Ahern Zeke, Corry Paul, Rabbani Wahi, Paz Alexander
School of Civil & Environment Engineering, Queensland University of Technology, 2 George Street, Brisbane, 4000 QLD, Australia.
School of Mathematical Sciences, Queensland University of Technology, 2 George Street, Brisbane, 4000 QLD, Australia.
Heliyon. 2024 Feb 23;10(5):e26634. doi: 10.1016/j.heliyon.2024.e26634. eCollection 2024 Mar 15.
Estimating crash data count models poses a significant challenge which requires extensive knowledge, experience, and meticulous hypothesis testing to capture underlying trends. Simultaneous consideration of multiple modelling aspects is required including, among others, functional forms, likely contributing factors, and unobserved heterogeneity. However, model development, frequently affected by time and knowledge, can easily overlook crucial modelling aspects such as identification of likely contributing factors, necessary transformations, and distributional assumptions. To facilitate model development and an estimation that can extract as many insights as possible, an optimization framework is proposed to generate and simultaneously test a diverse array of hypothesis. The framework comprises a mathematical programming formulation and three alternative solution algorithms. The objective function involves minimizing the Bayesian Information Criterion (BIC) to avoid overfitting. The solution algorithms include metaheuristics to deal with an NP-hard problem and search through a complex and nonconvex space. The metaheuristics also enable to handle unique datasets through varying search strategies. The effectiveness of the proposed framework was ascertained using three distinct datasets, and published models used as benchmarks. The results highlighted the ability of the proposed framework to estimate crash data count models, surpassing benchmark models in terms of insights and goodness-of-fit. The framework provides several advantages, such as robust hypothesis testing, uncovering unique specifications and vital insights in the data, and leveraging existing knowledge to enhance search efficiency. The framework also exposes the vulnerability of traditional analyst efforts to fall into local optima, bias, and limitations in creating more efficient models. In a compelling example using crash data from Washington, the proposed framework unveiled insights overlooked by a benchmark published model, identifying speed, interchanges, and grade breaks as likely crash contributors, and revealing the potential danger of excessively wide shoulders. Conversely, the benchmark model identified fewer contributing factors and missed a crucial non-linear relationship between crash safety and shoulder widths. While wider shoulders are typically associated with improved safety, the proposed models suggest a safety threshold beyond which further widening could decrease safety. The introduction of random parameters in the analysis revealed a more nuanced relationship with crash frequency, thereby underlining the limitations of models incapable of capturing heterogeneity.
估计碰撞数据计数模型是一项重大挑战，需要广泛的知识、经验和细致的假设检验来捕捉潜在趋势。需要同时考虑多个建模方面，包括函数形式、可能的影响因素以及未观察到的异质性等。然而，模型开发常常受到时间和知识的影响，很容易忽略关键的建模方面，如确定可能的影响因素、必要的变换和分布假设。为了促进模型开发以及能够提取尽可能多见解的估计，提出了一个优化框架来生成并同时测试各种假设。该框架包括一个数学规划公式和三种替代求解算法。目标函数是最小化贝叶斯信息准则（BIC）以避免过拟合。求解算法包括用于处理NP难问题并在复杂的非凸空间中搜索的元启发式算法。元启发式算法还能够通过不同的搜索策略处理独特的数据集。使用三个不同的数据集和作为基准的已发表模型确定了所提出框架的有效性。结果突出了所提出框架估计碰撞数据计数模型的能力，在见解和拟合优度方面超过了基准模型。该框架具有几个优点，如强大的假设检验、揭示数据中的独特规格和重要见解以及利用现有知识提高搜索效率。该框架还揭示了传统分析师在创建更高效模型时陷入局部最优、偏差和局限性的脆弱性。在一个使用华盛顿碰撞数据的引人注目的例子中，所提出的框架揭示了一个基准已发表模型忽略的见解，确定速度、立交和坡度变化为可能的碰撞促成因素，并揭示了过宽路肩的潜在危险。相反，基准模型确定的促成因素较少，并且错过了碰撞安全性与路肩宽度之间的关键非线性关系。虽然较宽的路肩通常与提高安全性相关，但所提出的模型表明存在一个安全阈值，超过该阈值进一步拓宽可能会降低安全性。在分析中引入随机参数揭示了与碰撞频率更细微的关系，从而强调了无法捕捉异质性的模型的局限性。
