Strategic sampling for large choice sets in estimation and application

Many discrete choice contexts in transportation deal with large choice sets, including destination, route, and vehicle choices. Model estimation with large numbers of alternatives remains computationally expensive. In the context of the multinomial logit (MNL) model, limiting the number of alternatives in estimation by simple random sampling (SRS) yields consistent parameter estimates, but estimator efficiency suffers. In the context of more general models, such as the mixed MNL, limiting the number of alternatives via SRS yields biased parameter estimates. In this paper, a new, strategic sampling scheme is introduced, which draws alternatives in proportion to updated choice-probability estimates. Since such probabilities are not known a priori, the first iteration uses SRS among all available alternatives. The sampling scheme is implemented here for a variety of simulated MNL and mixed-MNL data sets, with results suggesting that the new sampling scheme provides substantial efficiency benefits. Thanks to reductions in estimation error, parameter estimates are more accurate, on average. Moreover, in the mixed MNL case, where SRS produces biased estimates (due to violation of the independence of irrelevant alternatives property), the new sampling scheme appears to effectively eliminate such biases. Finally, it appears that only a single iteration of the new strategy (following the initialization step using SRS) is needed to deliver the strategy’s maximum efficiency gains.     

A behavioral housing search model: Two-stage hazard-based and multinomial logit approach to choice-set formation and location selection

Residential location search has become an important topic to both practitioners and researchers as more detailed and disaggregate land-use and transportation demand models are developed which require information on individual household location decisions. The housing search process starts with an alternative formation and screening stage. At this level households evaluate all potential alternatives based on their lifestyle, preferences, and utilities to form a manageable choice set with a limited number of plausible alternatives. Then the final residential location is selected among these alternatives. This two-stage decision making process can be used for both aggregate zone-level selection as well as searching disaggregate parcel or building-based housing markets for potential dwellings. In this paper a zonal level household housing search model is developed. Initially, a household specific choice set is drawn from the entire possible alternatives in the area based on the average household work distance to each alternative. Following the choice set formation step, a discrete choice model is utilized for modeling the final residential zone selection of the household. A hazard-based model is used for the choice set formation module while the final choice selection is modeled using a multinomial logit formulation with a deterministic sample correction factor. The approach presented in the paper provides a remedy for the large choice set problem typically faced in housing search models.     

Metropolis–Hastings sampling of paths

We consider the previously unsolved problem of sampling paths according to a given distribution from a general network. The problem is difficult because of the combinatorial number of alternatives, which prohibits a complete enumeration of all paths and hence also forbids to compute the normalizing constant of the sampling distribution. The problem is important because the ability to sample from a known distribution introduces mathematical rigor into many applications, including the estimation of choice models with sampling of alternatives that can be formalized as paths in a decision network (most obviously route choice), probabilistic map matching, dynamic traffic assignment, and route guidance.     

An assignment model with modified Logit,which obviates enumeration and overlapping problems

One of the main components of stochastic assignment models is the route choice model solved with implicit or explicit path enumeration algorithms. Such models are used both for congested networks within equilibrium or dynamic models and for non-congested networks within static or pseudo-dynamic network loading models. This paper proposes a C-Logit model specification within a Dial algorithm structure for the implicit assignment of network flows. The model and its solution algorithm, called D-C-Logit, combine several positive features found in the literature for choice set generation and choices from a given choice set: generation of a set of alternatives with a selective approach; calculation of the path choice probability in a closed form; simulation of the overlapping effect among alternative paths; computation of just one tree for each origin avoiding explicit path enumeration.This paper has two main objectives: the proposition of a Dial-like algorithm to solve a C-Logit assignment model and application of the algorithm to different networks in order to demonstrate certain properties.     

