Background: Any sample of individuals has its own, unique distribution of preferences for choices that they make. Discrete choice models try to capture these distributions. Mixed logits are by far the most commonly used choice model in health. A raft of parametric model specifications for these models are available. We test a range of alternatives assumptions, and model averaging, to test if or how model outputs are impacted. Design: Scoping review of current modelling practices. Seven alternative distributions, and model averaging over all distributional assumptions, were compared on four datasets: two were stated preference, one was revealed preference, and one was simulated. Analyses examined model fit, preference distributions, willingness-to-pay, and forecasting. Results: Almost universally, using normal distributions is the standard practice in health. Alternative distributional assumptions outperformed standard practice. Preference distributions and the mean willingness-to-pay varied significantly across specifications, and were seldom comparable to those derived from normal distributions. Model averaging offered distributions allowed for greater flexibility, further gains in fit, reproduced underlying distributions in simulations, and mitigated against analyst bias arising from distribution selection. There was no evidence that distributional assumptions impacted predictions from models. Limitations: Our focus was on mixed logit models since these models are the most common in health, though latent class models are also used. Conclusions: The standard practice of using all normal distributions appears to be an inferior approach for capturing random preference heterogeneity. Implications: Researchers should test alternative assumptions to normal distributions in their models.
Discrete choice models (DCMs) are used to analyze individual decision-making in contexts such as transportation choices, political elections, and consumer preferences. DCMs play a central role in applied econometrics by enabling inference on key economic variables, such as marginal rates of substitution, rather than focusing solely on predicting choices on new unlabeled data. However, while traditional DCMs offer high interpretability and support for point and interval estimation of economic quantities, these models often underperform in predictive tasks compared to deep learning (DL) models. Despite their predictive advantages, DL models remain largely underutilized in discrete choice due to concerns about their lack of interpretability, unstable parameter estimates, and the absence of established methods for uncertainty quantification. Here, we introduce a deep learning model architecture specifically designed to integrate with approximate Bayesian inference methods, such as Stochastic Gradient Langevin Dynamics (SGLD). Our proposed model collapses to behaviorally informed hypotheses when data is limited, mitigating overfitting and instability in underspecified settings while retaining the flexibility to capture complex nonlinear relationships when sufficient data is available. We demonstrate our approach using SGLD through a Monte Carlo simulation study, evaluating both predictive metrics--such as out-of-sample balanced accuracy--and inferential metrics--such as empirical coverage for marginal rates of substitution interval estimates. Additionally, we present results from two empirical case studies: one using revealed mode choice data in NYC, and the other based on the widely used Swiss train choice stated preference data.
Urban traffic congestion, exacerbated by inefficient parking management and cruising for parking, significantly hampers mobility and sustainability in smart cities. Drivers often face delays searching for parking spaces, influenced by factors such as accessibility, cost, distance, and available services such as charging facilities in the case of electric vehicles. These inefficiencies contribute to increased urban congestion, fuel consumption, and environmental impact. Addressing these challenges, this paper proposes a feedback control incentivisation-based system that aims to better distribute vehicles between city and suburban parking facilities offering park-and-charge/-ride services. Individual driver behaviours are captured via discrete choice models incorporating factors of importance to parking location choice among drivers, such as distance to work, public transport connectivity, charging infrastructure availability, and amount of incentive offered; and are regulated through principles of ergodic control theory. The proposed framework is applied to an electric vehicle park-and-charge/-ride problem, and demonstrates how predictable long-term behaviour of the system can be guaranteed.
This technical note provides comprehensive derivations of fundamental equations in two-level nested and sequential logit models for analyzing hierarchical choice structures. We present derivations of the Berry (1994) inversion formula, nested inclusive values computation, and multi-level market share equations, complementing existing literature. While conceptually distinct, nested and sequential logit models share mathematical similarities and, under specific distributional assumptions, yield identical inversion formulas-offering valuable analytical insights. These notes serve as a practical reference for researchers implementing multi-level discrete choice models in empirical applications, particularly in industrial organization and demand estimation contexts, and complement Mansley et al. (2019).
We introduce a novel model architecture that incorporates network effects into discrete choice problems, achieving higher predictive performance than standard discrete choice models while offering greater interpretability than general-purpose flexible model classes. Econometric discrete choice models aid in studying individual decision-making, where agents select the option with the highest reward from a discrete set of alternatives. Intuitively, the utility an individual derives from a particular choice depends on their personal preferences and characteristics, the attributes of the alternative, and the value their peers assign to that alternative or their previous choices. However, most applications ignore peer influence, and models that do consider peer or network effects often lack the flexibility and predictive performance of recently developed approaches to discrete choice, such as deep learning. We propose a novel graph convolutional neural network architecture to model network effects in discrete choices, achieving higher predictive performance than standard discrete choice models while retaining the interpretability necessary for inference--a quality often lacking in general-purpose deep learning architectures. We evaluate our architecture using revealed commuting choice data, extended with travel times and trip costs for each travel mode for work-related trips in New York City, as well as 2016 U.S. election data aggregated by county, to test its performance on datasets with highly imbalanced classes. Given the interpretability of our models, we can estimate relevant economic metrics, such as the value of travel time savings in New York City. Finally, we compare the predictive performance and behavioral insights from our architecture to those derived from traditional discrete choice and general-purpose deep learning models.
