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Deep neural networks (DNNs) frequently present behaviorally irregular patterns, significantly limiting their practical potentials and theoretical validity in travel behavior modeling. This study proposes strong and weak behavioral regularities as novel metrics to evaluate the monotonicity of individual demand functions (known as the "law of demand"), and further designs a constrained optimization framework with six gradient regularizers to enhance DNNs' behavioral regularity. The proposed framework is applied to travel survey data from Chicago and London to examine the trade-off between predictive power and behavioral regularity for large vs. small sample scenarios and in-domain vs. out-of-domain generalizations. The results demonstrate that, unlike models with strong behavioral foundations such as the multinomial logit, the benchmark DNNs cannot guarantee behavioral regularity. However, gradient regularization (GR) increases DNNs' behavioral regularity by around 6 percentage points (pp) while retaining their relatively high predictive power. In the small sample scenario, GR is more effective than in the large sample scenario, simultaneously improving behavioral regularity by about 20 pp and log-likelihood by around 1.7%. Comparing with the in-domain generalization of DNNs, GR works more effectively in out-of-domain generalization: it drastically improves the behavioral regularity of poorly performing benchmark DNNs by around 65 pp, indicating the criticality of behavioral regularization for enhancing model transferability and application in forecasting. Moreover, the proposed framework is applicable to other NN-based choice models such as TasteNets. Future studies could use behavioral regularity as a metric along with log-likelihood in evaluating travel demand models, and investigate other methods to further enhance behavioral regularity when adopting complex machine learning models.

Maximum simulated likelihood estimation of mixed multinomial logit (MMNL) or probit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as shuffled and scrambled Halton sequences and modified Latin hypercube sampling (MLHS) are workhorse methods for integral approximation. A few earlier studies explored the potential of sparse grid quadrature (SGQ), but this approximation suffers from negative weights. As an alternative to QMC and SGQ, we looked into the recently developed designed quadrature (DQ) method. DQ requires fewer nodes to get the same level of accuracy as of QMC and SGQ, is as easy to implement, ensures positivity of weights, and can be created on any general polynomial spaces. We benchmarked DQ against QMC in a Monte Carlo study under different data generating processes with a varying number of random parameters (3, 5, and 10) and variance-covariance structures (diagonal and full). Whereas DQ significantly outperformed QMC in the diagonal variance-covariance scenario, it could also achieve a better model fit and recover true parameters with fewer nodes (i.e., relatively lower computation time) in the full variance-covariance scenario. Finally, we evaluated the performance of DQ in a case study to understand preferences for mobility-on-demand services in New York City. In estimating MMNL with five random parameters, DQ achieved better fit and statistical significance of parameters with just 200 nodes as compared to 1000 QMC draws, making DQ around five times faster than QMC methods.

Variational Bayes (VB), a method originating from machine learning, enables fast and scalable estimation of complex probabilistic models. Thus far, applications of VB in discrete choice analysis have been limited to mixed logit models with unobserved inter-individual taste heterogeneity. However, such a model formulation may be too restrictive in panel data settings, since tastes may vary both between individuals as well as across choice tasks encountered by the same individual. In this paper, we derive a VB method for posterior inference in mixed logit models with unobserved inter- and intra-individual heterogeneity. In a simulation study, we benchmark the performance of the proposed VB method against maximum simulated likelihood (MSL) and Markov chain Monte Carlo (MCMC) methods in terms of parameter recovery, predictive accuracy and computational efficiency. The simulation study shows that VB can be a fast, scalable and accurate alternative to MSL and MCMC estimation, especially in applications in which fast predictions are paramount. VB is observed to be between 2.8 and 17.7 times faster than the two competing methods, while affording comparable or superior accuracy. Besides, the simulation study demonstrates that a parallelised implementation of the MSL estimator with analytical gradients is a viable alternative to MCMC in terms of both estimation accuracy and computational efficiency, as the MSL estimator is observed to be between 0.9 and 2.1 times faster than MCMC.

In multinomial response models, idiosyncratic variations in the indirect utility are generally modeled using Gumbel or normal distributions. This study makes a strong case to substitute these thin-tailed distributions with a t-distribution. First, we demonstrate that a model with a t-distributed error kernel better estimates and predicts preferences, especially in class-imbalanced datasets. Our proposed specification also implicitly accounts for decision-uncertainty behavior, i.e. the degree of certainty that decision-makers hold in their choices relative to the variation in the indirect utility of any alternative. Second, after applying a t-distributed error kernel in a multinomial response model for the first time, we extend this specification to a generalized continuous-multinomial (GCM) model and derive its full-information maximum likelihood estimator. The likelihood involves an open-form expression of the cumulative density function of the multivariate t-distribution, which we propose to compute using a combination of the composite marginal likelihood method and the separation-of-variables approach. Third, we establish finite sample properties of the GCM model with a t-distributed error kernel (GCM-t) and highlight its superiority over the GCM model with a normally-distributed error kernel (GCM-N) in a Monte Carlo study. Finally, we compare GCM-t and GCM-N in an empirical setting related to preferences for electric vehicles (EVs). We observe that accounting for decision-uncertainty behavior in GCM-t results in lower elasticity estimates and a higher willingness to pay for improving the EV attributes than those of the GCM-N model. These differences are relevant in making policies to expedite the adoption of EVs.