Route choice of cyclists in Zurich

This paper presents the first route choice model for bicyclists estimated from a large sample of GPS observations and overcomes the limitations inherent in the generally employed stated preference approach. It employs an improved mode detection algorithm for GPS post-processing to determine trips made by bicycle, which are map matched to an enriched street network. The alternatives are generated as a random sample from an exhaustive, but constrained search. Accounting for the similarity between the alternatives with the path-size factor the MNL estimates show that the elasticity with regards to trip length is nearly four times larger than that with respect to the share of bike paths. The elasticity with respect to the product of length and maximum gradient of the route is small. No other variable describing the routes had an impact. The heterogeneity of the cyclists is captured through interaction terms formulated on their average behaviour.     

Estimation of a constrained multinomial logit model

Identifying the set of available alternatives in a choice process after considering an individual’s bounds or thresholds is a complex process that, in practice, is commonly simplified by assuming exogenous rules in the choice set formation. The Constrained Multinomial Logit (CMNL) model incorporates thresholds in several attributes as a key endogenous process to define the alternatives choice/rejection mechanism. The model allows for the inclusion of multiple constraints and has a closed form. In this paper, we study the estimation of the CMNL model using the maximum likelihood function, develop a methodology to estimate the model overcoming identification problems by an endogenous partition of the sample, and test the model estimation with both synthetic and real data. The CMNL model appears to be suitable for general applications as it presents a significantly better fit than the MNL model under constrained behaviour and replicates the MNL estimates in the unconstrained case. Using mode choice real data, we found significant differences in the values of times and elasticities between compensatory MNL and semi-compensatory CMNL models, which increase as the thresholds on attributes become active.     

Expanding the applicability of random regret minimization for route choice analysis

The discrete choice paradigm of random regret minimization (RRM) has been recently proposed in several choice contexts. In the route choice context, the paradigm has been used to model the choice among three routes and to formulate regret-based stochastic user equilibrium. However, in the same context the RRM literature has not confronted three major challenges: (i) accounting for similarities across alternative routes, (ii) analyzing choice set composition effects on choice probabilities, and (iii) comparing RRM-based models with advanced RUM-based models. This paper looks into RRM-based route choice models from these three perspectives by (i) proposing utility-based and regret-based correction terms to account for similarities across alternatives, (ii) analyzing the variation of choice set probabilities with the choice set composition, and (iii) comparing RRM-based route choice models with C-Logit, Path Size Logit and Paired Combinatorial Logit. The results illustrate the definition of the correction terms within the regret function, the effect of the choice set specificity of RRM-based route choice models, and the positive performance of these models when compared to advanced RUM-based models.     

Modeling heterogeneous risk-taking behavior in route choice: A stochastic dominance approach

This paper proposes a unified approach to modeling heterogonous risk-taking behavior in route choice based on the theory of stochastic dominance (SD). Specifically, the first-, second-, and third-order stochastic dominance (FSD, SSD, TSD) are respectively linked to insatiability, risk-aversion and ruin-aversion within the framework of utility maximization. The paths that may be selected by travelers of different risk-taking preferences can be obtained from the corresponding SD-admissible paths, which can be generated using general dynamic programming. This paper also analyzes the relationship between the SD-based approach and other route choice models that consider risk-taking behavior. These route choice models employ a variety of reliability indexes, which often make the problem of finding optimal paths intractable. We show that the optimal paths with respect to these reliability indexes often belong to one of the three SD-admissible path sets. This finding offers not only an interpretation of risk-taking behavior consistent with the SD theory for these route choice models, but also a unified and computationally viable solution approach through SD-admissible path sets, which are usually small and can be generated without having to enumerate all paths. A generic label-correcting algorithm is proposed to generate FSD-, SSD-, and TSD-admissible paths, and numerical experiments are conducted to test the algorithm and to verify the analytical results.     

