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Discrete choice modeling is widely applied in transportation studies. However, the need to consider correlation between observations creates a challenge. In spatial econometrics, a spatial lag term with a pre-defined weight matrix is often used to capture such a correlation. In most previous studies, the weight matrix is assumed to be exogenous. However, this assumption is invalid in many cases, leading to biased and inconsistent parameter estimates. Although some attempts have been made to address the endogenous weight matrix issue, none has focused on discrete choice modeling. This paper fills an existing gap by developing a Spatial Autoregressive Binary Probit Model with Endogenous Weight Matrix (SARBP-EWM). The SARBP-EWM model explicitly considers the endogeneity by using two equations whose error terms are correlated. Markov Chain Monte Carlo (MCMC) method is used to estimate the model. Model validation with simulated data shows that the model parameters can converge to their true values and the endogenous weight matrix can be reliably recovered. The model is then applied to a simplified firm relocation choice problem, assuming that similar size firms influence one another. The model quantifies the peer effect, and takes into consideration other independent variables including industry type and population density. The estimation results suggest that peer influence among firms indeed affect their relocation choices. The application results offer important insights into business location choice and can inform future policy making. The sample size for applying the model is currently limited to hundreds of observations. This paper contributes to the existing literature on discrete choice modeling and spatial econometrics. It provides a new tool to discover spatial correlations that are hidden in a wide range of transportation issues, such as land development, location choice, and various travel behavior. Those hidden spatial correlations are otherwise difficult to identify and estimation results may be biased. Establishing a new model that explicitly considers endogenous weight matrix and applying the model to a real life transportation issue represent a significant contribution to the body of literature.

This paper proposes a new econometric formulation and an associated estimation method for a finite discrete mixture of normals (FDMN) version of the multiple discrete–continuous probit (MDCP) model. To our knowledge, this is the first such formulation and application of an MDCP model in the econometric literature. Using the New Zealand Domestic Travel Survey data set, the model is applied to analyze individual-level decisions regarding recreational destination locations and the number of trips to each destination. The results provide insights into the demographic and other factors that influence individuals’ preferences for different destinations, and show that the FDMN MDCP model is able to identify different segments of the sample, each one of them with different effects of the exogenous variables on destination choice.

This study focuses on how to use multiple data sources, including loop detector counts, AVI Bluetooth travel time readings and GPS location samples, to estimate macroscopic traffic states on a homogeneous freeway segment. With a generalized least square estimation framework, this research constructs a number of linear equations that map the traffic measurements as functions of cumulative vehicle counts on both ends of a traffic segment. We extend Newell’s method to solve a stochastic three-detector problem, where the mean and variance estimates of cell-based density and flow can be analytically derived through a multinomial probit model and an innovative use of Clark’s approximation method. An information measure is further introduced to quantify the value of heterogeneous traffic measurements for improving traffic state estimation on a freeway segment.

The current paper proposes the use of the multivariate skew-normal distribution function to accommodate non-normal mixing in cross-sectional and panel multinomial probit (MNP) models. The combination of skew-normal mixing and the MNP kernel lends itself nicely to estimation using Bhat’s (2011) maximum approximate composite marginal likelihood (MACML) approach. Simulation results for the cross-sectional case show that our proposed approach does well in recovering the underlying parameters, and also highlights the pitfalls of ignoring non-normality of the continuous mixing distribution when such non-normality is present. At the same time, the proposed model obviates the need to assume a pre-specified parametric distribution for the mixing, and allows the estimation of a very flexible, but still parsimonious, mixing distribution form.

This paper proposes a multivariate ordered-response system framework to model the interactions in non-work activity episode decisions across household and non-household members at the level of activity generation. Such interactions in activity decisions across household and non-household members are important to consider for accurate activity-travel pattern modeling and policy evaluation. The econometric challenge in estimating a multivariate ordered-response system with a large number of categories is that traditional classical and Bayesian simulation techniques become saddled with convergence problems and imprecision in estimates, and they are also extremely cumbersome if not impractical to implement. We address this estimation problem by resorting to the technique of composite marginal likelihood (CML), an emerging inference approach in the statistics field that is based on the classical frequentist approach, is very simple to estimate, is easy to implement regardless of the number of count outcomes to be modeled jointly, and requires no simulation machinery whatsoever. The empirical analysis in the paper uses data drawn from the 2007 American Time Use Survey (ATUS) and provides important insights into the determinants of adults' weekday activity episode generation behavior. The results underscore the substantial linkages in the activity episode generation of adults based on activity purpose and accompaniment type. The extent of this linkage varies by individual demographics, household demographics, day of the week, and season of the year. The results also highlight the flexibility of the CML approach to specify and estimate behaviorally rich structures to analyze inter-individual interactions in activity episode generation.

