Accident Analysis and Prevention 84 (2015) 38–40
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Short Communication
A random parameters probit model of urban and rural intersection crashes Richard Tay School of Business IT and Logistics, RMIT University, Melbourne, Victoria, Australia
a r t i c l e
i n f o
Article history: Received 6 July 2015 Received in revised form 12 July 2015 Accepted 14 July 2015 Available online 27 August 2015 Keywords: Intersection crashes Urban intersection Rural intersection Random parameters probit model
a b s t r a c t Intersections are hazardous locations and many studies have been conducted to identify the factors contributing to the frequency and severity of intersection crashes. However, little attention has been devoted to investigating the differences between crashes at urban and rural intersections, which have different road, traffic and environmental characteristics. By applying a random parameters probit model to the data from the Canadian Province of Alberta between 2008 and 2012, we find that urban intersection crashes are more likely to be associated with hit and run behaviours, roads with higher traffic volume, wet surfaces, four lanes and skewed intersections, and crashes on weekdays and off-peak hours, whereas rural crashes are likely to be associated with increases in fatalities and injuries, roads with higher speed limits, special road features, exit and entrance terminals, gravel, curvature and two lanes, crashes during weekends, peak hours and night-time, run-off-road crashes, and police visit to crash scene. Hence, road safety professionals in urban and rural areas should consider these differences when designing and implementing counter-measures to improve intersection safety, especially their safety audits and reviews, enforcement activities and education campaigns, to target the more vulnerable times and locations in the different areas. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Background and rationale Among the different road segments, intersections are widely recognised as hazardous locations because of the crossing traffic streams. This safety concern is supported by crash statistics from around the world. For examples, about 43% of all crashes in the United States occurred at or near an intersection (Lord et al., 2005) and about 40% of all casualty crashes in Norway occurred at junctions (Elvik and Vaa, 2004). In Singapore, more than one-third of crashes (34.31%) occurred at intersections during 1992–2002 (Tay and Rifaat, 2007). In Canada, more than 30% of the road deaths and 40% of the serious injuries on the roads occurred at intersections (Barua et al., 2010). In Australia, intersection crashes comprised 54.2% of total crashes and 20.8% of fatal crashes in the State of New South Wales in 2010 (RTA, 2010). Hence, in order to improve road safety significantly, we need to address the safety challenges at intersections. Increasing the safety performance of intersections will require us to have a
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better understanding of the factors contributing to crashes at these hazardous locations in order to develop more targeted countermeasures. It is thus not surprising that the literature on intersection crashes is extensive (see Tay, in press). While most of the studies examined all intersections, some studies examined only urban intersections whereas others examined only rural intersections. The segmentation of the urban and rural intersections is based on the fact that they have very different road, traffic and environmental characteristics. Although many studies have been conducted to examine the differences between urban and rural crashes in general (e.g., Burgess, 2005), no study has been conducted yet to identify the differences between crashes at urban and rural intersections. Extant research has found significant differences in the factors contributing to intersection and non-intersection crashes (see Tay, in press).
1.2. Objective of study The aims of this study are to determine if urban and rural intersection crashes have different crash characteristics and to identify the crash contributing factors that will differentiate between an urban and a rural intersection crash. Based on the factors
R. Tay / Accident Analysis and Prevention 84 (2015) 38–40
identified, some evidence-based recommendations will be provided to improve intersection safety.