Modeling park 'n ride and kiss 'n ride as submodal choices

The logit modeling methodology is applied to include transit access mode choices in conjunction with the automobile vs. transit travel choice decision. The practical problems that arise when the choice set expands beyond two alternatives are identified and addressed. In particular, the complexities that must be resolved in order to use ULOGIT or a similar program include the definition of independent choices (the Independence of Irrelevant Alternatives Property (IIA)), a sequential binary or multinomial logit model (MNL) structure, specification and testing of variables, and the potential for transferring the model to new areas for transportation planning purposes. It was found that the available options cannot be reduced to a single modeling strategy. However, the analysis showed certain concepts which can reduce the uncertainties in related applications of the logit model. It was determined that as many independent choices as possible should be hypothesized and tested for inclusion in the model, but the IIA must be carefully considered because it limits the number of choices that can be represented. Although binary calibration techniques are conceptually appealing, the large number of calibrations for studies involving more than three alternatives suggests that the MNL approach is most practical. Application of the MNL model requires that not only must variables be selected that best explain choice, but they must also be placed in the disutility function of the specific mode or modes to which they are most unique. Finally, it was shown that if choice sets and homogeneous market segments are properly defined, the models can be transferred among different urban areas even though the urban areas exhibit different aggregate characteristics. All observations lead to the general conclusion that the logit modeling methodology can now best be advanced with implementation experience.     

On the flexibility of using marginal distribution choice models in traffic equilibrium

Traffic equilibrium models are fundamental to the analysis of transportation systems. The stochastic user equilibrium (SUE) model which relaxes the perfect information assumption of the deterministic user equilibrium is one such model. The aim of this paper is to develop a new user equilibrium model, namely the MDM-SUE model, that uses the marginal distribution model (MDM) as the underlying route choice model. In this choice model, the marginal distributions of the path utilities are specified but the joint distribution is not. By focusing on the joint distribution that maximizes expected utility, we show that MDM-SUE exists and is unique under mild assumptions on the marginal distributions. We develop a convex optimization formulation for the MDM-SUE. For specific choices of marginal distributions, the MDM-SUE model recreates the optimization formulation of logit SUE and weibit SUE. Moreover, the model is flexible since it can capture perception variance scaling at the route level and allows for modeling different user preferences by allowing for skewed distributions and heavy tailed distributions. The model can also be generalized to incorporate bounded support distributions and discrete distributions which allows to distinguish between used and unused routes within the SUE framework. We adapt the method of successive averages to develop an efficient approach to compute MDM-SUE traffic flows. In our numerical experiments, we test the ability of MDM-SUE to relax the assumption that the error terms are independently and identically distributed random variables as in the logit models and study the additional modeling flexibility that MDM-SUE provides on small-sized networks as well as on the large network of the city of Winnipeg. The results indicate that the model provides both modeling flexibility and computational tractability in traffic equilibrium.     

Study on mean-standard deviation shortest path problem in stochastic and time-dependent networks: A stochastic dominance based approach

This paper studies a mean-standard deviation shortest path model, also called travel time budget (TTB) model. A route’s TTB is defined as this route’s mean travel time plus a travel time margin, which is the route travel time’s standard deviation multiplied with a factor. The TTB model violates the Bellman’s Principle of Optimality (BPO), making it difficult to solve it in any large stochastic and time-dependent network. Moreover, it is found that if path travel time distributions are skewed, the conventional TTB model cannot reflect travelers’ heterogeneous risk-taking behavior in route choice. This paper proposes to use the upper or lower semi-standard deviation to replace the standard deviation in the conventional TTB model (the new models are called derived TTB models), because these derived TTB models can well capture such heterogeneous risk-taking behavior when the path travel time distributions are skewed. More importantly, this paper shows that the optimal solutions of these two derived TTB models must be non-dominated paths under some specific stochastic dominance (SD) rules. These finding opens the door to solve these derived TTB models efficiently in large stochastic and time-dependent networks. Numerical examples are presented to illustrate these findings.     

