Advancing the behavioural realism of largescale-applicable choice models

Sustainable decision-making is vital, particularly as the climate crisis demands urgent behavioural changes. Individual choices, such as the mode of transport we use to commute or travel, impact the demand for infrastructure, energy, and services. Understanding the factors that drive these choices is essential to encourage sustainable behaviours on a larger scale. Discrete choice modelling plays a crucial role in this process. Using a quantitative approach, discrete choice models (also called choice models) help identify the key influences on decisions, enabling policymakers to focus on the most effective levers for change. For instance, choice models can show how pricing, convenience, or social norms impact the decision to shift towards more sustainable habits. Additionally, discrete choice modelling is important for predicting traffic flows, optimising infrastructure investments, and guiding political decisions.

Modern tools and technologies allow the collection of large-scale data on individual choices, offering deeper insights into behaviour patterns. However, these datasets present challenges. Computational complexity arises from the vast amount of data, and ensuring that the data is representative can be difficult, as individuals may contribute to its collection at different rates and over varying periods.

Among discrete choice models, the Multinomial Logit (MNL) model is the most popular due to its simplicity and strong connection to economic utility theory. It is closed-form and simple to interpret, which makes it a main tool for researchers and practitioners. Despite these advantages, the MNL model builds on simplifying assumptions of choice behaviour that limit its ability to represent real-world decision-making processes. One major issue is the Independence from Irrelevant Alternatives (IIA) assumption, which implies that the relative odds of choosing between any two alternatives remain unaffected by the presence or characteristics of other options. This assumption is often violated, particularly in
contexts like route choice, where alternatives can be highly correlated. Furthermore, the model’s simple error structure does not account for important behavioural aspects like choice set formation and heteroscedasticity, and the commonly used linear utility specification does not allow for alternative decision rules to utility maximisation. These effects are known to produce biased estimates and incorrect forecasts, which, in turn, may lead to incoherent decision-making and a lack of trust in the models.

While researchers have made significant strides over the past decades to address these shortcomings, there remains a persistent gap in the choice modelling field. This gap exists in two critical areas: i) the ability of models to simultaneously account for multiple effects (e.g., the correlation between alternatives, taste heterogeneity and heteroscedasticity) without risking poor identifiability and confounding, and ii) the applicability to large-scale complex choice situations while avoiding extreme computation times. These challenges highlight the necessity for further innovation, particularly in developing be-haviorally rich and computationally feasible frameworks. Models with closed-form choice probabilities that do not include a too-large set of parameters usually achieve faster estimation times. This PhD thesis seeks to develop closed-form and parsimonious choice models that enhance behavioural realism and practical usability, especially in large-scale scenarios, while maintaining high interpretability.

Throughout the thesis, most models and estimation techniques are applied in the context of route choice. This choice task is notoriously difficult to model due to the vast amount of alternatives in transport networks, which have complex overlapping patterns. Still, many of these methods are versatile and can be applied to various choice situations beyond this specific domain. The thesis consists of four articles, whose content is summarised in the following paragraphs.

Nowadays, technologies allow for the collection of a large amount of choice data, such as crowdsourced GPS data, but this poses significant issues. For instance, these datasets may be highly imbalanced because individuals have different trip frequencies and have participated in the data collection for different periods. Modelling choices with these datasets can be particularly challenging, with results that may be difficult to interpret unless the sample structure is carefully considered. Paper 1 tackles this issue by exploring using logit models on imbalanced datasets. It begins by examining whether the average preferences of panel members can be accurately recovered when estimating a Panel Mixed Logit (PMXL) model on an imbalanced panel where some individuals are overrepresented.

A controlled simulation experiment reveals that the MNL, MXL, and PMXL models all exhibit bias towards the most represented members in the dataset. To address this bias, the paper introduces methods for bias reduction, including subsampling observations and using a weighted maximum likelihood approach. The simulation study demonstrates that applying a weighting strategy that equalises the likelihood contribution of each individual effectively reduces bias while preserving the high efficiency of the model estimates.

Additionally, subsampling by randomly truncating observations for overrepresented individuals significantly reduces bias, though it comes at the cost of reduced efficiency in the estimates. Building on these findings, the paper applies these bias reduction techniques to a large-scale bicycle route choice case study using an imbalanced panel dataset. The study provides practical recommendations for achieving an optimal balance between bias reduction, efficiency, and estimation time. These insights help ensure the resulting models are accurate and computationally feasible, offering a useful framework for working with imbalanced datasets.