Table 1 Summary statistics. Variable
2. Methodology 2.1. Data The data used in study was obtained from the Alberta collision database maintained by Alberta Transportation. Between 2008 and 2012, there were 116,511 intersection crashes, of which only 13,798 had complete information, resulting in 4201 urban intersection crashes and 9597 rural intersection crashes. Although the sample size was very large, it included only a small proportion of the total intersection crashes. Hence, the results obtained in this study should be treated as exploratory. Nevertheless, it should provide some useful insights into the differences between the factors contributing to crashes at urban and rural intersections. In Alberta, any crash resulting in injury or property damage costing more than $1000 would need to be reported to the police. The crash records contained the common types of information on traffic collision, including the time, location and severity of collisions as well as data on the driver, crash type, vehicle, environment and any special road features at the crash locations. Based on the information available in the dataset, 16 factors were selected for analysis. Following some preliminary analyses, three statistically insignificant factors were excluded and 13 factors were retained in the final analysis. The three excluded factors were weather, road gradient and number of vehicles. The descriptive statistics of the variables included in the final model are reported in Table 1. 2.2. Data analysis In this study, the response variable, urban or rural intersection crash, is a binary or dichotomous variable. Therefore, the binary regression models are suitable techniques to use because they are developed to predict a binary dependent variable as a function of predictor variables. To allow for heterogeneous effects and correlations in unobserved factors, a random parameter binary probit model will be used in this study. Random parameters models, especially the random parameter logit or mixed logit model, have increasingly been used in traffic safety studies to analyse both crash frequency and severity (Lord and Mannering, 2010; Savolainen et al., 2011). In a random parameter model, some or all of the parameters are assumed to be random and will vary across observations. In this study, the random parameters are assumed to be normally distributed with a constant mean and variance. Since the normal distribution is symmetric and continuous, the coefficient for the same factor may be positive for some observations but negative for other observations even though the mean effect is positive (or negative). Also, if the variance or scale parameter is zero, then the parameter is not random and the factor will have the same effect across all observations. The random parameter binary probit model will be estimated using NLogit version 5. 3. Results and discussion The estimation results were summarised and shown in Table 2. Overall, the model fitted the data very well, with 19 fixed parameters and five random parameters estimated. The random parameters were associated with injury outcome, hit-and-run behaviour, run-off-road crash type, and roads with 90 and 100 km/h posted limits. Compared to urban intersection crashes, rural intersection crashes were found to be more likely to result in fatalities and injuries. This result was expected as the emergency medical
39
Rural
Categorical variables (column percentages shown) Crash severity Fatal 2.1 Injury 33.1 Property damage only 64.9 Hit and run Yes 3.7 No/unknown/missing (ref) 96.3 Police visit Yes 59.5 No/unknown/missing 40.5 Day of week Weekday 75.3 Weekend 24.7 Time of day Morning peak 15.6 Daytime off peak 36.6 Afternoon peak 24.2 Night 23.5 Road surface Dry 54.5 Wet 6.4 Snow 22.4 Other/unknown/missing 16.7 Special road facility Yes (bridges, tunnels, etc.) 16.7 No/unknown/missing 83.3 Crash type Angle 36.3 Sideswipe 10.3 Run-off-road 22.6 Rear end 28.3 Other 2.5 Road type Gravel 1.2 2 lane 64.5 4 lane divided 29.7 4 lane undivided <0.1 Other 4.6 Curve Yes 10.5 No/unknown/missing 89.5 Intersection type X-junction 47.0 X-junction skewed 17.2 T-junction 15.7 T-junction skewed 5.3 Entry or exit terminal 12.2 Other 2.6 Speed limit 50 K <0.1 60 K <0.1 70 K <0.1 80 K 7.0 90 K 1.8 100 K 82.7 110 K 8.4 Continuous variable AADT (10,000) Mean Standard deviation
1.058 1.384
Urban
0.2 21.1 78.6 5.8 94.2 55.1 44.9 79.6 20.4 13.4 43.8 25.3 17.6 54.0 7.3 23.1 15.6 3.3 96.7 37.6 12.0 6.3 41.8 2.3 0.1 60.8 38.0 1.2 0.0 6.1 93.9 49.8 25.1 14.1 8.2 2.1 0.7 8.0 1.8 0.8 22.6 0.7 66.1 0.0
1.133 0.988
response might not be as quickly available due to lower capacity and coverage in rural areas. Also, the lower traffic volume in rural areas might increase the notification time. Interestingly, hit-and-run behaviour was found to be more likely in urban intersection crashes than rural intersection crashes. With a lower traffic volume, one would expect the presence of witness and subsequent detection would be lower in rural areas. Also, compared to urban intersection crashes, rural intersections were more likely to occur at night, which also would decrease the likelihood of detection. However, rural intersection crashes were found to be
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R. Tay / Accident Analysis and Prevention 84 (2015) 38–40
Table 2 Estimation results of random parameters binary probit model. Dependent variable: urban Number of observations: 13,798 Log likelihood function: −6919.8 Restricted log likelihood: −6952.4 Chi-square statistics: 65.17 Significance level: <0.0001 Variable
Coefficient
Std. err.
Constant Fatal Injury Hit and run Police visit Weekday Morning peak Afternoon peak Night Wet Special road facility Run-off-road Gravel 4 lane undivided 4 lane divided Curve X-junction skewed T-junction skewed Entry or exit terminal 60 K speed limit 70 K speed limit 90 K speed limit 100 K speed limit AADT
0.1603 −1.7751 −0.4428 0.2566 −0.3359 0.1430 −0.2689 −0.1126 −0.2214 0.1306 −1.7591 −1.2307 −1.9594 2.9123 0.5947 −0.4692 0.4652 0.4276 −0.6730 2.0640 1.1887 −1.4396 −1.0780 0.1763
0.0564 0.2078 0.0375 0.0747 0.0326 0.0370 0.0465 0.0379 0.0430 0.0585 0.0983 0.0617 0.3711 0.6327 0.0398 0.0654 0.0379 0.0708 0.1114 0.3044 0.3463 0.1946 0.0408 0.0224
Scale
Std. err.
