Statistical Analysis of Transport Data

Transport is one of the economic sectors that generate the largest volumes of automated and often spatially explicit data. These include records on the movement of passengers, goods and vehicles, as well as information on ticket purchases, the condition of the transport network, traffic counts, financial transactions, and a wide range of performance indicators.

This abundance of data gives rise to confusion for at least two reasons. First, while transport operators and agencies possess vast amounts of data, they are often uncertain how to use it effectively. At the same time, the costs of data storage and compliance with privacy regulations are increasing.

Second, as I often emphasise on this website, transport is an inherently interdisciplinary field. Economists, engineers and social scientists approach transport data with very different traditions and methodological toolkits. It is essential that both researchers and practitioners recognise the importance of addressing statistical uncertainty appropriately and of distinguishing causal relationships from mere correlations. These principles are well understood in some parts of the community, but remain largely unfamiliar or overlooked in others.

Most of the research projects I work on involve statistics and data analysis to some extent, ranging from purely empirical studies to predominantly theoretical work where we use randomised quantitative methods to assess model sensitivity. Below, the relevant research outputs are grouped into four categories.

I. Causal inference methods in transport research

How can we distinguish cause-effect relationships from mere correlations in transport data? In my experience, while most people are aware of this challenge, only a few transport researchers apply causal methods with sufficient confidence. The essence of causal inference lies in recognising that the impact of a policy (often referred to as a ‘treatment’) can only be inferred by comparing the observed outcomes of treated units with those of untreated ones.

The baseline approach in causal inference is the standard difference-in-differences technique. This involves two key steps: (1) confirming, based on pre-treatment behaviour, that the outcomes of treated and untreated groups follow parallel (though not necessarily identical) trends, and (2) inferring the average treatment effect from their diverging responses after the policy is introduced. In general, this inference is valid when the treatment is randomly assigned within the data, creating a quasi-experimental setting.

In practice, however, random treatment assignment is rare, and the treated and untreated groups may not follow parallel trends even before the policy takes effect. In such cases, one approach is to match treated units with untreated counterparts that would have had the same probability of receiving treatment, based on a statistical model. This is known as propensity score matching. Another method involves combining a set of untreated units so that their weighted average outcome mirrors the pre-treatment trend of the treated unit; this is referred to as the synthetic control approach. A further option is to use instrumental variables to eliminate statistical endogeneity by removing the correlation between the main explanatory variable in a regression and the error term.

I had the privilege of spending more than a decade as a member of Professor Dan Graham’s research group at Imperial College London. He is one of the pioneers of causal inference in the global transport research community.

If you or your students are looking for a concise yet comprehensive overview of causal inference in transport research, covering both fundamental principles and recent methodological advances, I recommend this recently published guide by Dan Graham.

Graham, D.J. (2025). Causal inference for transport research. Transportation Research Part A: Policy and Practice, 104324.

And here is an incomplete list of the collaborative causal inference projects in which I participated in recent years.

Zhang, N., Hörcher, D., Bansal, P., & Graham, D. J. (2023). Causal inference for disruption management in urban metro networks. arXiv preprint arXiv:2310.07514.Anupriya, Graham, D. J., Bansal, P., Hörcher, D., & Anderson, R. (2023). Optimal congestion control strategies for near-capacity urban metros: Informing intervention via fundamental diagrams. Physica A: Statistical Mechanics and its Applications, 609, 128390.Zhang, N., Graham, D. J., Hörcher, D., & Bansal, P. (2021). A causal inference approach to measure the vulnerability of urban metro systems. Transportation, 48(6), 3269-3300.Anupriya, Graham, D. J., Hörcher, D., Anderson, R. J., & Bansal, P. (2020). Quantifying the ex-post causal impact of differential pricing on commuter trip scheduling in Hong Kong. Transportation Research Part A: Policy and Practice, 141, 16-34.

II. Travel demand modelling and discrete choice models

Demand modelling is an indispensable part of a transport researcher’s knowledge and toolkit. Since Daniel McFadden’s contributions to random utility discrete choice models, this methodology has become the backbone of (1) the most widely used four-stage transport models, (2) the estimation of the value of travel time savings, (3) many theoretical models in transport economics where imperfect modal substitution and/or route choice is present, and (4) tailor-made empirical demand models aimed at inferring travellers’ responses to new policies and technologies. Travel demand modelling also draws heavily on quantitative behavioural sciences, which has made this field one of the fastest growing areas in transport, attracting both young talent and substantial research funding.