This paper develops a new method to solve multivariate discrete–continuous problems and applies the model to measure the influence of residential density on households’ vehicle fuel efficiency and usage choices. Traditional discrete–continuous modelling of vehicle holding choice and vehicle usage becomes unwieldy with large numbers of vehicles and vehicle categories. I propose a more flexible method of modelling vehicle holdings in terms of number of vehicles in each category, using a Bayesian multivariate ordinal response system. I also combine the multivariate ordered equations with Tobit equations to jointly estimate vehicle type/usage demand in a reduced form, offering a simpler alternative to the traditional discrete/continuous analysis. Using the 2001 National Household Travel Survey data, I find that increasing residential density reduces households’ truck holdings and utilization in a statistically significant but economically insignificant way. The results are broadly consistent with those from a model derived from random utility maximization. The method developed above can be applied to other discrete–continuous problems.

This paper investigates the relationship between mode choice and the complexity of trip chaining patterns. An understanding of the causality between these two choice behaviors may aid in the development of tour-based travel demand modeling systems that attempt to incorporate models of trip chaining and mode choice. The relationship between these two aspects of travel behavior is represented in this paper by considering three different causal structures: one structure in which the trip chaining pattern is determined first and influences mode choice, another structure in which mode choice is determined first and influences the complexity of the trip chaining pattern, and a third structure in which neither is predetermined but both are determined simultaneously. The first two structures are estimated within a recursive bivariate probit modeling framework that accommodates error covariance. The simultaneous logit model is estimated for the third structure that allows a bidirectional simultaneous causality. The analysis and model estimation are performed separately for work tour and non-work tour samples drawn from the 2000 Swiss Microcensus travel survey. Model estimation results show that the causal structure in which trip chain complexity precedes mode choice performs best for both work and non-work tour samples. The structure in which mode choice precedes trip chaining pattern choice was found to give significantly inferior goodness-of-fit measures. These findings have important implications for the development of activity-based and tour-based modeling systems and for the design and planning of public transport systems.

This paper formulates a Stochastic Social Optimum (SSO) that relates to the Stochastic User Equilibrium (SUE) in the same way as the Social Optimum (SO) relates to the User Equilibrium (UE) in a deterministic environment. At the SSO solution, the total of the users perceived costs is minimised. The\ud formulation and analysis is carried out in a general utility-maximising framework, with the probit and logit\ud models being special cases. Conditions for the SSO flow pattern are derived, from which it can be seen that\ud the marginal social costs play the same role in the SSO as the standard costs play in SUE. In particular, it is\ud shown that the SSO solution can be obtained through the use of an algorithm for SUE, but with the marginal costs replacing the standard costs in the stochastic loading and that optimal tolls are the differences\ud between the marginal social costs and the standard costs. For the case of the logit model an explicit path-\ud based objective function is obtained which is of a pleasing symmetrical form when compared with the\ud objective functions for SUE, SO and UE. Additionally, a link-based objective function for the general utility-maximising case is formulated for SSO, which is similar in form to the SUE objective function of Sheffi\ud and Powell.

The probit-based stochastic user equilibrium (SUE) model has the advantage of being able to represent perceptual differences in utility across the driver population, while taking proper account of the natural correlations in these utilities between overlapping routes within the network (which the simpler logit SUE is unable to do). Its main drawback is the potentially heavy computational demands, and this has previously been thought to preclude a consideration of the sensitivity analysis of probit-based SUE, whereby an approximation to changes in the equilibrium solution is deduced as its input parameters (specifically origin/destination (O–D) flows and link cost-flow function parameters) are perturbed. In the present paper, an efficient computational method for performing such an analysis for general networks is described. This approach uses information on SUE path flows, but is not specific to any particular equilibrium solution algorithm. Problems inherent in the consideration of general network topologies are identified, and methods proposed for overcoming them. The paper concludes with an application of the method to a realistic network, and compares the approximate solutions with those obtained by direct estimation methods.

The objective of this paper is to investigate the impact of pre-trip information on auto commuters’ choice behavior. The analysis is based on an extensive home-interview survey of commuters in the Taichung metropolitan area in Taiwan. A joint model for route and departure time decisions with and without pre-trip information is formulated. The model specifications are developed for both the systematic and random components. In particular, econometric issues associated with specifying the random error structure are addressed for parameter estimation purposes. Insights into the effects of attributes are obtained through the analysis of the model's performance and estimated parameter values. A probit model form is used for the joint model, allowing the introduction of state dependence and correlation in the model specification. The results underscore the important relationship between the different characteristics and the propensity of commuter choice behavior under two scenarios, with and without pre-trip information.