0.4652 1.0147
0.0305 0.0820
intersections might be a bigger safety challenge for drivers to traverse safely in urban areas. On the other hand, special road facilities, such as bridges and tunnels, appeared to be a bigger challenge for drivers to negotiate safely in rural areas. As expected, crashes on gravel roads were found to be associated more with crashes at rural intersections than urban intersections whereas crashes on four lane roads were found to be associated more with urban intersections than rural intersections. Also, as expected, crashes on roads with posted speed limits of 60 km/h or 70 km/h were more likely to occur in urban areas which would have more arterial roads, whereas crashes on roads with posted speed limits of 90 km/h or 100 km/h were more likely to occur in rural areas which would have more open roads or rural highways. 4. Conclusion
0.9094
0.0557
1.2361 1.3320
0.2037 0.0264
All estimates are statistically significant at ˛ = 0.05.
more likely to be visited by police. Police attendance at a crash scene would significantly increase the likelihood of detection and prosecution. With respect to time, urban intersection crashes were found to be more likely during weekdays and day time off-peak hours. These results were somewhat expected as the exposure or traffic during these times would be much higher in urban areas compared to rural areas. For the same reason, the findings that rural intersection crashes were more likely during peak hours and night time were somewhat surprising. The higher likelihood of rural intersection crashes occurring at night might be due to lack of street lighting and higher speed limits on rural roads while the lower likelihood of urban intersection crashes to occur during peak hours might be attributed to lower operating speeds. As expected, run-off-road crashes were found to be more likely to occur in rural areas, probably because of the higher speeds, longer travel distances and higher incidences of driving while fatigued. Crashes on curved roads were also found to be more likely to occur at rural intersections but crashes at skewed intersections were more likely to be located in urban areas, indicating that skewed
As expected, there are significant differences in the characteristics of crashes at urban and rural intersections. Urban intersection crashes are more likely to result in hit-and-run, occur during weekdays, on wet roads, on four lane roads, skewed intersections, arterial roads (60–70 K), and roads with heavier traffic volume. On the other hand, rural intersection crashes are more likely to occur on high speed roads (≥90 K) and curved roads, at entry or exit terminals, at locations with special facility, on gravel roads, during night-time and peak hours, being visited by police, and resulting in injury or fatality. Hence, road safety professionals in urban and rural areas should consider these differences when designing and implementing counter-measures to improve intersection safety, especially their safety audits and reviews, enforcement activities and education campaigns, to target the more vulnerable times and locations in the different areas. References Barua, U., Azad, A., Tay, R., 2010. Fatality risks of intersection crashes in rural undivided highways of Alberta, Canada. Transp. Res. Rec. 2148, 107–115. Burgess, M., 2005. Contrasting Rural and Urban Fatal Crashes 1994–2003, Technical Report DOT HS 809 896. National Highway Traffic Safety Administration. Elvik, R., Vaa, T., 2004. The Handbook of Road Safety Measures. Elsevier Science, Amsterdam. Lord, D., Schalkwyk, I., Staplin, L., Chrysler, S., 2005. Reducing Older Driver Injuries at Intersection Using More Accommodating Design Practices. Texas Transportation Institute, College Station. Lord, D., Mannering, F., 2010. The statistical analysis of crash-frequency data: a review and assessment of methodological alternatives. Transp. Res. A 44, 291–305. RTA, 2010. Road Traffic Crashes in New South Wales: Statistical Statement for the Year Ended 31 December 2010. Road Transport Authority, NSW. Savolainen, P., Mannering, F., Lord, D., Quddus, M., 2011. The statistical analysis of highway crash-injury severities: a review and assessment of methodological alternatives. Accid. Anal. Prev. 43, 1666–1676. Tay, R., 2015. Urban and rural intersection crash factors: a review of recent statistical studies. In: Lord, D., Washington, S. (Eds.), Safe Mobility: Background, Challenges and Solutions. Emerald, Bingley (in press). Tay, R., Rifaat, S., 2007. Factors contributing to the severity of crashes at intersections. J. Adv. Transp. 41 (3), 245–265.