The accuracy of the multinomial logit model as an approximation to the multinomial probit model of travel demand

The multinomial probit model of travel demand is considerably more general but much less tractable than the better-known multinomial logit model. In an effort to determine the effects of using the relatively simple logit model in situations where the assumptions of probit modeling are satisfied but those of logit modeling are not, the accuracy of the multinomial logit model as an approximation to a variety of three-alternative probit models has been evaluated. Multinomial logit can give highly erroneous estimates of the choice probabilities of multinomial probit models. However, logit models appear to give asymptotically accurate estimates of the ratios of the coefficients of the systematic components of probit utility functions, even when the logit choice probabilities differ greatly from the probit ones. Large estimation data sets are not necessarily needed to enable likelihood ratio tests to distinguish three-alternative probit models from logit models that give seriously erroneous estimates of the probit choice probabilities. Inclusion of alternative-specific dummy variables in logit utility functions cannot be relied upon to reduce significantly the errors of logit approximations to the choice probabilities of probit models whose utility functions do not contain the dummies.     

A utility maximizing model of the demand for multi-destination non-work travel

The multinomial probit model of travel demand is considerably more general but much less tractable than the better-known multinomial logit model. In an effort to determine the effects of using the relatively simple logit model in situations where the assumptions of probit modeling are satisfied but those of logit modeling are not, the accuracy of the multinomial logit model as an approximation to a variety of three-alternative probit models has been evaluated. Multinomial logit can give highly erroneous estimates of the choice probabilities of multinomial probit models. However, logit models appear to give asymptotically accurate estimates of the ratios of the coefficients of the systematic components of probit utility functions, even when the logit choice probabilities differ greatly from the probit ones. Large estimation data sets are not necessarily needed to enable likelihood ratio tests to distinguish three-alternative probit models from logit models that give seriously erroneous estimates of the probit choice probabilities. Inclusion of alternative-specific dummy variables in logit utility functions cannot be relied upon to reduce significantly the errors of logit approximations to the choice probabilities of probit models whose utility functions do not contain the dummies.     

Effects of incorporating latent and attitudinal information in mode choice models

Abstract

Hybrid choice modelling approaches allow latent variables in mode choice utility functions to be addressed. However, defining attitude and behavior as latent variables is influenced by the researcher's assumptions. Therefore, it is better to capture the effects of latent behavioral and attitudinal factors as latent variables than defining behaviors and attitudes per se. This article uses a hybrid choice model for capturing such latent effects, which will herein be referred to as modal captivity effects in commuting mode choice. Latent modal captivity refers to the unobserved and apparently unexplained attraction towards a specific mode of transportation that is resulting from latent attitude and behavior of passengers in addition to the urban transportation system. In empirical models, the latent modal captivity variables are explained as functions of different observed variables. Empirical models show significant improvement in fitting observed data as well as improved understanding of travel behavior.     

Modeling discrete choice behavior using concepts from fuzzy set theory,approximate reasoning and neural networks

Models of discrete choice analysis are usually based on the random utility framework. They assume that decision makers make decisions that maximize their utility. Alternative formulations of the problem have also been proposed in the literature. These approaches model the decision makers’ perceptions of the attributes of the various alternatives using fuzzy sets and linguistic variables, and the decision process itself, using concepts from approximate reasoning and fuzzy control. The underlying assumption is that decision makers use a few simple rules that relate their vague perceptions of the various attributes to their preferences towards the available alternatives. The paper extends this approach by incorporating rule weights, which capture the importance of a particular rule in the decision process. It also presents an approach for calibrating the weights using concepts from neural networks. A case study, involving mode choice, is used to demonstrate the potential of the approach and compare it to alternative formulations and methodologies.     

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.     

An automatic segmentation procedure for studying variations in mode choice behaviour

Urban areas are very complex and heterogeneous in terms of their population composition and activity systems. The transport system, modal choices and service levels available to the population also varies considerably across space and time. These similarities and differences in choices and levels of explanatory variables facing individual tripmakers have to be explicitly considered in any study of transport behvior. The common practice has been to include user attributes, in addition to the system characteristics, in the modal utility functions to help capture differences in choice behavior across individuals. However, it could well be that the mode-choice behavior of a segment of the population is fundamentally different from other segments of the population. In view of this, some studies have applied segmentation schemes to help identify the subgroups of presumably different travel responses. Typically, such schemes have been based on stratification of the population by a single variable, chosen either based on a priori notions or one-way cross tabulations. These have their shortcomings. Thus, this paper develops an analytical procedure that simultaneously deals with level of service, socioeconomic and spatial factors to determine the relative role each plays in determining travel behavior. The procedure is applied to data from the Toronto region to illustrate its use.     