Estimation and counterfactual experiments in dynamic discrete choice models with large state spaces pose computational difficulties. This paper develops a novel model-adaptive approach to solve the linear system of fixed point equations of the policy valuation operator. We propose a model-adaptive sieve space, constructed by iteratively augmenting the space with the residual from the previous iteration. We show both theoretically and numerically that model-adaptive sieves dramatically improve performance. In particular, the approximation error decays at a superlinear rate in the sieve dimension, unlike a linear rate achieved using conventional methods. Our method works for both conditional choice probability estimators and full-solution estimators with policy iteration. We apply the method to analyze consumer demand for laundry detergent using Kantar's Worldpanel Take Home data. On average, our method is 51.5% faster than conventional methods in solving the dynamic programming problem, making the Bayesian MCMC estimator computationally feasible.
A growing number of empirical models exhibit set-valued predictions. This paper develops a tractable inference method with finite-sample validity for such models. The proposed procedure uses a robust version of the universal inference framework by Wasserman et al. (2020) and avoids using moment selection tuning parameters, resampling, or simulations. The method is designed for constructing confidence intervals for counterfactual objects and other functionals of the underlying parameter. It can be used in applications that involve model incompleteness, discrete and continuous covariates, and parameters containing nuisance components.
This paper introduces a framework for capturing stochasticity of choice probabilities in neural networks, derived from and fully consistent with the Random Utility Maximization (RUM) theory, referred to as RUM-NN. Neural network models show remarkable performance compared with statistical models; however, they are often criticized for their lack of transparency and interoperability. The proposed RUM-NN is introduced in both linear and nonlinear structures. The linear RUM-NN retains the interpretability and identifiability of traditional econometric discrete choice models while using neural network-based estimation techniques. The nonlinear RUM-NN extends the model's flexibility and predictive capabilities to capture nonlinear relationships between variables within utility functions. Additionally, the RUM-NN allows for the implementation of various parametric distributions for unobserved error components in the utility function and captures correlations among error terms. The performance of RUM-NN in parameter recovery and prediction accuracy is rigorously evaluated using synthetic datasets through Monte Carlo experiments. Additionally, RUM-NN is evaluated on the Swissmetro and the London Passenger Mode Choice (LPMC) datasets with different sets of distribution assumptions for the error component. The results demonstrate that RUM-NN under a linear utility structure and IID Gumbel error terms can replicate the performance of the Multinomial Logit (MNL) model, but relaxing those constraints leads to superior performance for both Swissmetro and LPMC datasets. By introducing a novel estimation approach aligned with statistical theories, this study empowers econometricians to harness the advantages of neural network models.
Discrete choice models are essential for modelling various decision-making processes in human behaviour. However, the specification of these models has depended heavily on domain knowledge from experts, and the fully automated but interpretable modelling of complex human behaviours has been a long-standing challenge. In this paper, we introduce the differentiable discrete choice model (Diff-DCM), a fully data-driven method for the interpretable modelling, learning, prediction, and control of complex human behaviours, which is realised by differentiable programming. Solely from input features and choice outcomes without any prior knowledge, Diff-DCM can estimate interpretable closed-form utility functions that reproduce observed behaviours. Comprehensive experiments with both synthetic and real-world data demonstrate that Diff-DCM can be applied to various types of data and requires only a small amount of computational resources for the estimations, which can be completed within tens of seconds on a laptop without any accelerators. In these experiments, we also demonstrate that, using its differentiability, Diff-DCM can provide useful insights into human behaviours, such as an optimal intervention path for effective behavioural changes. This study provides a strong basis for the fully automated and reliable modelling, prediction, and control of human behaviours.
