Trend shifts in road traffic collisions: An application of Hidden Markov Models and Generalised Additive Models to assess the impact of the 20 mph speed limit policy in Edinburgh

Valentin Popov,Paul Kelly,Andrew James Williams,Karen Milton,Michael Kelly,Ruth Jepson,Glenna Nightingale

doi:10.1177/2399808320985524

Abstract

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.

Highlights

The United Kingdom’s Department for Transport (DfT) reported that in the 12 months up to September 2018, 27,295 people were killed or seriously injured on British roads
Hidden Markov Models (HMMs) and Generalised Additive Models (GAMs) helped us learn about the trend, seasonality and the impact of the intervention on the road traffic collisions (RTCs) in Edinburgh. Both approaches serve different purposes in our study – detecting shifts in the trend for the HMMs and explicit modelling of the intervention for GAMs – but a natural question is how do the two models compare to each other. We address this question by using forecasts as a comparison measure for the performance of the best performing HMM and GAM from the model fits
The reduction of RTCs is a ‘real-world’ problem for which the analytical tools for assessment deal with primarily, count data. We demonstrate successfully, both the application and advantage of using HMMs and GAMs in evaluations conducted within a public health natural experiment framework

Summary

Introduction

The 20 mph speed limit, which on we will refer to as the intervention, is a suitable example of an event that can potentially be associated with a structural change in the trend of RTCs and is of particular interest for the policy makers. In addressing the challenges of modelling outcomes such as RTCs at smaller scales like individual cities, we gain an understanding of the trends and seasonality of the RTCs in Edinburgh as well as the effects of the 20 mph speed limit policy that was introduced in 2016. Key approaches to modelling RTCs and related phenomena include Autoregressive Integrated Moving Average (ARIMA) models, Poisson count models, Negative Binomial models, Multivariate/Binomial logistic models, HMMs and GAMs. ARIMA models are important for quantifying the trend in collisions (by week/month/ year), facilitating forecasting of collisions and assessing for seasonality. This early exploratory analysis shows indications for serial dependence, trend and seasonality, which will be addressed in the methodology section

Methodology

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Findings

Discussion