Travel mode choice and travel satisfaction: bridging the gap between decision utility and experienced utility

Over the past decades research on travel mode choice has evolved from work that is informed by utility theory, examining the effects of objective determinants, to studies incorporating more subjective variables such as habits and attitudes. Recently, the way people perceive their travel has been analyzed with transportation-oriented scales of subjective well-being, and particularly the satisfaction with travel scale. However, studies analyzing the link between travel mode choice (i.e., decision utility) and travel satisfaction (i.e., experienced utility) are limited. In this paper we will focus on the relation between mode choice and travel satisfaction for leisure trips (with travel-related attitudes and the built environment as explanatory variables) of study participants in urban and suburban neighborhoods in the city of Ghent, Belgium. It is shown that the built environment and travel-related attitudes—both important explanatory variables of travel mode choice—and mode choice itself affect travel satisfaction. Public transit users perceive their travel most negatively, while active travel results in the highest levels of travel satisfaction. Surprisingly, suburban dwellers perceive their travel more positively than urban dwellers, for all travel modes.     

Semiparametric specification of the utility function in a travel mode choice model

We propose a semiparametric approach that can capture the nonlinearity of deterministic components of the utility functions in discrete choice models and demonstrate it by analyzing travel mode choice behaviour for an interregional trip. The proposed smoothing spline-based specification method can be used to make ex ante evaluations regarding the parametric specifications of the deterministic utility functions in discrete choice models.     

Mixed RP/SP models incorporating interaction effects

In order to analyse the impact of a new train service in Cagliari (Italy) a databank including information from a revealed preference (RP) and a stated preference (SP) survey was set up. The RP data concern choice between car, bus and train; the SP data consider the binary choice between a new train service (quicker, more frequent, with a lower fare and more stations than the current one) and the alternative currently chosen by car and bus users. Logit models allowing for correlation among RP alternatives were estimated for this mixed RP/SP data set using the artificial tree structure method. The analysis included level-of-service variables measured with an unusually high level of precision, latent or second order variables (such as comfort), inertia and interaction variables. Different specifications of the utility function were tested, including the expenditure rate model, and the effects of these specifications on modelling results are highlighted. Our results show that for a population mainly composed of fixed income workers, the expenditure rate model is superior to the traditional wage rate model, yielding lower and more significant subjective values of time. Moreover, we found that the non-linear specifications appear to be more suitable as not only better model results were obtained, but also the real distribution of the error terms was revealed (i.e. highlighting correlation among public transport options).     

A class of RUM choice models that includes the model in which the utility has logistic distributed errors

A class of random utility maximization (RUM) models is introduced. For these RUM models the utility errors are the sum of two independent random variables, where one of them follows a Gumbel distribution. For this class of RUM models an integral representation of the choice probability generating function has been derived which is substantially different from the usual integral representation arising from the RUM theory. Four types of models belonging to the class are presented. Thanks to the new integral representation, a closed-form expression for the choice probability generating function for these four models may be easily obtained. The resulting choice probabilities are fairly manageable and this fact makes the proposed models an interesting alternative to the logit model. The proposed models have been applied to two samples of interurban trips in Japan and some of them yield a better fit than the logit model. Finally, the concavity of the log-likelihood of the proposed models with respect to the utility coefficients is also analyzed.     

Valuation of road projects with uncertain outcomes

This is a practical implementation of a multicriteria methodology developed to assess the risk involved in investment or policy projects. It is based on the specification of a non-linear, but piecewise linear, additive utility function, where the partial utility functions are specified as recursive exponential functions of only one curvature parameter. This allows for a reduction of the quantity of information necessary to build the utility function in a context of uncertainty. It is introduced in an aggregation model whereby the partial utility functions are built separately through a specific questioning process. The methodology is applied to the selection of road infrastructure projects of the Walloon Region in Belgium with several experts and civil servants from the Transport Ministry whose individual utility functions are derived. Software called MUSTARD is used, which stepwise and interactively helps the decision-makers to formulate the problem, build the criteria's distributions and state their preferences. The projects are ranked according to their rate of return computed on the basis of the projects' certain equivalent money values.     