Residential location choices are traditionally modelled using factors related to accessibility and socioeconomic environments, neglecting the importance of local street-level conditions. Arguably, this neglect is due to data practices. Today, however, street-level images -- which are highly effective at encoding street-level conditions -- are widely available. Additionally, recent advances in discrete choice models incorporating computer vision capabilities offer opportunities to integrate street-level conditions into residential location choice analysis. This study leverages these developments to investigate the spatial distribution of utility derived from street-level conditions in residential location choices on a city-wide scale. In our case study of Rotterdam, the Netherlands, we find that the utility derived from street-level conditions varies significantly on a highly localised scale, with conditions rapidly changing even within neighbourhoods. Our results also reveal that the high real-estate prices in the city centre cannot be attributed to attractive street-level conditions. Furthermore, whereas the city centre is characterised by relatively unattractive residential street-level conditions, neighbourhoods in the southern part of the city -- often perceived as problematic -- exhibit surprisingly appealing street-level environments. The methodological contribution of this paper is that it advances the discrete choice models incorporating computer vision capabilities by introducing a semantic regularisation layer to the model. Thereby, it adds explainability and eliminates the need for a separate pipeline to extract information from images, streamlining the analysis. As such, this paper's findings and methodological advancements pave the way for further studies to explore integrating street-level conditions in urban planning.
Through exposing items to users, implicit feedback recommender systems influence the logged interactions, and, ultimately, their own recommendations. This effect is called exposure bias and it can lead to issues such as filter bubbles and echo chambers. Previous research employed the multinomial logit model (MNL) with exposure information to reduce exposure bias on synthetic data. This extended abstract summarizes our previous study in which we investigated whether (i) these findings hold for human-generated choices, (ii) other discrete choice models mitigate bias better, and (iii) an item's estimated relevance can depend on the relevances of the other items that were presented with it. We collected a data set of biased and unbiased choices in a controlled online user study and measured the effects of overexposure and competition. We found that (i) the discrete choice models effectively mitigated exposure bias on human-generated choice data, (ii) there were no significant differences in robustness among the different discrete choice models, and (iii) only multivariate discrete choice models were robust to competition between items. We conclude that discrete choice models mitigate exposure bias effectively because they consider item-co-exposure. Moreover, exposing items alongside more or less popular items can bias future recommendations significantly and item exposure must be tracked for overcoming exposure bias. We consider our work vital for understanding what exposure bias it, how it forms, and how it can be mitigated.
In dynamic discrete choice models, some parameters, such as the discount factor, are being fixed instead of being estimated. This paper proposes two sensitivity analysis procedures for dynamic discrete choice models with respect to the fixed parameters. First, I develop a local sensitivity measure that estimates the change in the target parameter for a unit change in the fixed parameter. This measure is fast to compute as it does not require model re-estimation. Second, I propose a global sensitivity analysis procedure that uses model primitives to study the relationship between target parameters and fixed parameters. I show how to apply the sensitivity analysis procedures of this paper through two empirical applications.
This paper studies the finite sample performance of the flexible estimation approach of Farrell, Liang, and Misra (2021a), who propose to use deep learning for the estimation of heterogeneous parameters in economic models, in the context of discrete choice models. The approach combines the structure imposed by economic models with the flexibility of deep learning, which assures the interpretebility of results on the one hand, and allows estimating flexible functional forms of observed heterogeneity on the other hand. For inference after the estimation with deep learning, Farrell et al. (2021a) derive an influence function that can be applied to many quantities of interest. We conduct a series of Monte Carlo experiments that investigate the impact of regularization on the proposed estimation and inference procedure in the context of discrete choice models. The results show that the deep learning approach generally leads to precise estimates of the true average parameters and that regular robust standard errors lead to invalid inference results, showing the need for the influence function approach for inference. Without regularization, the influence function approach can lead to substantial bias and large estimated standard errors caused by extreme outliers. Regularization reduces this property and stabilizes the estimation procedure, but at the expense of inducing an additional bias. The bias in combination with decreasing variance associated with increasing regularization leads to the construction of invalid inferential statements in our experiments. Repeated sample splitting, unlike regularization, stabilizes the estimation approach without introducing an additional bias, thereby allowing for the construction of valid inferential statements.
Discrete choice models (DCMs) have been widely utilized in various scientific fields, especially economics, for many years. These models consider a stochastic environment influencing each decision maker's choices. Extensive research has shown that the agents' socioeconomic characteristics, the chosen options' properties, and the conditions characterizing the decision-making environment all impact these models. However, the complex interactions between these factors, confidentiality concerns, time constraints, and costs, have made real experimentation impractical and undesirable. To address this, simulations have gained significant popularity among academics, allowing the study of these models in a controlled setting using simulated data. This paper presents multidisciplinary research to bridge the gap between DCMs, experimental design, and simulation. By reviewing related literature, the authors explore these interconnected areas. We then introduce a simulation method integrated with experimental design to generate synthetic data based on behavioral models of agents. A utility function is used to describe the developed simulation tool. The paper investigates the discrepancy between simulated data and real-world data.