Crowding in public transport systems: Effects on users,operation and implications for the estimation of demand

The effects of high passenger density at bus stops, at rail stations, inside buses and trains are diverse. This paper examines the multiple dimensions of passenger crowding related to public transport demand, supply and operations, including effects on operating speed, waiting time, travel time reliability, passengers’ wellbeing, valuation of waiting and in-vehicle time savings, route and bus choice, and optimal levels of frequency, vehicle size and fare. Secondly, crowding externalities are estimated for rail and bus services in Sydney, in order to show the impact of crowding on the estimated value of in-vehicle time savings and demand prediction. Using Multinomial Logit (MNL) and Error Components (EC) models, we show that alternative assumptions concerning the threshold load factor that triggers a crowding externality effect do have an influence on the value of travel time (VTTS) for low occupancy levels (all passengers sitting); however, for high occupancy levels, alternative crowding models estimate similar VTTS. Importantly, if demand for a public transport service is estimated without explicit consideration of crowding as a source of disutility for passengers, demand will be overestimated if the service is designed to have a number of standees beyond a threshold, as analytically shown using a MNL choice model. More research is needed to explore if these findings hold with more complex choice models and in other contexts.     

Latent variables and route choice behavior

In the last decade, a broad array of disciplines has shown a general interest in enhancing discrete choice models by considering the incorporation of psychological factors affecting decision making. This paper provides insight into the comprehension of the determinants of route choice behavior by proposing and estimating a hybrid model that integrates latent variable and route choice models. Data contain information about latent variable indicators and chosen routes of travelers driving regularly from home to work in an urban network. Choice sets include alternative routes generated with a branch and bound algorithm. A hybrid model consists of measurement equations, which relate latent variables to measurement indicators and utilities to choice indicators, and structural equations, which link travelers’ observable characteristics to latent variables and explanatory variables to utilities. Estimation results illustrate that considering latent variables (i.e., memory, habit, familiarity, spatial ability, time saving skills) alongside traditional variables (e.g., travel time, distance, congestion level) enriches the comprehension of route choice behavior.     

Capturing correlation with a mixed recursive logit model for activity-travel scheduling

Representing activity-travel scheduling decisions as path choices in a time–space network is an emerging approach in the literature. In this paper, we model choices of activity, location, timing and transport mode using such an approach and seek to estimate utility parameters of recursive logit models. Relaxing the independence from irrelevant alternatives (IIA) property of the logit model in this setting raises a number of challenges. First, overlap in the network may not fully characterize perceptual correlation between paths, due to their interpretation as activity schedules. Second, the large number of states that are needed to represent all possible locations, times and activity combinations imposes major computational challenges to estimate the model. We combine recent methodological developments to build on previous work by Blom Västberg et al. (2016) and allow to model complex and realistic correlation patterns in this type of network. We use sampled choices sets in order to estimate a mixed recursive logit model in reasonable time for large-scale, dense time-space networks. Importantly, the model retains the advantage of fast predictions without sampling choice sets. In addition to estimation results, we present an extensive empirical analysis which highlights the different substitution patterns when the IIA property is relaxed, and a cross-validation study which confirms improved out-of-sample fit.     

Where do cyclists ride? A route choice model developed with revealed preference GPS data

To better understand bicyclists’ preferences for facility types, GPS units were used to observe the behavior of 164 cyclists in Portland, Oregon, USA for several days each. Trip purpose and several other trip-level variables recorded by the cyclists, and the resulting trips were coded to a highly detailed bicycle network. The authors used the 1449 non-exercise, utilitarian trips to estimate a bicycle route choice model. The model used a choice set generation algorithm based on multiple permutations of path attributes and was formulated to account for overlapping route alternatives. The findings suggest that cyclists are sensitive to the effects of distance, turn frequency, slope, intersection control (e.g. presence or absence of traffic signals), and traffic volumes. In addition, cyclists appear to place relatively high value on off-street bike paths, enhanced neighborhood bikeways with traffic calming features (aka “bicycle boulevards”), and bridge facilities. Bike lanes more or less exactly offset the negative effects of adjacent traffic, but were no more or less attractive than a basic low traffic volume street. Finally, route preferences differ between commute and other utilitarian trips; cyclists were more sensitive to distance and less sensitive to other infrastructure characteristics for commute trips.     