The paper presents a framework for public traffic assignment that builds on the probit-based model of Sheffi and Powell [Sheffi, Y., Powell, W.B., 1981. A comparison of stochastic and deterministic traffic assignment over congested networks. Transportation Res. B. 15 (1), 53–64; Sheffi, Y., Powell, W.B., 1982. An algorithm, for the equilibrium assignment problem with random link Times. Networks 12 (2), 191–207.]. Hereby, the problems with overlapping routes that occur in many public transport models can be avoided. The probit-based model with modifications similar to the principles in Nielsen [Nielsen, O.A., 1996. Do stochastic traffic assignment models consider differences in road users utility functions? Twentyfourth European Transport Forum (PTRC Annual Meeting). London, UK, Seminar M.] is used as a starting point. This makes it possible to describe passengers’ different preferences towards different sub-modes and against transfers. This also considers dependencies of choices through chains of sub-modes. The simulation of perceived travel times is extended to describe differences in the distribution of travel- and waiting times for different sub-modes. Parallel lines are frequency aggregated in order to handle waiting times appropriately. Initial tests on a full-scale case show that the methodology can describe route choices in public transport very well. This is both due to the model’s ability to describe overlapping routes and due to the many different coefficients, error components and distributions that make it possible to calibrate the model. In practice, the many parameters might also be the main weakness, since this complicates the calibration. At the end of the paper, proposals to coefficients are presented based on a Danish SP-analysis. This demonstrated the applicability of the method.

Auto ownership modeling plays an important role in travel demand analysis because it is a key determinant of the travel behavior of individuals and households. Discrete-choice auto ownership models use either an ordered-response choice mechanism or an unordered-response choice mechanism. The ordered-response mechanism is based on the hypothesis that an uni-dimensional continuous latent auto ownership propensity index determines the level of car ownership. The unordered-response mechanism is based on the Random Utility Maximization principle. This paper presents the underlying theoretical structures, and identifies the advantages and disadvantages, of the two alternative response mechanisms. The paper also compares the ordered-response mechanism (represented by the ordered-response logit model) and the unordered-response mechanism (represented by the multinomial logit model) empirically using several data sets. This comparative analysis offers strong evidence that the appropriate choice mechanism is the unordered-response structure. As a general guideline, auto ownership modeling must be pursued using the unordered-response class of models (such as the multinomial logit or probit model) and not using the ordered-response class of models (such as the ordered-response logit or probit).

We propose another version of the multinomial probit model with a structured covariance matrix to represent any overlapped relation between route alternatives. The fundamental ideas of the model were presented in Yai et al. (1993) and Yai and Iwakura (1994). The assumptions introduced in the model may be more realistic for route choice behaviors on a dense network than the strict assumption of the independent alternative property of the multinomial logit model. As the nested logit model assumes an identical dispersion parameter between two modeling levels for all trip makers, the model has difficulty in expressing individual choice-tree structures. To improve the applicability of the multinomial probit model to route choice behaviors, we introduce a function which represents an overlapped relation between pairs of alternatives and propose a multinomial probit model in which the structured covariance matrix uses the function in order to consider the individual choice-tree structures in the matrix and the estimatability of the new alternative's covariances. After examining the applicability of the multinomial probit model using empirical route choice data in a Tokyo metropolitan region, we also propose a method for evaluating consumer benefits on complicated networks based on the multinomial probit model.

In discrete choice analysis, the multinational probit (MNP) provides the most flexible framework to allow for general interdependencies among the alternatives. These interdependencies are usually modeled through the correlation structure of the error term. This framework suffers from two serious impediments, however. The first and major one is computational and is related to the evaluation of the response probabilities, which are multidimensional normal integrals. In the past, this has restricted its utilization to studies involving less than five alternatives where using numerical integration remains practical. A recent solution to the dimensionality problem consists in replacing the choice probabilities with easy to compute efficient simulators. The second impediment arises in models with large choice sets when a fully unconstrained error correlation structure is postulated. In that case, the large number of nuisance parameters to estimate in the error covariance matrix becomes a problematic issue that can exacerbate the estimation process. To tackle that problem, a first-order generalized autoregressive [GAR(1)] error approach is suggested. The approach enables one to approximate general correlation structures with parsimonious parametric specifications. The key feature of the approach is that the number of nuisance parameters grows linearly with the number of alternatives considered. The methodology is most useful in models with large choice sets where the estimation also requires to use probability simulators. The paper focuses on the GAR(1) solution to the error covariance matrix estimation problem. The issue of identification of the nuisance parameters is examined in detail and a rank condition is suggested. Some theoretical and numerical examples based on synthetic data are presented.

