Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluations

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

Robust discrete choice models with t-distributed kernel errors

Models that are robust to aberrant choice behaviour have received limited attention in discrete choice analysis. In this paper, we analyse two robust alternatives to the multinomial probit (MNP) model. Both alternative models belong to the family of robit models, whose kernel error distributions are heavy-tailed t-distributions. The first model is the multinomial robit (MNR) model in which a generic degrees of freedom parameter controls the heavy-tailedness of the kernel error distribution. The second alternative, the generalised multinomial robit (Gen-MNR) model, has not been studied in the literature before and is more flexible than MNR, as it allows for alternative-specific marginal heavy-tailedness of the kernel error distribution. For both models, we devise scalable and gradient-free Bayes estimators. We compare MNP, MNR and Gen-MNR in a simulation study and a case study on transport mode choice behaviour. We find that both MNR and Gen-MNR deliver significantly better in-sample fit and out-of-sample predictive accuracy than MNP. Gen-MNR outperforms MNR due to its more flexible kernel error distribution. Also, Gen-MNR gives more reasonable elasticity estimates than MNP and MNR, in particular regarding the demand for under-represented alternatives in a class-imbalanced dataset

Empowering revealed preference survey with a supplementary stated preference survey: demonstration of willingness-to-pay estimation within a mode choice case

Mode choice models play a pivotal role in transport demand modelling and help transport planners, engineers and researchers with policy and infrastructure investment evaluation. Recent mode choice studies primarily use revealed preference (RP) data to reflect individuals’ true behaviour. However, this may not be the best practice, given the lack of information in RP data. This study uses a nonlinear utility specification for a multinomial logit mode choice model development using high-quality travel data collected by a GPS-based smartphone application complemented by stated preference (SP) data. The model results highlight the impact of sociodemographic variables on mode choice behaviour and individuals’ willingness-to-pay (WTP) when the model is jointly developed compared to stand-alone SP and RP models. The main message of this study is that in addition to collecting RP, which is a reliable and unbiased source of data, collecting complementary SP data is beneficial as it provides information that is not otherwise available in RP data. This may include a proper variation in the public transport cost variable as demonstrated in this study. Moreover, to better understand the travellers' behaviour regarding the trade-off between time and cost a mixed multinomial logit (MMNL) model in the willingness to pay space is developed on the SP data. capturing the unobserved heterogeneity within the estimated WTPs, the MMNL model outputs reveal a higher variation in WTP of car in-vehicle travel time compared to bus in-vehicle travel time

Resolving time conflicts in activity-based scheduling: A case study of Lausanne

In this paper, we present a novel activity-based scheduling model that combines a continuous optimisation framework for temporal scheduling decisions (i.e. activity timings and durations) with traditional discrete choice models for non-temporal choice dimensions (i.e. activity participation, number and type of tours, and considered destinations). The central concept of our approach is that individuals resolve time conflicts that arise from overlapping activities, e.g. needing to work and desiring to shop at the same time, in order to maximise their derived utility. Our proposed framework has three primary advantages over existing activity scheduling approaches: (i) the time-conflicts between different temporal scheduling decisions are considered and resolved jointly; (ii) individual behavioural preferences are incorporated in the scheduling problem using a utility-maximisation approach; and (iii) the framework is computationally scalable and can be used to estimate and simulate a city-scale case study in reasonable time. We introduce an estimation routine for the framework that allows model parameters to be calibrated using real-world historic data, as well as an efficient mixed-integer linear solver to optimally resolve temporal conflicts in simulated schedules. The estimation routine is applied and calibrated to a set of observed schedules in the Swiss mobility and transport microcensus. We then use the optimisation program with the estimated parameters to simulate activity schedules for a synthetic population for the city of Lausanne, Switzerland. We validate the model results against reported schedules in the microcensus data. The results demonstrate the capabilities of our approach to simulate realistic, flexible schedules for a real-world case-stud