Making use of respondent reported processing information to understand attribute importance: a latent variable scaling approach

In recent years we have seen an explosion of research seeking to understand the role that rules and heuristics might play in improving the predictive capability of discrete choice models, as well as delivering willingness to pay estimates for specific attributes that may (and often do) differ significantly from estimates based on a model specification that assumes all attributes are relevant. This paper adds to that literature in one important way—it explicitly recognises the endogeneity issues raised by typical attribute non-attendance treatments and conditions attribute parameters on underlying unobserved attribute importance ratings. We develop a hybrid model system involving attribute processing and outcome choice models in which latent variables are introduced as explanatory variables in both parts of the model, explaining the answers to attribute processing questions and explaining heterogeneity in marginal sensitivities in the choice model. The resulting empirical model explains how lower latent attribute importance leads to a higher probability of indicating that an attribute was ignored or that it was ranked as less important, as well as increasing the probability of a reduced value for the associated marginal utility coefficient in the choice model. The model does so by treating the answers to information processing questions as dependent rather than explanatory variables, hence avoiding potential risk of endogeneity bias and measurement error.     

A microeconomic interpretation for the system optimal traffic assignment problem with nonadditive path cost

Using a Bergson–Samuelson welfare function, we outline a microeconomic interpretation of the effects of the non-linearity in the time/cost relationship for travellers in a congested transport network. It is demonstrated that a marginal cost traffic flow assignment following Wardrop's second principle, although it minimizes the total cost of a transport network, may reduce social welfare compared to the market equilibrium assignment based on Wardrop's first principle. A welfare-maximizing assignment model is presented and used to show that if the travellers' utility functions are linear, the assignment that maximizes social welfare will be the same as the assignment that minimizes total network cost, but if users' utility functions are non-linear (reflecting the traditional non-satiation and diminishing marginal utility axioms), the two assignments will be different. It is further shown that the effects of this non-linearity are such that a welfare-maximizing assignment will meet with less user resistance than a minimum total network cost assignment.     

Benders Decomposition for Discrete–Continuous Linear Bilevel Problems with application to traffic network design

We propose a new fast solution method for linear Bilevel Problems with binary leader and continuous follower variables under the partial cooperation assumption. We reformulate the Bilevel Problem into a single-level problem by using the Karush–Kuhn–Tucker conditions. This non-linear model can be linearized because of the special structure achieved by the binary leader decision variables and subsequently solved by a Benders Decomposition Algorithm to global optimality. We illustrate the capability of the approach on the Discrete Network Design Problem which adds arcs to an existing road network at the leader stage and anticipates the traffic equilibrium for the follower stage. Because of the non-linear objective functions of this problem, we use a linearization method for increasing, convex and non-linear functions based on continuous variables. Numerical tests show that this algorithm can solve even large instances of Bilevel Problems.     

Determining the Monetary Value of Quality Attributes in Freight Transportation Using a Stated Preference Approach

It is commonly accepted that the modal choice of a shipper is influenced not only by the pure economic attributes of transportation – time and cost – but also by more qualitative factors. These quality attributes relate to frequency, reliability, flexibility, transport duration and risk of loss or damage; they are usually difficult to quantify in monetary terms. Different techniques exist that help to understand better how these different quality attributes of freight transportation influence modal choice. In this paper we apply a stated preference design. Using real business data, the aim is then to derive partial utility functions that allow us to calculate monetary values for these different quality attributes.     

Incorporating trip chaining into analysis of destination choice

A model of destination choice is developed in this study employing “prospective utility” of a destination zone as its attraction measure. The prospective utility accounts for future dependency of destination choice and makes possible relevant treatment of interdependent choices in a trip chain. A parameter is included in the model to represent the magnitude of the future dependency. Empirical estimation results show that destination choice is in fact future dependent and coefficients of travel time and zonal attribute variables may be biased if this depedency is not accounted for.     

Experience as a conditioning effect on choice: Does it matter whether it is exogenous or endogenous?

