Development of Safety Performance Functions: Incorporating Unobserved Heterogeneity and Functional Form Analysis

Abstract

To improve transportation safety, this study applies Highway Safety Manual (HSM) procedures to roadways while accounting for unobserved heterogeneity and exploring alternative functional forms for Safety Performance Functions (SPFs). Specifically, several functional forms are considered in Poisson and Poisson-gamma modeling frameworks. Using five years (2011)(2012)(2013)(2014)(2015) of crash, traffic, and road inventory data for two-way, two-lane roads in Tennessee, fixed-and random-parameter count data models are calibrated. The models account for important methodological concerns of unobserved heterogeneity and omitted variable bias. With a validation dataset, the calibrated and uncalibrated HSM SPFs and eight new Tennessee-specific SPFs are compared for prediction accuracy. The results show that the statewide calibration factor is 2.48, suggesting rural two-lane, two-way road segment crashes are at least 1.48 times greater than what HSM SPF predicts. Significant variation in four different regions in Tennessee is observed with calibration factors ranging between 2.02 and 2.77. Among all the SPFs considered, fully specified Tennessee-specific random parameter Poisson SPF outperformed all competing SPFs in predicting out-ofsample crashes on these road segments. The best-fit random parameter SPF specification for crash frequency includes the following variables: annual average daily traffic, segment length, shoulder width, lane width, speed limit, and the presence of passing lanes. Significant heterogeneity is observed in the effects of traffic exposure-related variables on crash frequency. The study shows how heterogeneity-based models can be specified and used by practitioners for obtaining accurate crash predictions.

Investigation of the Factors Influencing the Crash Frequency in Expressway Tunnels: Considering Excess Zero Observations and Unobserved Heterogeneity

“…Road designs with sharp horizontal curves [20], [24], acute curve deflection angles [25] and steep slopes [26], [27] can all increase the likelihood of crashes. Similarly, it has been reported that the crash frequency decreases with decreasing radius and length of horizontal curves [28], decreasing longitudinal slope [29], and increasing curvature [30]. In addition, Bauer and Harwood [23] focused on exploring the effects of horizontal and vertical alignments on road safety, which showed that the combination of horizontal curves with higher curvature and steeper slopes had a higher crash frequency.…”

“…Road design [16]- [30], traffic conditions [25], [30]- [34], pavement conditions [35]- [39], and weather conditions [22], [24], [59], [60] are potential causes of traffic crashes. Road designs with sharp horizontal curves [20], [24], acute curve deflection angles [25] and steep slopes [26], [27] can all increase the likelihood of crashes.…”

Applying a Correlated Random Parameters Negative Binomial Lindley Model to Examine Crash Frequency Along Highway Tunnels in China

“…In terms of the impacts of road design characteristics on the crash frequency, some scholars found that the geometric shape of a highway crosssection is related to the crash frequency. For example, studies [11], [12], [16] verified that highway sections with narrow shoulders and a small offset of longitudinal separation columns have a higher crash frequency. The safety effects of adding lanes are debatable.…”

“…However, the relationship between curves and safety remains a topic of discussion. Studies [11], [12], [15], [16] believed that curve segments increase the operating difficulty of drivers and may lead to a higher crash frequency. Other studies [13], [20], [22] showed that drivers pay more attention and drive at a comfortable speed in most cases when driving on a curved segments, which reduce the crash frequency of these segments.…”

“…For example, considering the impacts of the lighting indicator on the crash frequency of highway tunnels (assuming that the value of the variable is 1 if lighting exists; otherwise, it is 0), due to the different types of terrain, lighting conditions and degrees of fatigue of drivers in different highway tunnels, the variable of the lighting indicator has different influences on crash frequency, even if the values of lighting indicators are the same. Therefore, if the estimated parameters of the lighting indicator are limited to fixed values in all segments, biased estimation will inevitably occur [12], [45]. Ignoring unobserved heterogeneity and limiting the effects of observed variables to be the same in all segments, namely, fixed parameter (FP) models [15], [46], will usually lead to biased estimation, which in turn leads to incorrect inference and prediction.…”