This thesis documents the results of 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 SPFs using negative binomial and hierarchical Bayesian modeling techniques. SPFs estimate the safety of a roadway entity, such as a segment or intersection, in terms of number of crashes. The new SPFs were developed for comparison to the calibrated HSM SPF. This research was performed for the Utah Department of Transportation (UDOT).The study area was the state of Utah. Crash data from 2005-2007 on 157 selected study segments provided a 3-year observed crash frequency to obtain a calibration factor for the HSM SPF and develop new SPFs. The calibration factor for the HSM SPF for rural two-lane two-way roads in Utah is 1.16. This indicates that the HSM underpredicts the number of crashes on rural two-lane two-way roads in Utah by sixteen percent. The new SPFs were developed from the same data that were collected for the HSM calibration, with the addition of new data variables that were hypothesized to have a significant effect on crash frequencies. Negative binomial regression was used to develop four new SPFs, and one additional SPF was developed using hierarchical (or full) Bayesian techniques. The empirical Bayes (EB) method can be applied with each negative binomial SPF because the models include an overdispersion parameter used with the EB method. The hierarchical Bayesian technique is a newer, more mathematically-intense method that accounts for high levels of uncertainty often present in crash modeling. Because the hierarchical Bayesian SPF 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 SPF has its own strengths and weaknesses, which include its data requirements and predicting capability. This thesis recommends that UDOT use Equation 5-11 (a new negative binomial SPF) for predicting crashes, because it predicts crashes with reasonable accuracy while requiring much less data than other models. The hierarchical Bayesian process should be used for evaluating observed crash frequencies to identify segments that may benefit from roadway safety improvements.



College and Department

Ira A. Fulton College of Engineering and Technology; Civil and Environmental Engineering



Date Submitted


Document Type





safety performance functions, Highway Safety Manual, crash modification factors, negative binomial, empirical Bayes, hierarchical Bayes, safety