We formalize one aspect of reliability in the context of Mobility-on-Demand (MoD) systems by acknowledging the uncertainty in the pick-up time of these services. This study answers two key questions: i) how the difference between the stated and actual pick-up times affect the propensity of a passenger to choose an MoD service? ii) how an MoD service provider can leverage this information to increase its ridership? We conduct a discrete choice experiment in New York to answer the former question and adopt a micro-simulation-based optimization method to answer the latter question. In our experiments, the ridership of an MoD service could be increased by up to 10\% via displaying the predicted wait time strategically.

Transportation Network Companies (TNCs) are changing the transportation ecosystem, but micro-decisions of drivers and users need to be better understood to assess the system-level impacts of TNCs. In this regard, we contribute to the literature by estimating a) individuals' preferences of being a rider, a driver, or a non-user of TNC services; b) preferences of ridehailing users for ridepooling; c) TNC drivers' choice to switch to vehicles with better fuel economy, and also d) the drivers' decision to buy, rent or lease new vehicles with driving for TNCs being a major consideration. Elicitation of drivers' preferences using a unique sample (N=11,902) of the U.S. population residing in TNC-served areas is the key feature of this study. The statistical analysis indicates that ridehailing services are mainly attracting personal vehicle users as riders, without substantially affecting demand for transit. Moreover, around 10% of ridehailing users reported postponing the purchase of a new car due to the availability of TNC services. The model estimation results indicate that the likelihood of being a TNC user increases with the increase in age for someone younger than 44 years, but the pattern is reversed post 44 years. This change in direction of the marginal effect of age is insightful as the previous studies have reported a negative association. We also find that postgraduate drivers who live in metropolitan regions are more likely to switch to fuel-efficient vehicles. These findings would inform transportation planners and TNCs in developing policies to improve the fuel economy of the fleet.

The standard Gibbs sampler of Mixed Multinomial Logit (MMNL) models involves sampling from conditional densities of utility parameters using Metropolis-Hastings (MH) algorithm due to unavailability of conjugate prior for logit kernel. To address this non-conjugacy concern, we propose the application of P\'olygamma data augmentation (PG-DA) technique for the MMNL estimation. The posterior estimates of the augmented and the default Gibbs sampler are similar for two-alternative scenario (binary choice), but we encounter empirical identification issues in the case of more alternatives ($J \geq 3$)., Comment: arXiv admin note: text overlap with arXiv:1904.03647

Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substantially faster than MCMC at practically no compromises in predictive accuracy. In this paper, we address two critical gaps concerning the usage and understanding of VB for MMNL. First, extant VB methods are limited to utility specifications involving only individual-specific taste parameters. Second, the finite-sample properties of VB estimators and the relative performance of VB, MCMC and maximum simulated likelihood estimation (MSLE) are not known. To address the former, this study extends several VB methods for MMNL to admit utility specifications including both fixed and random utility parameters. To address the latter, we conduct an extensive simulation-based evaluation to benchmark the extended VB methods against MCMC and MSLE in terms of estimation times, parameter recovery and predictive accuracy. The results suggest that all VB variants with the exception of the ones relying on an alternative variational lower bound constructed with the help of the modified Jensen's inequality perform as well as MCMC and MSLE at prediction and parameter recovery. In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is up to 16 times faster than MCMC and MSLE. Thus, VB-NCVMP-Delta can be an attractive alternative to MCMC and MSLE for fast, scalable and accurate estimation of MMNL models.

Mobility-on-Demand (MoD) systems are generally designed and analyzed for a fixed and exogenous demand, but such frameworks fail to answer questions about the impact of these services on the urban transportation system, such as the effect of induced demand and the implications for transit ridership. In this study, we propose a unified framework to design, optimize and analyze MoD operations within a multimodal transportation system where the demand for a travel mode is a function of its level of service. An application of Bayesian optimization (BO) to derive the optimal supply-side MoD parameters (e.g., fleet size and fare) is also illustrated. The proposed framework is calibrated using the taxi demand data in Manhattan, New York. Travel demand is served by public transit and MoD services of varying passenger capacities (1, 4 and 10), and passengers are predicted to choose travel modes according to a mode choice model. This choice model is estimated using stated preference data collected in New York City. The convergence of the multimodal supply-demand system and the superiority of the BO-based optimization method over earlier approaches are established through numerical experiments. We finally consider a policy intervention where the government imposes a tax on the ride-hailing service and illustrate how the proposed framework can quantify the pros and cons of such policies for different stakeholders., Comment: 31 pages, 11 figures. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/