Recently developed computational methods have greatly reduced the difficulty of estimating multinomial probit models and may soon make multinomial probit a computationally feasible option in applied travel demand modeling. This paper discusses some of the benefits and costs that are associated with the use of multinomial probit in demand modeling. It is argued that although there are situations in which multinomial probit is essential for achieving a satisfactory model, most problems with existing demand models are unlikely to be mitigated by the use of multinomial probit.

The logit model is the simplest and best-known probabilistic choice model. Nevertheless according to the deficient flexibility there are problems of making use of the multinomial logit model. In this paper a generalized logit model, which is essentially more flexible than the traditional multinomial logit model, is presented. Furthermore, the usual modal choice models are compared in respect to their flexibility. This is done by calculating the partial derivatives of the choice probability functions at a fixed point. The generalized logit model shows the same flexibility (in a precise sense) as the probit model, but is much more tractable. At the end of this paper an example is set to show the differences in the functional forms between the new model and the traditional models (logit and probit).

Random utility models often involve terms which represent alternative-specific errors, and the main attractive feature of the multinomial probit (MNP) model is that it allows a rather general covariance structure for these errors. However, since observed choices only reveal information regarding utility differences, and since scale cannot be determined, not all parameters in an arbitrary MNP specification may be identified. This paper examines identification restrictions that arise in the linear-in-parameters multinomial probit framework, and provides discussion and recommendations for estimation and analysis of probit normalizations.

Methods of estimating choice probabilities between multiple alternatives are described, within the context of various methods of specifying the degree of correlation between the alternatives. A utility maximising framework is assumed. The models described are based either on the logit family or multinomial probit. Two new methods of analytical approximation for the multinomial probit model are introduced, which appear to show significant advantages over the traditional Clark method. Some comparative results of choice probability estimates are presented to support this contention. The conclusion discusses the relative usefulness of different choice estimation methods for different types of problem.

This paper presents the dogit model. That model is flexible enough to permit the choice among specific pairs of alternatives to be consistent with the independence from irrelevant alternatives axiom, as in a logit model, but it simultaneously allows the choice among other pairs not to be. Dogit parameters add an “income effect” to the “substitution effect” already built into the logit model; alternatively, they allow for the joint presence of compulsive and discretionary elements in consumer behavior, or for the identification of captive markets. Eventual estimation of the values of the parameters of the dogit model appears simpler than for the probit model.

Multinomial logit models of travel demand are subject to a variety of specification errors that can severely affect the accuracy the models' forecasts. This paper describes some of the important sources of specification errors in logit models, presents numerical illustrations of the errors' effects on forecasts of travel behavior, and evaluates the ability of several informal and formal statistical procedures to identify and diagnose the errors. Among the tests considered, the most powerful are a test against a probit model and the McFadden, Tye and Train (1976) test based on the universal logit method. The least powerful tests are a test based on extrapolating the logit model and informal tests based on examination of the signs, t -statistics and ratios of the estimated parameters of the logit function.

Traditional gap acceptance functions have been estimated based on the first gap observed. In this paper we show that the critical gap of drivers is decreasing on the average, as they are waiting for an acceptable gap. Our gap acceptance function is based on a probit model which assumes a normal distribution of gaps across gaps and drivers.

The multinomial probit model is a statistical tool that is well suited to analyze some transportation problems. Modal split, gap acceptance, and route choice are some examples of application contexts. This paper presents an in-depth analysis of its statistical properties and an estimation method for the trinomial case. In the statistical part of the paper it is shown that for multinomial probit models with specifications that are linear in the parameters, the global maximum of the log-likelihood function is consistent if the data do not exhibit multicollinearity as defined in the text. For the special case with three alternatives, lack of multicollinearity is also shown to guarantee asymptotic efficiency and normality, and the uniqueness of any root of the likelihood equations. In addition, it is also shown that for the trinomial probit model certain goodness-of-it measures and test statistics can be easily calculated. The methods part of the paper introduces an estimation process that solves the likelihood equations using a special purpose table of the bivariate normal distribution and analytical derivatives of the log-likelihood function. The method is very accurate, can be applied to nonlinear specifications, and is considerably faster than current computer programs. For linear specifications, the method can be mathematically proven to converge if the log-likelihood equations have a root.

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 particular parameter estimability problem in the multinomial probit model is considered. Making use of a model discussed in the literature, some problems with the usual method of specification are discussed. Some general comments are made on the problem of selecting a normalisation when using the multinomial probit model.