consequently, the results show that a mis-specified dispersion parameter can significantly undermine empirical Bayes (EB) estimates as well as the estimation of confidence intervals for the gamma mean and predicted response. The paper ends with recommendations about minimizing the likelihood of producing Poisson-gamma models with a mis-specified dispersion parameter for modeling motor vehicle crashes.

01020180

06-2337

English

35p

2006

Transportation Research Board 85th Annual Meeting

CD-ROM

Figures (2) ; References; Tables (10)

Bayes' theorem; Crash analysis; Crash tests; Gamma distributions; Highway safety; Motor vehicles; Poisson ratio; Regression analysis

Empirical Bayes method

Toronto (Canada)

Data and Information Technology; Highways; Research; Safety and Human Factors; I81: Accident Statistics

Transportation Research Board Annual Meeting 2006 Paper #06-2337

TRIS, TRB

Mar 3 2006 10:57AM