Utility maximisation is the traditional decision rule used in choice models. It assumes that individuals weigh every alternative’s attributes in an often linear utility function and choose the alternative that maximises this function. This assumption has been challenged for several reasons: first, it has been observed that, in complex choice situations with many alternatives or attributes and where choices are made under time constraints, individuals tend to minimise their cognitive effort by using some heuristics. For instance, they may screen some alternatives or choose any satisfying alternative that meets some criteria. While most choice models rely on utility maximisation as the decision rule, this approach does not always align with observed choice behaviour. Second, psychological research has shown that the driver of choices can be context-dependent. For example, it has been observed that decision-makers may be influenced by reference alternatives, which may bias their perception of the other ones (e.g., the decoy effect). Paper 2 introduces an innovative choice model based on the disjunctive decision rule, which differs from traditional utility maximisation. This model termed the Generalised Random Disjunctive Model (GRDM), allows alternatives to be assigned high probabilities as long as they perform best in at least one attribute, even if they might seem unrealistic according to a utility-maximising perspective. The GRDM extends the previously developed Random Disjunctive Model (RDM), incorporating weights to prioritise the most influential attributes. The GRDM can be represented as a logit model, and its marginal rates
of substitution and elasticities are examined. The study combines the GRDM with the MNL model within a Latent Class framework to explore the complementarity of different decision rules. This combined model is tested in two large-scale route choice case studies. One is focused on public transport, and the other on cycling in the Greater Copenhagen Area. The results demonstrate that integrating multiple decision rules provides better explanatory and predictive power than relying solely on taste heterogeneity. Around 27.4% of the cyclists’ route choice observations and 8.5% of the public transport observations were better explained by the disjunctive decision rule. In particular, it reveals that some individuals are inelastic to changes in certain attributes, a phenomenon that the MNL model cannot account for. Furthermore, the GRDM effectively captures traveller behaviours that traditional models fail to explain, even when incorporating taste heterogeneity or non-linear preferences.

The two last papers build on the Bounded Choice Model (BCM). The BCM is an extension of the MNL, assuming that individuals do not consider alternatives that perform relatively poorly in utility compared to a reference alternative. Being derived from first principles by assuming a left-truncated Logistic distribution for the error term difference, the BCM is a simple yet efficient one-stage choice set formation model. However, it suffers from drawbacks similar to the MNL, including its IIA property and homoscedasticity. Moreover, the left truncation makes it non-differentiable, an undesirable property for practical applications. Papers 3 and 4 aim to solve these main limitations and help improve the versatility and usability of the BCM.

The Smooth Bounded Choice Model (SBCM), presented in Paper 3, addresses the nondifferentiability issue in the original BCM by introducing a left-truncated smooth logistic distribution and a smooth approximation of the reference alternative using the Boltzmann function. These enhancements increase the model’s flexibility and allow it to approximate BCM and MNL models under certain conditions. The paper also presents analytical closed-form expressions for key metrics like choice probabilities gradients, Hessian, and elasticities. Additionally, a Smooth Bounded Path-Size (SBPS) model is developed to manage route overlap consistently. The SBCM capabilities are demonstrated through three large-scale case studies in the Greater Copenhagen Area, proving its superior ability to capture complex choice behaviours compared to traditional models like MNL and BCM. For example, SBCM offers a more nuanced interpretation of behaviour in the mode choice case study than the MNL. Specifically, SBCM reveals that walking is excluded from the consideration set in many cases where the car is chosen, resulting in a much smaller elasticity of car probabilities to walking travel time than the MNL. This indicates that the MNL likely overestimates the impact of walking travel time on car choices. Furthermore, the SBCM shows that a marginal increase in cycling travel time significantly affects walking’s predicted share, especially when the car is not an option and public transport is less attractive. This suggests that SBCM provides a more accurate prediction of behavioural changes in response to pro-cycling policies.

Paper 4 addresses the limitations of the BCM in accounting for heteroscedasticity and correlation between alternatives in route choice scenarios. The paper introduces the Bounded q-Product Logit (BqPL) model, which integrates the distributional assumptions of the existing q-Product Logit (qPL) and the BCM models. This results in a heteroscedastic model incorporating choice set formation through a left-truncated q-log-logistic distribution. The BqPL model is extended to the Bounded Path-Size q-Product Logit (BPSqPL) model to account for route correlation consistently. These models can be interpreted through the relationship between costs’ systematic and stochastic components. Alternatively, it can be understood in terms of how decision-makers evaluate route costs within a choice set, whether by considering differences (as in the MNL), ratios (as in Weibit models), or an intermediate q-ratio (as in the qPL). The BPSqPL model is applied to a
large-scale route choice case study, demonstrating its superior ability to fit and predict behaviour compared to less sophisticated models. One key finding from this model is that cyclists tend to evaluate route costs in a way that is closer to a ratio rather than a simple difference.

In summary, this thesis advances the field of choice modelling by addressing key limitations
of the MNL model and proposing new models that better balance behavioural realism and
practical applicability. The developed models treat some of the key topics of the current
choice modelling literature, such as handling emerging crowdsourced datasets, modelling
decision rule heterogeneity, accounting for choice set formation and heteroscedasticity.
The developed models aim to provide a possibility to address these deficiencies jointly,
mitigating the risk of confounding and extensive estimation times by providing simple
closed-form extensions of the MNL and RDM models. As a result, the developed models
retain a high behavioural interpretability, as they include extra parameters with parsimony.

Fixing some of these parameters permits the models to collapse to well-known developed
models, such as the MNL or its Weibit counterpart. The models’ behavioural properties
were demonstrated on both small-scale examples and large-scale case studies, where the
fit and predictive abilities were also benchmarked with other existing models. Further work
should make it possible to unify the work of the four papers altogether and to develop
an even more robust modelling framework that would be applicable to a wide range of
choice situations with large-scale datasets.