Transportation Safety Data and Analysis. Volume 2: Calibration of the Highway Safety Manual and Development of New Safety Performance Functions

This report documents the calibration of the Highway Safety Manual (HSM) safety performance function (SPF) for rural two-lane two-way roadway segments in Utah and the development of new models using negative binomial and hierarchical Bayesian modeling techniques. Crash data from 2005-2007 on 157 selected study segments in Utah provided a 3-year observed crash frequency to obtain a calibration factor for the HSM SPF and develop new models. The calibration factor for the HSM SPF for rural two-lane two-way roads in Utah is 1.16, indicating that the HSM underpredicts the number of crashes on these roads by 16 percent. Negative binomial regression was used to develop four new models, and one additional model was developed using hierarchical (or full) Bayesian techniques. The empirical Bayes (EB) method can be applied with each negative binomial model because the models include an overdispersion parameter used with the EB method. The hierarchical Bayesian technique accounts for high levels of uncertainty. Because the hierarchical Bayesian model produces a density function of a predicted crash frequency, a comparison of this density function with an observed crash frequency can help identify segments with significant safety concerns. Each model has its own strengths and weaknesses, which include its data requirements and predicting capability. This report recommends that UDOT use the negative binomial model with transformed average annual daily traffic (AADT) at a 95 percent confidence level (Equation 5-11) for predicting crashes. This model produces accurate results and requires less data than other models. The hierarchical Bayesian process should be used for identifying segments with extreme crash frequencies that may benefit from safety improvements.