Comparative Evaluation of Crash Hotspot Identification Methods: Empirical Bayes vs. Potential for Safety Improvement Using Variants of Negative Binomial Models

Comparative Evaluation of Crash Hotspot Identification Methods: Empirical Bayes vs. Potential for Safety Improvement Using Variants of Negative Binomial Models

3. Data

This study utilised the data for the urban road segments of Antwerp, Belgium. Police-reported crash data over six years were used for analysis. Crashes were divided into all crashes, injury crashes, injury and fatal crashes, and property damage only (PDO) crashes to estimate frequency models for each severity level. The road geometry data were derived from the official database of the Flemish government called the Flanders Road Register. It consisted of road width, number of lanes, road type, and pavement conditions. Following HSM guidelines, the roadway segments were separated from intersections [7], and homogeneous segments were defined. The original data did not contain the lane width variable. Using the definition as in Hauer [54], it was computed as the width from curb to curb or an edge-line to edge-line of a roadway segment (correcting for drains if present) divided by the number of lanes in that segment. The on-street parking data (i.e., the presence, arrangement, and type of parking) were obtained from the road marking database and verified via Google Maps. Lantis, a mobility company responsible for traffic operations in Antwerp, provided the traffic flow data for the study period. The crash, traffic, and roadway data were combined for model estimation using an open-source geographical information system application package QGIS.

The total length of the road network used in the current study was 268.80 km, divided into 2467 homogeneous road segments. Only roadway segments with known traffic data were selected for modelling. The segments with missing or erroneous data were removed from the final database. Similarly, crashes on the road segments were used for the analysis, while crashes on or within the intersection influence area were removed.

Table 1 shows a descriptive summary of the variables used to estimate the crash prediction models. It also provides the descriptive summary of the crash data aggregated into three subperiods (P1: 2010–2011, P2: 2012–2013, P3: 2014–2015) for the HSID performance evaluation tests of the estimated models, as discussed in Section 2.3 and Section 4.2.

4. Results

This paper used only 75% of the data to estimate crash predictive models for HSID. The remaining 25% of the data was utilised for the performance evaluation of alternative HSID methods. The explanatory variables consisted of exposure (i.e., traffic volume and segment length), roadway cross-section (i.e., lane width and the number of lanes), and on-street parking (i.e., parking type and parking arrangement). The number of lanes, parking type, and parking arrangement were categorical variables, while others were scale variables. Before modelling, multicollinearity diagnosis was performed using the variance inflation factor (VIF) [55]. The parking arrangement variable resulted in multicollinearity and thus was eliminated from the modelling process.

4.1. Crash Prediction Models

Table 2 provides the coefficient estimates of the two derivatives of NB models, that is, the varying dispersion parameter negative binomial model (VDPNB) and random parameter negative binomial model (RPNB) for different crash severity levels. The confidence level for retaining variables in the model was 95%. Following Tang et al. [37], the random parameters were determined through 200 Halton draws.

Both models produced coefficient estimates that indicate plausible signs and direction. For instance, the coefficient estimates of the significant variables are similar in the two different regression models for each crash severity level. However, the magnitude of the estimated coefficients for predictor variables varies across different severity levels. This observation supports estimating separate models for different severity levels, acknowledging potential differences in crash-contributing factors across these levels.

Traffic volume, segment length, lane width, number of lanes, and parking types were significant variables in both models for all crashes and PDO crashes. For injury crashes and injury and fatal crashes, all variables were significant in the VDPNB model except the number of lanes. Moreover, in the RPNB model, the standard deviations of two parameters (traffic volume and lane width) significantly differed from zero. Thus, they were estimated as random parameters.

The crash frequency is positively associated with the traffic variable and segment length for all crash severity levels in the developed models, meaning that an increased traffic volume will result in a higher expected crash frequency. However, it is noteworthy that the resulting increase in expected crash frequency is not uniform across severity levels. The variable ‘number of lanes’ shows an interesting association with the crash frequency. It has a significant negative relationship with all crashes and PDO crashes, but it is an insignificant predictor of injury crashes and injury and fatal crashes. The lane width shows a significant negative association with crash frequency for all severity levels and both model types. The negative impact is the highest for PDO crashes. Parking type is a significant predictor for all crashes and PDO crashes. However, for injury crashes and injury and fatal crashes, only one parking type (i.e., parallel parking) is significant.

