In the safety literature, motor vehicle crashes are modelled predominately using single equation regression models, albeit with a variety of distributional assumptions and econometric enhancements. These models rely on a single linear additive predictive equation—which becomes multiplicative with a log transform—to specify the expected mean crash count conditioned on predictors. The models also specify the distribution of observations around the conditional mean, with common examples including the Poisson, Negative Binomial, and Conway-Maxwell distribution among others. This mainstream probabilistic conceptualization (i.e. model) of motor vehicle crash causation assumes that crashes are well-approximated by a single source of risk, wherein several contributing factors exert their collective, non-independent influences on the occurrence of crashes via a linear predictor.

This study first postulates, and then demonstrates empirically, that crash occurrence may be more complex than can be adequately captured by a single equation regression model. The total crash count recorded at a transport network location (e.g. road segment) may arise from multiple simultaneous and inter-dependent sources of risk, rather than one. Each of these sources may uniquely contribute to the total observed crash count. For instance, a site’s crash occurrence may be dominated by contributions from driver behaviour issues (e.g. speeding, impaired driving), while another site’s crashes might arise predominately from design and operational deficiencies such as deteriorating pavements and worn lane markings. Stated succinctly, this research hypothesises that the unobserved heterogeneity in the accumulation of motor vehicle crashes at transport network locations arises because multiple sources of risk, not one, better captures complexity in the crash occurrence process.

A stochastic multiple risk source methodological approach is developed to correspond with and empirically test this hypothesis. A joint econometric model with random parameters and instrumental variables demonstrates the applicability of the proposed theory and the corresponding methodological approach. The proposed model assumes that complexity of crash occurrence is well approximated using three sources of risk comprised of engineering, unobserved spatial, and driver behavioural factors. It is empirically tested using crash data from state controlled roads in Queensland, Australia. Finally, the multiple risk source model is compared to the traditional single risk source model to assess the viability of the proposed approach based on the sample data.

The multiple risk source model significantly outperformed the single risk source model in terms of prediction ability and goodness of fit measures. In addition, while the single risk source model predicts total crash counts for individual sites, the multiple risk source model predicts crash count proportions contributed by each source of risk, and predicts crashes by risk source. The improvement in fit combined with the theoretical appeal of a multiple risk source model to explain unobserved heterogeneity in crashes suggests—at least for the sample used in the study—that the complexity in crash occurrence is better explained using multiple equation linear predictors. Further research should examine other datasets for repeatability and should further explore and test risk sources.

在安全文献中，尽管有各种分布假设和计量经济学上的增强，但机动车碰撞事故主要是使用单方程回归模型建模的。这些模型依靠单个线性加性预测方程式（通过对数变换可乘以该方程式）来指定以预测器为条件的预期平均崩溃次数。这些模型还指定了条件均值周围的观测值分布，常见示例包括泊松，负二项式和Conway-Maxwell分布等。机动车碰撞因果关系的这种主流概率概念化（即模型）假设碰撞是由单一风险源很好地逼近的，其中几个贡献因素通过线性预测变量对碰撞的发生施加其集体的，非独立的影响。

这项研究首先假设，然后凭经验证明，碰撞发生可能比单个方程回归模型所能捕获的更为复杂。在运输网络位置（例如，路段）记录的总事故计数可能来自多个同时且相互依赖的风险来源，而不是一个。这些来源中的每一个都可能对观察到的总崩溃计数有独特的贡献。例如，一个站点的撞车事故可能是由驾驶员行为问题（例如，超速，驾驶不便）造成的，而另一个站点的撞车事故可能主要是由于设计和操作缺陷（例如人行道恶化和车道标志磨损）引起的。简而言之，

随机多风险源方法论方法被开发出来，以与该假设相对应并通过经验检验。具有随机参数和工具变量的联合计量经济学模型证明了所提出的理论和相应的方法论方法的适用性。所提出的模型假设使用三个风险源（包括工程，未观察到的空间和驾驶员行为因素）可以很好地估计碰撞发生的复杂性。使用来自澳大利亚昆士兰州政府控制的道路的碰撞数据进行了实证测试。最后，将多风险源模型与传统的单风险源模型进行比较，以基于样本数据评估所提出方法的可行性。

在预测能力和拟合优度方面，多风险源模型明显优于单风险源模型。此外，虽然单一风险源模型可以预测单个站点的总崩溃计数，但是多重风险源模型可以预测每个风险源贡献的崩溃计数比例，并可以按风险源预测崩溃。拟合度的提高与多风险源模型的理论吸引力相结合，可以解释撞车中未观察到的异质性，至少对于研究中的样本而言，这表明，使用多方程线性预测变量可以更好地解释撞车发生的复杂性。进一步的研究应检查其他数据集的可重复性，并应进一步探索和测试风险来源。