Previous choice studies have proposed a way to condition the utility of each alternative in a choice set on experience with the alternatives accumulated over previous periods, defined either as a mode used or not in a most recent trip, or the mode chosen in their most recent trip and the number of similar one-way trips made during the last week. The paper found that the overall statistical performance of the mixed logit model improved significantly, suggesting that this conditioning idea has merit. Experience was treated as an exogenous influence linked to the scale of the random component, and to that extent it captures some amount of the heterogeneity in unobserved effects, purging them of potential endogeneity. The current paper continues to investigate the matter of endogeneity versus exogeneity. The proposed approach implements the control function method through the experience conditioning feature in a choice model. We develop two choice models, both using stated preference data. The paper extends the received contribution in that we allow for the endogenous variable to have an impact on the attributes through a two stage method, called the Multiple Indicator Solution, originally implemented in a different context and for a single (quality) attribute, in which stage two is the popular control function method. In the first stage, the entire utility expression associated with all observed attributes is conditioned on the prior experience with an alternative. Hence, we are capturing possible correlates associated with each and every attribute and not just one selected attribute. We find evidence of potential endogeneity. The purging exercise however, results in both statistical similarities and differences in time and cost choice elasticities and mean estimates of the value of travel time savings. We are able to identify a very practical method to correct for possible endogeneity under experience conditioning that will encourage researchers and practitioners to use such an approach in more advanced non-linear discrete choice models as a matter of routine.

     

Inference on mode preferences,vehicle purchases,and the energy paradox using a Bayesian structural choice model

Discrete choice modeling is experiencing a reemergence of research interest in the inclusion of latent variables as explanatory variables of consumer behavior. There are several reasons that motivate the integration of latent attributes, including better-informed modeling of random consumer heterogeneity and treatment of endogeneity. However, current work still is at an early stage and multiple simplifying assumptions are usually imposed. For instance, most previous applications assume all of the following: independence of taste shocks and of latent attributes, exclusion restrictions, linearity of the effect of the latent attributes on the utility function, continuous manifest variables, and an a priori bound for the number of latent constructs. We derive and apply a structural choice model with a multinomial probit kernel and discrete effect indicators to analyze continuous latent segments of travel behavior, including inference on the energy paradox. Our estimator allows for interaction and simultaneity among the latent attributes, residual correlation, nonlinear effects on the utility function, flexible substitution patterns, and temporal correlation within responses of the same individual. Statistical properties of the Bayes estimator that we propose are exact and are not affected by the number of latent attributes.     

Structural equation approach to investigate trip-chaining and mode choice relationships in the context of developing countries

This paper investigates empirical relationships between trip chain type and mode class choice for developing countries. To formulate these two sets of decisions, four empirical models are developed using structural equation modeling (SEM). Those models are calibrated using one-month travel diary data collected in Dhaka city. SEM correlates the observed variables and identifies their relationship with trip-chaining type utility and mode class choice utility. The fitted models are selected based on statistical results and similarity with the real-life situation. Direct relationships between trip-chaining and mode choice utilities are found insignificant. However, several socio-demographic factors influence both simultaneously. Consequently, it is essential to consider mode class choice concurrently for modeling trip chains. This study also investigates the influencing factors for work-based and non-work-based trip chains separately and effects of road users’ heterogeneity. The research results can be utilized to perceive trip chain-mode choice patterns for developing countries.     

Should I stay or should I go? Investigating route switching behavior from revealed preferences data

A large variety of factors influence the route choice decisions of road users, and modelers consider these factors within the perceived utility that road users are assumed to maximize. However, this perceived utility may be different even for the same origin–destination pair and this leads road users to choose different routes for different trips. In this study, we focus on this particular phenomenon of route switching behavior by estimating discrete choice models with the aim of understanding the key factors at its foundation. The estimated route choice models account for route characteristics, socio-economic information, activity based data, inertial mechanism and learning effects, and they are applied to revealed preference data consisting of 677 actual day by day route choices (referred to 77 road users) collected by GPS in Cagliari (Italy). Route switching models were estimated with both fixed and random coefficient models. The model estimation results show that the variables referred to habit and learning have an important relevance on explaining the route switching phenomenon. Specifically, the higher is the travel habit, the less is the propensity of the road users to switch their route. Moreover, the learning effect shows that the accumulation of past experiences has more influence on the choice than the most recent ones.