Although I do not consider myself a die-hard discrete choice modeller (that is, I have never attended the International Choice Modelling Conference or the International Conference on Travel Behaviour Research, and I have not published in the Journal of Choice Modelling), my research has overlapped with demand modelling in several ways in recent years. For example, my PhD on the economics of crowding in public transport aimed to improve how we measure the disutility of crowding, resulting in an often-cited revealed preference paper based on large-scale metro smart card data.

Hörcher, D., Graham, D. J., & Anderson, R. J. (2017). Crowding cost estimation with large scale smart card and vehicle location data. Transportation Research Part B: Methodological, 95, 105-125.

I also had the chance to contribute to a follow-up paper in collaboration with Prateek Bansal in which we add numerous advanced behavioural features to our baseline route choice framework in Hörcher et al. (2017).

Bansal, P., Hörcher, D., & Graham, D. J. (2022). A dynamic choice model to estimate the user cost of crowding with large-scale transit data. Journal of the Royal Statistical Society Series A: Statistics in Society, 185(2), 615-639.

This previous experience in random utility discrete choice modelling proved valuable in several theoretical analyses of transport economics problems. One example is a numerical model of Mobility as a Service, in which travellers make joint decisions on transport mode, subscription purchases, and car ownership within a three-level nested discrete choice framework.

Hörcher, D., & Graham, D. J. (2020). MaaS economics: Should we fight car ownership with subscriptions to alternative modes. Economics of Transportation, 22(100167), 10-1016.

This background knowledge, which forms part of many transport researchers’ training, also proves useful when working on papers on quantitative spatial models (QSMs), a core line of research of mine. Location choice decisions in QSMs are based on the same random utility framework introduced by McFadden in 1978, which has been widely applied in transport research for nearly half a century. The only minor technical difference in QSMs is that they employ multiplicative utility functions combined with Fréchet-distributed idiosyncratic shocks, in contrast to the additive specification with Gumbel-distributed random utility used in the vast majority of transport models. You can read more about quantitative spatial models here.

III. Processing large-scale automated data

Modern transport systems generate vast quantities of digital information. Each time a user purchases a ticket, enters a station, closes a train door or passes a trackside signal, they may leave a digital trace. These data form large-scale datasets that capture both passenger flows and indicators of technological performance. While such data offer significant potential for planning, policymaking and academic research, our experience suggests that many transport agencies struggle to make effective use of them. Despite the availability of rich datasets from electronic fare payment and signalling systems, these are often underutilised or discarded before their analytical value is realised. The main challenge lies in the lack of accessible, targeted methods for extracting actionable insights.

In recent years, research based on automated transport data has gained considerable traction in the academic community, resulting in a growing body of work with varying levels of rigour. Part of this research is empirical in nature, aiming to assess impacts, identify cause-effect relationships, and validate existing hypotheses through the evidence hidden in the data. Large datasets are also well suited to calibrating complex models, such as representations of transport networks and travel behaviour. Big data in transport is increasingly used for pure prediction purposes as well, where the underlying mechanisms are not necessarily important but the goal is to maximise predictive performance; for example, through data-intensive machine learning methods.

Processing large-scale automated data is a cross-cutting theme in my research rather than a separate strand. We have used big data in a variety of empirical applications, including causal inference exercises in Theme I, discrete choice models in Theme II, and large-scale spatial models in another theme. Based on this experience, I believe we are well placed to answer one of the most frequently asked questions from transport companies today: how can we make effective use of the many new data sources that have become available in recent years?

IV. Benchmarking public transport performance

Benchmarking in the public transport industry means standardised data collection for a predefined set of key performance indicators and a systematic cyclical evaluation with the aim of identifying best practices. I had the chance to work for more than a decade as a researcher at the Transport Strategy Centre at Imperial College London, which is a global leader in public transport benchmarking, collaborating with more than a hundred public transport operators worldwide. My PhD studentship and employment at Imperial enabled me to follow the regular activities of metro, bus, light rail, suburban and mainline rail benchmarking groups. Such activities include the evaluation of longitudinal KPI data and the completion of benchmarking case studies focusing on specific aspects of operations, finance, environmental performance, customer satisfaction, safety and security.

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