Bayesian Modeling of Frequency-Severity Indeterminacy with an Application to Traffic Crashes on Two-Lane Highways

The basis for traffic safety research studies, which have developed numerous countermeasures to treat deficiencies in highway design features, surface conditions, traffic control devices, and driving behavior, comes from police reported crash data. However, a significant number of crashes go unreported. Studies show that severe crashes are more likely to be reported than those with lower severity. This issue is called frequency-severity indeterminacy. Because of frequency-severity indeterminacy, it is difficult to determine if a change in the number of reported crashes is caused by an actual change in number of crashes, a shift in severity proportions, or a mixture of both. Using underreported data tends to create the issue of frequency-severity indeterminacy, further producing a biased picture of traffic safety and by extension ineffective treatments. This paper presents a new approach addressing the issue of frequency-severity indeterminacy with a modified latent Poisson regression model. With recent advancements in crash modeling and Bayesian statistics, the parameter estimation is implemented within the Bayesian paradigm using two Gibbs Samplers and a Metropolis-Hastings (M-H) algorithm. The methodology is then empirically applied to investigate the issue of frequency-severity indeterminacy in traffic crashes that occurred on Washington two-lane highways.