Table 2 also provides the results for the overdispersion parameter estimated as a function of various predictor variables in the VDPNB models. It shows that the segment length positively correlates with dispersion in all models. At the same time, traffic volume negatively affects the dispersion parameter, similar to Khodadadi et al. [43]. The number of lanes is another significant predictor of the dispersion in the data, only for all and PDO crashes. The nature of the relationship is positive. The number of lanes is insignificant for injury and injury and fatal crashes. The lane width is not associated with dispersion in any model. Parking type and dispersion in the data have a significant negative association for all models except the PDO crash model’s perpendicular, angled, and mixed parking variables.
Before comparing the hotspot identification performance, the developed models were examined for the goodness of fit via log-likelihood, AIC, and cumulative residual (CURE) plots. The smaller the log-likelihood and AIC values, the better the model performance. The CURE plots are tools used to assess the performance of different models visually and objectively. According to Hauer [15], when residual plots closely oscillate around the zero line, it indicates a better model fit to the data. Moreover, the CURE plots for unbiased SPF typically fall within the boundaries of two standard deviations.
The CURE plots indicated that RPNB models outperformed VDPNB models across all severity levels as the obtained estimates oscillated closely to the zero line for RPNB models. These results are consistent with findings from the likelihood and AIC values. In addition, most estimates were clustered on the left side, which was anticipated due to the low traffic volume of several road segments. In general, the CURE plots remained within two standard deviations for most AADT values except for the extreme right ends of the plots. Figure 1 presents the CURE plots for VDPNB and RPNB models by crash severity.

4.2. Hotspot Identification Comparison

Table 3, Table 4 and Table 5 show the results for HCCT, CSCT, and ARDT, respectively, which compare the HSID performance of the EB and PSI estimates for VDPNB and RPNB models for total, PDO, injury, and injury and fatal crashes. To find hotspots, the road segments were ranked by the level of risk (i.e., EB estimate and PSI measure) they were characterised by, and those with the highest risk were considered hotspots. The current study assessed the HSID performance for the top 2.5%, 5.0%, 7.5%, and 10.0% sites. The higher the values for HCCT and CSCT scores and the lower the values for ARDT, the better the HSID performance of the given method.
Guo et al. [31] advised to divide the data into at least two subperiods for more accurate evaluation. This allows us to check whether the performance of the given HSID method changes between the initial and the subsequent periods. However, Guo et al. [31] further noticed that the aggregation of crash data into only two subperiods may only be suboptimal in terms of the accuracy of the performance evaluation of HSID methods. Therefore, analysts should consider more than two subperiods. This study computes the HSID performance comparison criteria scores for more than two subperiods. Therefore, we divided six-year crash data into three different subperiods, each with two years (i.e., P1: 2010–11, P2: 2012–13, P3: 2014–15). In addition, test scores were computed for two different setups to confirm the robustness of the results, with one setup using P1 as the first period and P2 and P3 as the subsequent periods. Another setup used P2 as the initial period and P3 as the subsequent period. Please refer to Guo et al. (2020) for more information about subperiods [31].
It is shown in Table 3 that from the point of view of the HCCT, the best-performing method of the two (i.e., EB and PSI) was the EB estimates for both RPNB and VDPNB models in ranking the top 2.5%, 5.0%, 7.5%, and 10.0% hazardous sites. Moreover, RPNB models outperformed the VDPNB models when HCCT evaluated the EB estimates for these two modelling frameworks. These results apply to both setups (i.e., (a. (P1 *, P2, P3) and b. (P2 *, P3)), where a period with the asterisk denotes the initial period in each target setting). For example, for all crashes, the EB method for RPNB models provides the highest scores for the HCCT in identifying hotspots compared to the EB estimates of the VDPNB model. The results for PDO, injury, and injury and fatal crashes also confirmed that EB estimates for the RPNB model provide better hotspot identification performance than other estimates. Among the two modelling frameworks (i.e., VDPNB and RPNB) and HSID methods (i.e., EB and PSI), the PSI estimates for VDPNB models resulted in low scores on HCCT, indicating the worst performance.
Similarly, the scores on the CSCT showed that EB estimates perform better than the corresponding PSI estimates in identifying the top 2.5%, 5.0%, 7.5%, and 10.0% of hotspots for both RPNB and VDPNB models (Table 4). Comparing the EB estimates for VDPNB and RPNB models, the scores of the CSCT favoured the RPNB model for all crash severity levels. Among the two modelling frameworks (i.e., VDPNB and RPNB) and HSID methods (i.e., EB and PSI), the PSI estimates for VDPNB models resulted in low scores on CSCT, indicating the worst performance.
Table 5 illustrates the performance analysis based on ARDT. Like the HCCT and CSCT, the EB method outperformed the PSI method on ARDT in both comparison periods. However, the comparison of the performance of the EB method for VDPNB and RPNB models revealed that the former performed better than the latter (i.e., lowest values of the EB method have resulted for VDPNB model in both setups (i.e., (a. (P1 *, P2, P3) and b. (P2 *, P3)) for the top 2.5%, 5.0%, 7.5%, and 10.0% of hotspots). Among the two modelling frameworks (i.e., VDPNB and RPNB) and HSID methods (i.e., EB and PSI), the PSI estimates for VDPNB resulted in extremely high scores on ARDT in most cases, indicating the worst performance.

