零截尾负二项模型在交叉口事故预测中的应用

事故预测模型是广泛采用的交通安全定量分析方法，但往往要求具有完备的道路、交通和事故数据。然而，基础数据相对不健全是包括中国在内的发展中国家交通安全管理面临的主要问题之一，例如仅有发生事故路段或者交叉口的相关属性特征（即零截尾数据）。为此，为确保基础数据不全的情况下交叉口事故预测的准确性，提出了基于零截尾的广义负二项回归模型；采集了246个非信号控制交叉口的交通与事故数据，采用传统负二项模型和新提出的零截尾负二项模型对全数据和零截尾数据分别进行对比分析。结果表明：在针对截尾数据的分析中，零截尾负二项模型明显优于传统负二项模型，并且零截尾负二项模型的参数估计值与基于全数据的负二项基准模型的估计值非常接近；在所有模型中，交叉口的主路交通量和支路交通量与交叉口的安全性之间存在较大的正关联。此外，同等条件下，十字形交叉口的事故数量高于T形交叉口的事故数量；利用传统负二项分布模型分析截尾数据得到的事故预测模型与使用全数据的基准模型有显著差异，其结果不可靠；采用零截尾负二项分布模型的参数结果与基准模型基本一致，截尾模型的置信区间包含基准模型相应的参数估计值。当受条件所限无法获取全部数据时，可以考虑使用零截尾负二项模型进行安全分析。

Modeling Intersection Traffic Crashes Using a Zero-truncated Negative Binomial Model

Safety performance functions (SPFs) are a widely used quantitative method in roadway safety management. Conventional SPFs require complete roadway inventory, traffic and crash information. However, lack of data is a challenge in most developing countries, including China. For example, the data only include roadway or intersection inventories where crashes have occurred (this type of dataset is called zero-truncated data). To investigate how to develop reliable intersection SPFs when some data are missing (i.e., zero-truncated data), this paper proposed a zero-truncated negative binomial model. Traffic and crash data were collected at 246 unsignalized intersections. The traditional negative binomial model and the proposed zero-truncated negative binomial model were used to develop SPFs using full data (i.e., 246 intersections) as well as zero-truncated sub-set data. An analysis of the results indicates that when zero observations are truncated in the data, the zero-truncated negative binomial model is significantly better than the traditional negative binomial model. Further, the estimated parameters of the zero-truncated negative binomial model are comparable to those of the conventional negative binomial model based on full data. In all the models, major road traffic volume and minor road traffic volume are positively associated with the number of crashes at intersections. Additionally, in the same situations (e.g., similar traffic volume), the number of crashes at a 4-leg intersection is higher than that at a 3-leg intersection. SPFs developed by applying the traditional negative binomial model to zero-truncated data are biased and unreliable. SPFs developed using the zero-truncated negative binomial model are more accurate. The confidence intervals of the zero-truncated model include the corresponding parameter estimates of the base model using full data. When full data are not available, safety analysts are encouraged to use the zero-truncated negative binomial model to develop SPFs.