Empirical study of road traffic collision (RTCs) rates is challenging at small geographies due to the relative rarity of collisions and the need to account for secular and seasonal trends. In this paper, we demonstrate the successful application of Hidden Markov Models (HMMs) and Generalised Additive Models (GAMs) to describe RTCs time series using monthly data from the city of Edinburgh (STATS19) as a case study. While both models have comparable level of complexity, they bring different advantages. HMMs provide a better interpretation of the data-generating process, whereas GAMs can be superior in terms of forecasting. In our study, both models successfully capture the declining trend and the seasonal pattern with a peak in the autumn and a dip in the spring months. Our best fitting HMM indicates a change in a fast-declining-trend state after the introduction of the 20 mph speed limit in July 2016. Our preferred GAM explicitly models this intervention and provides evidence for a significant further decline in the RTCs. In a comparison between the two modelling approaches, the GAM outperforms the HMM in out-of-sample forecasting of the RTCs for 2018. The application of HMMs and GAMs to routinely collected data such as the road traffic data may be beneficial to evaluations of interventions and policies, especially natural experiments, that seek to impact traffic collision rates.

由于碰撞的相对稀少以及需要考虑长期趋势和季节性趋势，因此在较小的地区对道路交通碰撞率进行实证研究具有挑战性。在本文中，我们演示了使用隐马尔可夫模型（HMM）和广义加性模型（GAM）来成功描述爱丁堡市（STATS19）每月数据来描述RTC时间序列的成功案例。虽然这两种模型的复杂程度相当，但它们带来了不同的优势。HMM对数据生成过程提供了更好的解释，而GAM在预测方面可能更胜一筹。在我们的研究中，两个模型都成功地捕获了下降趋势和季节模式，秋季出现峰值，春季出现下降。我们最合适的HMM表示自2016年7月引入20 mph时速限制后，在快速下降趋势状态中发生了变化。我们首选的GAM明确为这种干预建模，并提供了RTC进一步大幅下降的证据。在两种建模方法的比较中，GAM在2018年RTC的样本外预测中优于HMM。将HMM和GAM应用于例行收集的数据（如道路交通数据）可能有助于评估干预措施以及旨在影响交通碰撞率的政策，尤其是自然实验。