To summarise, with only a few exceptions to the general trend, it can be safely concluded that the EB method outperforms the PSI in the HSID for all crash severity levels studied in this paper.

5. Discussion

Identification of crash hotspots based on statistical modelling-based approaches, such as the EB or PSI methods, requires analysts to choose the model specification that best handles the heterogeneity associated with the crash data. While the traditional NB model can effectively approximate the underlying crash occurrences, it has certain limitations [17]. Therefore, more flexible models are recommended since overdispersion in crash data can arise from various sources and is unknown to analysts. The above results evaluate the hotspot identification performance of the EB and PSI estimates obtained for the VDPNB and RPNB models. However, we briefly discuss the modelling results before discussing HSID results, following Lord and Park [44], who indicated that it is vital for transportation safety analysts to understand the structure of the mean function. Thus, the first part of this section discusses the relationship between covariates and crash frequency. The second part is more focused on discussing the HSID performance of the EB and PSI methods for the VDPNB model with the RPNB model.
The data modelling revealed a positive association between crash frequency and exposure variables (i.e., traffic volume and segment length). This was not surprising as an increase in the number of vehicles on roadways increases the risk of conflicts, which are converted into actual collisions in a few instances. With the unchanging design and monotonous traffic conditions, drivers tend to speed more on longer homogenous segments. Given the acknowledged association between speed and the risk of crash involvement [56], this might lead to more collisions when the segments are long. The coefficients of traffic volume in injury and injury and fatal crash models were higher than those in PDO and all crash models. This is somewhat counterintuitive and needs further explanation. Antwerp is in Flanders, a Belgian region with the highest proportion of people who commute to work by bike (around 17%). Antwerp is also one of the region’s most bike-friendly cities, with a large proportion of people (around 29%) who use bikes to commute [57]. The higher the proportion of cyclists in traffic, the higher the exposure to crash risk and, thus, the higher the number of crashes involving cyclists. It has been a fact that vulnerable road users, including cyclists, are more involved in severe injury crashes than motorists. For instance, only in the European Union do vulnerable road users form about 46% of all traffic fatalities and 53% of all seriously injured crash victims [58]. Thus, the higher presence of cyclists in traffic can result in more severe injury crashes. This effect was captured by higher coefficients for traffic volume in the estimated injury and injury and fatal crash models.
The lane width was found to have a significant adverse effect on the crash frequency, indicating improved road safety due to wider lanes. Mohammed [59] attempted to explain this association and argued that it makes sense to assume that wider lanes improve safety because they provide an additional space and time threshold that allows drivers to take corrective actions and avoid collision compared to narrower lanes.
The number of lanes was a significant predictor of crash frequency only in all crash and PDO crash models. The nature of the association was negative, meaning a decrease in crash frequency as the number of lanes increased. This finding surprised us since it contradicts other studies, for instance, Noland and Oh [60]. A potential reason can be that an additional lane decreases the traffic density on the roadways, contributing to more safety, particularly for PDO crashes. Also, an additional lane(s), similar to a wider lane, provides the driver extra space and time to take corrective action.
Parking type (including parallel, perpendicular, angle, and mixed parking) was a significant predictor of crash frequency in all and PDO crash models. However, only parallel parking was significant in the case of injury crashes and injury and fatal crash models, while other parking types were insignificant. It was observed that the association was not uniform across different parking types and models. All and PDO crashes increased more for other types of parking than parallel parking. In contrast, injury and injury and fatal crashes were more prevalent in the case of parallel parking. This can be explained by the fact that when drivers encounter complex parking designs, e.g., perpendicular, angle, or mixed, they drive cautiously and relatively slower, which helps them avoid severe crashes. However, this cautious behaviour appeared less effective in avoiding the PDO crashes and, subsequently, all crashes. In addition, perpendicular and angle parking provide greater separation (buffer zone) between the vehicles and vulnerable road users compared to parallel parking or no parking, which can be another reason for less severe crashes in the case of perpendicular, angle, or mixed parking settings and more injury crashes in case of parallel parking. These results can interest policymakers because higher injury severity crashes often lead to higher social costs [56], and minimizing those crashes will have economic advantages to society and help improve the sustainability of the transportation system.
The developed VDPNB models provided crucial information about the sources of the overdispersion in the data. Characterizing the dispersion parameter as a function of the covariates helped account for the extra variation in the data. The results suggested that all predictor variables except the lane width influence the overdispersion parameter. This was a preconceived outcome as the descriptive analysis (Table 1) provided clues about overdispersion in the data. For instance, there was an abundance of shorter homogenous segments in the data, probably because of the urban context and the studied road class, i.e., the accessibility objective of the local roads. According to Cafiso et al. [42], dispersion parameter variation matters more in shorter segments than in longer ones. In another instance, a little over 1550 of 2467 segments in the dataset had parallel parking, while only 164 had other parking categories. The excessive presence of parallel parking in the study area may have significantly contributed to this overdispersion. Similar trends were also observed for the number of lanes.
The estimated models were used to compute the EB estimates and PSI, which were tested for the HSID performance using three generalised criteria (i.e., HCCT, CSCT, and ARDT). The CSCT measured how well the methods can consistently identify sites with poor safety performance over time. The HCCT evaluated the methods for the number of the same hotspots identified in subsequent periods. These tests established that the EB estimates for the RPNB model (except for ARDT) outperformed the PSI estimates for the RPNB and VDPNB models and the corresponding EB estimates for the VDPNB model. A solid theoretical basis supports this because the EB method takes advantage of the observed and predicted values in its statistics, which in turn increases the reliability of its results and thus improves the precision of safety estimation. Moreover, the EB method also corrects for regression to the mean bias. All these characteristics of the EB method for estimating the safety of the highway network sites allow for the identification of the relative contributions of random variation, general factors, and local factors to the observed number of crashes. In practice, the EB method proved its efficiency in the current and other studies [10,12,19,22]. The PSI methods, on the other hand, seem to be reasonably inconsistent in most cases as opposed to the findings by Li and Wang [19]. The PSI method is primarily affected by the predicted value and, consequently, the validity of the developed crash prediction model. As crashes’ predicted value increases, a site’s likelihood of being selected as a hotspot increases.