Travel choice analysis is crucial for understanding individual travel behavior to develop appropriate transport policies and recommendation systems in Intelligent Transportation Systems (ITS). Despite extensive research, this domain faces two critical challenges: a) modeling with limited survey data, and b) simultaneously achieving high model explainability and accuracy. In this paper, we introduce a novel prompt-learning-based Large Language Model(LLM) framework that significantly improves prediction accuracy and provides explicit explanations for individual predictions. This framework involves three main steps: transforming input variables into textual form; building of demonstrations similar to the object, and applying these to a well-trained LLM. We tested the framework's efficacy using two widely used choice datasets: London Passenger Mode Choice (LPMC) and Optima-Mode collected in Switzerland. The results indicate that the LLM significantly outperforms state-of-the-art deep learning methods and discrete choice models in predicting people's choices. Additionally, we present a case of explanation illustrating how the LLM framework generates understandable and explicit explanations at the individual level.
This paper extends the work of Arcidiacono and Miller (2011, 2019) by introducing a novel characterization of finite dependence within dynamic discrete choice models, demonstrating that numerous models display 2-period finite dependence. We recast finite dependence as a problem of sequentially searching for weights and introduce a computationally efficient method for determining these weights by utilizing the Kronecker product structure embedded in state transitions. With the estimated weights, we develop a computationally attractive Conditional Choice Probability estimator with 2-period finite dependence. The computational efficacy of our proposed estimator is demonstrated through Monte Carlo simulations.
We revisit a classical question of how individual consumer preferences and incomes shape aggregate behavior. We develop a method that applies to populations with homothetic preferences and reduces the hard problem of aggregation to simply computing a weighted average in the space of logarithmic expenditure functions. We apply the method to identify aggregation-invariant preference domains, characterize aggregate preferences from common domains like linear or Leontief, and describe indecomposable preferences that do not correspond to the aggregate behavior of any non-trivial population. Applications include robust welfare analysis, information design, discrete choice models, pseudo-market mechanisms, and preference identification.
This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve estimators to estimate the control function nonparametrically, followed by Bayesian methods to estimate the structural parameters. This combination leverages the advantages of both frequentist tractability for nonparametric estimation and Bayesian computational efficiency for complicated structural models. We analyze the asymptotic properties of the resulting quasi-posterior distribution, finding that its mean provides a consistent estimator for the parameters of interest, although its quantiles do not yield valid confidence intervals. However, bootstrapping the quasi-posterior mean accounts for the estimation uncertainty from the first stage, thereby producing asymptotically valid confidence intervals.
This paper introduces the Mixed Aggregate Preference Logit (MAPL, pronounced "maple'') model, a novel class of discrete choice models that leverages machine learning to model unobserved heterogeneity in discrete choice analysis. The traditional mixed logit model (also known as "random parameters logit'') parameterizes preference heterogeneity through assumptions about feature-specific heterogeneity distributions. These parameters are also typically assumed to be linearly added in a random utility (or random regret) model. MAPL models relax these assumptions by instead directly relating model inputs to parameters of alternative-specific distributions of aggregate preference heterogeneity, with no feature-level assumptions required. MAPL models eliminate the need to make any assumption about the functional form of the latent decision model, freeing modelers from potential misspecification errors. In a simulation experiment, we demonstrate that a single MAPL model specification is capable of correctly modeling multiple different data-generating processes with different forms of utility and heterogeneity specifications. MAPL models advance machine-learning-based choice models by accounting for unobserved heterogeneity. Further, MAPL models can be leveraged by traditional choice modelers as a diagnostic tool for identifying utility and heterogeneity misspecification.
The decision making involved behind the mode choice is critical for transportation planning. While statistical learning techniques like discrete choice models have been used traditionally, machine learning (ML) models have gained traction recently among the transportation planners due to their higher predictive performance. However, the black box nature of ML models pose significant interpretability challenges, limiting their practical application in decision and policy making. This study utilised a dataset of $1350$ households belonging to low and low-middle income bracket in the city of Bengaluru to investigate mode choice decision making behaviour using Multinomial logit model and ML classifiers like decision trees, random forests, extreme gradient boosting and support vector machines. In terms of accuracy, random forest model performed the best ($0.788$ on training data and $0.605$ on testing data) compared to all the other models. This research has adopted modern interpretability techniques like feature importance and individual conditional expectation plots to explain the decision making behaviour using ML models. A higher travel costs significantly reduce the predicted probability of bus usage compared to other modes (a $0.66\%$ and $0.34\%$ reduction using Random Forests and XGBoost model for $10\%$ increase in travel cost). However, reducing travel time by $10\%$ increases the preference for the metro ($0.16\%$ in Random Forests and 0.42% in XGBoost). This research augments the ongoing research on mode choice analysis using machine learning techniques, which would help in improving the understanding of the performance of these models with real-world data in terms of both accuracy and interpretability.