Residential mobility and location choice: a nested logit model with sampling of alternatives

Residential mobility and relocation choice are essential parts of integrated transportation and land use models. These decision processes have been examined and modeled individually to a great extent but there remain gaps in the literature on the underlying behaviors that connect them. Households may partly base their decision to move from or stay at a current location on the price and quality of the available alternatives. Conversely, households that are on the market for a new location may evaluate housing choices relative to their previous residence. How and the degree to which these decisions relate to each other are, however, not completely understood. This research is intended to contribute to the body of empirical evidence that will help answer these questions. It is hypothesized that residential mobility and location choice are related household decisions that can be modeled together using a two-tier hierarchical structure. This paper presents a novel nested logit (NL) model with sampling of alternatives and a proposed procedure for sampling bias correction. The model was estimated using full-information maximum likelihood estimation methods. The results confirm the applicability of this NL model and support similar findings from other empirical studies in the residential mobility and location choice literature.     

Constrained nested logit model: formulation and estimation

A model of traveller behaviour should recognise the exogenous and endogenous factors that limit the choice set of users. These factors impose constraints on the decision maker, which constraints may be considered implicitly, as soft constraints imposing thresholds on the perception of changes in attribute values, or explicitly as hard constraints. The purpose of this paper is twofold: (1) To present a constrained nested logit-type choice model to cope with hard constraints. This model is derived from the entropy-maximizing framework. (2) To describe a general framework to deal with (dynamic) non-linear utilities. This approach is based on Reproducing Kernel Hilbert Spaces. The resulting model allows the dynamic aspect and the constraints on the choice process to be represented simultaneously. A novel estimation procedure is introduced in which the utilities are viewed as the parameters of the proposed model instead of attribute weights as in the classical linear models. A discussion on over-specification of the proposed model is presented. This model is applied to a synthetic test problem and to a railway service choice problem in which users choose a service depending on the timetable, ticket price, travel time and seat availability (which imposes capacity constraints). Results show (1) the relevance of incorporating constraints into the choice models, (2) that the constrained models appear to be a better fit than the counterpart unconstrained choice models; and (3) the viability of the approach, in a real case study of railway services on the Madrid–Seville corridor (Spain).     

A nested recursive logit model for route choice analysis

We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modeled as a sequence of link choices and the model does not require any sampling of choice sets. Furthermore, the model can be consistently estimated and efficiently used for prediction.A key challenge lies in the computation of the value functions, i.e. the expected maximum utility from any position in the network to a destination. The value functions are the solution to a system of non-linear equations. We propose an iterative method with dynamic accuracy that allows to efficiently solve these systems.We report estimation results and a cross-validation study for a real network. The results show that the NRL model yields sensible parameter estimates and the fit is significantly better than the RL model. Moreover, the NRL model outperforms the RL model in terms of prediction.     

Formulating the within-day dynamic stochastic traffic assignment problem from a Bayesian perspective

This study proposes a formulation of the within-day dynamic stochastic traffic assignment problem. Considering the stochastic nature of route choice behavior, we treat the solution to the assignment problem as the conditional joint distribution of route traffic, given that the network is in dynamic stochastic user equilibrium. We acquire the conditional joint probability distribution using Bayes’ theorem. A Metropolis–Hastings sampling scheme is developed to estimate the characteristics (e.g., mean and variance) of the route traffic. The proposed formulation has no special requirements for the traffic flow models and user behavior models, and so is easily implemented.     

Modelling shopping destination choice behaviour using the basic multinomial logit model and some of its extensions

This paper reviews basic multinomial logit (MNL) models of shopping destination choice and some extensions to the basic MNL model. Issues include the identification and form of inclusion of measures of destination attractiveness, identification of the appropriate destination choice set, modelling multidestination tours and choices over time, and linking destination choice models with activity measures. The paper begins with a discussion of modelling philosophy and forecasting‐related informational needs and concludes with a summary of areas requiring further research.