An Analysis of Factors Influencing Freeway Crashes with a Negative Binomial Model
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摘要: 为分析高速公路交通事故的影响因素，构建基于负二项分布的事故分析模型，探究事故数与交通特性、公路线形及路面性能间关系。鉴于传统固定参数模型难以刻画各因素对事故风险影响的异质性，引入了随机参数建模方法。结果表明：相比于固定参数负二项模型，构建的随机参数负二项模型有更好的拟合优度，且能更合理地反映各因素对事故的作用效果；将随机参数分布的均值设置为其他变量的函数形式，可进一步挖掘各因素对事故风险的交互影响；交通量、路段长度、货车比例、平曲线曲率、纵坡坡度及车辙深度均与事故数正相关，且其每增加1%，事故数分别增加0.299%，1.029%，0.093%，0.079%，0.068%和0.054%；结构强度系数与事故数负相关，其每增加1%，事故数降低0.064%；增加路缘带宽度有益于交通安全；单向3车道或4车道路段的事故数多于同等条件下的2车道路段；弯坡组合路段的事故风险明显高于单纯的平曲线路段；货车比例高的下坡路段事故风险尤其高。Abstract: In this study, a negative binomial model is developed to investigate factors influencing crashes on freeways such as traffic flow, freeway alignment and pavement conditions. Since traditional fixed-effects models are incapable of capturing the heterogeneous effects of these factors on crash risk, a random-effects modeling method is introduced. Results indicate that the proposed random-effects negative binomial model has a better goodness-of-fit compared with its fixed-effects counterpart. In addition, the model explains the impact of the related factors on road safety in a more reasonable way. The interactions of the impact factors used in the model can be further studied by setting up the mean of a random parameter to be a functional form of other variables. It is found that traffic volume, length of road section, proportion of truck traffic, curvature, longitudinal grade and rutting depth are all positively correlated with crash frequency and 1% of increase in aforementioned variables increases the expected crash risk by 0.299%, 1.029%, 0.093%, 0.079%, 0.068%, and 0.054%, respectively. The pavement structural strength index is negatively correlated with crashes, and one percent of increase of the index will reduce the expected crash risk by 0.064%. Increasing the width of marginal strip is found to be beneficial to enhance safety. Three- or four-lane one-way freeway sections are found to experience more crashes than two-lane one-way freeway sections. It is also found that a segment with the combined alignment of curves and slopes is significantly more dangerous than a flat curved segment and the crash risk is considerably higher for downhill segments with a high proportion of truck flow.
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Key words:
- traffic engineering /
- influencing factors /
- negative binomial model /
- geometric alignment /
- freeway
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表 1 建模变量的统计特性
Table 1. Statistics of considered variables for modeling
变量名称 连续变量 离散变量 均值 标准差 最小值 最大值 样本量 比例/% 事故数/次 0.65 1.32 0 21 路段长度/km 0.55 0.32 0.16 5.37 AADT/（103 veh/d） 5.66 4.15 2.77 10.23 货车比例 0.38 0.18 0.16 0.51 车道数/条 2* 11 108 56.3 3 4 558 23.1 4 4 064 20.6 路缘带宽度/m 0.5* 1 144 5.8 0.75 18 586 94.2 平曲线曲率（/km） 0.21 0.30 0 2 纵坡坡度/% 1.00 0.92 0.03 4 纵坡方向 上坡* 9 687 49.1 下坡 10 043 50.9 路面破损率/% 0.07 0.18 0 4.57 车辙深度/mm 6.93 2.52 0.13 24 结构强度系数 2.95 2.15 0.32 6.76 注：“*”表示该变量为基准变量。 
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表 2 模型标定结果（剔除不显著变量）
Table 2. Estimation results for models (excluded non-significant variables)
变量名称 固定参数负二项模型 随机参数负二项模型 参数估计值 标准误 z值 参数估计值 标准误 z值 常数项 0.618 0.190 3.247 0.683 0.162 4.215 参数分布标准差 0.578 0.007 77.282 AADT的对数# 0.309 0.020 15.694 0.299 0.016 19.124 路段长度的对数# 0.992 0.021 47.513 1.029 0.019 58.170 货车比例 0.210 0.077 2.712 0.184 0.080 2.311 车道数_3 0.087 0.033 2.657 0.069 0.030 2.285 车道数_4 0.284 0.031 9.077 0.245 0.026 9.396 路缘带宽度_0.75 m -0.299 0.040 -7.411 -0.270 0.044 -6.107 参数分布标准差 0.057 0.009 4.094 平曲线曲率 0.363 0.029 12.355 0.192 0.035 5.534 均值影响因素：纵坡坡度 0.031 0.012 2.632 参数分布标准差 0.210 0.022 9.743 纵坡坡度 0.078 0.011 7.335 0.068 0.010 6.589 纵坡方向_下坡 0.066 0.020 3.356 0.046 0.017 2.770 均值影响因素：货车比例 0.102 0.014 2.286 参数分布标准差 0.231 0.011 20.960 路面破损率 -0.184 0.085 -2.163 车辙深度 0.021 0.004 5.897 0.019 0.004 5.154 参数分布标准差 0.010 0.001 9.213 结构强度系数 -0.016 0.005 -3.165 -0.020 0.005 -3.815 参数分布标准差 0.044 0.002 21.010 过离散参数α 0.617 0.018 35.156 5.148 0.346 14.861 样本数量 19 730 19 730 参数数量 13 22 对数似然值 -26 698 -26 588 AIC值 53 422 53 220 ρ2 0.147 0.151 注：“#”为AADT与路段长度为模型中的暴露变量。
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表 3 事故次数对各显著变量的敏感性
Table 3. Sensitivities of crash for significant variables
变量名称 弹性系数Ek 边际效应系数Dl 95%置信区间 AADT 0.299 (0.303,0.371) 路段长度 1.029 (0.877,0.944) 货车比例 0.093 (0.038,0.148) 车道数_3 0.041 (0.013,0.069) 车道数_4 0.142 (0.113, 0.170) 路缘带宽度_0.75 m -0.159 (-0.201, -0.117) 平曲线曲率 0.079 (0.032,0.126) 纵坡坡度 0.068 (0.033,0.104) 纵坡方向_下坡 0.026 (0.009,0.042) 路面破损率 -0.011 (-0.016,-0.005) 车辙深度 0.054 (0.043,0.065) 结构强度系数 -0.064 (-0.117, -0.01)
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