This study has some limitations. For example, while interpreting those results, it should be noted that the current study did not explore its different possible parametrisation or functional forms while estimating the dispersion parameter as a function of different variables in the VDPNB models. Thus, we can not comment on the most appropriate parametrisation of the dispersion parameter for the current data and, hence, the consequent HSID results. Nevertheless, the results for the HSID favoured the EB estimates compared to the PSI in general, thereby confirming the findings of several past studies. In this study, different levels of severity were investigated (i.e., all, PDO, injury, and injury and fatal). However, different crash types (e.g., angle, head-on, rear-end, and sideswipe) can be considered in future studies. Furthermore, future studies can reproduce this type of analysis for other road facilities (e.g., intersections) and other road types (e.g., rural roads or expressways). The findings of this study are based on the analysis of actual data. Without an a priori knowledge of which sites are truly hazardous and which are relatively safe, detecting false positives (i.e., erroneous selection of relatively safe sites as hotspots) becomes problematic. Future research can focus on achieving more conclusive outcomes by simulating collision data that establish which sites are hazardous in advance, allowing for an assessment of whether the proposed method can accurately identify these hazardous locations.

6. Conclusions

The principal aim of this paper was to evaluate the performance of two HSID methods (i.e., EB and PSI) using the estimates obtained from two different variants of the NB model (i.e., VDPNB and RPNB). The VDPNB models allow the dispersion parameter to vary across observations, while in the RPNB model, the coefficient estimates of each parameter can vary across observations. Predictive models were developed for all crashes, PDO crashes, injury crashes, and injury and fatal crashes. The explanatory variables included the length of homogenous road segments, the traffic volume, the lane width, the number of lanes, and the on-street parking type. The findings revealed significant associations between crash frequency and site characteristics in both models. Moreover, the results also identified an association between the dispersion parameter and site characteristics in the VDPNB models. The VDPNB and RPNB model results were used in computing EB estimates and PSI measures for HSID.

Three generalised criteria were used to evaluate the performance of the HSID methods (i.e., EB estimates and PSI measures) obtained from the VDPNB and RPNB models. These HSID performance criteria indicated stable, consistent, and robust results in identifying the top 2.5%, 5.0%, 7.5%, and 10.0% of the hazardous sites utilizing the EB estimates of the VDPNB and RPNB models compared to the PSI method. When the EB estimates were compared for two variants of the NB model, the RPNB model outperformed the VDPNB model in most cases. The reliable HSID method accurately detects the potential crash-prone sites and consequently makes sure to use public funds related to road safety efficiently. This ultimately leads to safer roads and improved overall safety. Additionally, inaccurately identifying crash hotspots can lead to inefficient allocation of limited resources, putting the effectiveness of sustainable safety interventions at risk.

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