The inverse power transformation logit and dogit mode choice models

This paper explores the properties of inverse Box-Cox and Box-Tukey transformations applied to the exponential functions of logit and dogit mode choice models. It is suggested that inverse power transformations allow for the introduction of modeler ignorance in the models and solve the “thin equal tails” problem of the logit model; it is also shown that they allow for asymmetry of response functions in both logit and dogit models by introducing alternative-specific parameters which make cross elasticities of demand among alternatives generally asymmetric. In the dogit model, modeler ignorance and consumer captivity remain conceptually distinct. Standard logit and dogit models appear as very special “perfect knowledge” cases in broad spectra of models which also include, among others, the reciprocal extreme value or log-Weibull variants. These improvements over the simple symmetric-thin-equal-tail-perfect-knowledge logit and the symmetric-pure-captivity dogit are achieved at the cost of introducing at the most two new parameters per alternative considered in the original logit and dogit mode choice models.     

Testing the dogit model with aggregate time-series and cross-sectional travel data

This paper compares dogit and logit specifications of market share models, taking into account the possibility that conclusions might depend on transformations of the explanatory variables of these models. Parameter estimates are obtained both for a time-series urban transit mode of payment model and for a cross-sectional intercity mode choice model. It is demonstrated, using current maximum likelihood techniques extended to take multiple-order autocorrelation of the residuals into account, that the dogit specification is at least equal to, and sometimes clearly superior to, the logit specification irrespective of transformations of explanatory variables.     

A generalised extreme value model admitting substitution and complementarity between alternatives

A model of comparatively simple structure, yet free of the IIA restrictions, is developed, but unlike many non-IIA models no intrinsically nonlinear parameters are introduced and estimation is similar to the logit. Complementary as well as substitute alternatives are allowable as well as complementary pairwise relationships between two alternatives without affecting substitutional relationships between other alternatives. Cross-elasticities, which in the logit depend only on characteristics and parameters of the alternative changed, now depend also on the alternative affected and on other previously “irrelevant” alternatives.     

Nested logit models for mixed-mode travel in urban corridors

The nested logit (NL) model is a generalisation of the well-known multinomial logit (MNL) model which copes with its “independence from irrelevant alternatives” problem, at the expense of more difficult calibration and use. Mixed-mode movements (i.e. park-and-ride) are by nature not independent of competing single-mode options and have, therefore, traditionally been inadequately modelled in most empirical applications. This paper reports on the specification, estimation, testing and comparison of MNL and NL models using disaggregate data of work trips in an urban corridor, where choice was among several alternatives including mixed-mode options. It was found that the more general NL model was more adequate, not only in theory but in practice. The paper concludes by comparing the disaggregate NL model with previously calibrated aggregate NL models for the same corridor using a different data set.     

Estimating choice probabilities among nested alternatives

In several travel choice situations (e.g. automobile ownership level and trip frequency) the alternatives available to an individual randomly chosen from the population exhibit some internal choice-related ranking: the choice of a given alternative implies that all lower-ranked alternatives have been chosen. Such alternatives are referred to as “nested”. This paper presents a model for estimating choice probabilities among nested alternatives. The model is devised from the well known logit model and uses existing logit maximum-likelihood estimation techniques (and computer packages). The approach is shown to be more attractive than the multinomial logit and linear regression models, from a theoretical point of view, yet cheaper than the multinomial probit model. The model is developed in a disaggregate, utility maximization framework. An example application, estimating probabilities of trip frequencies by elderly individuals is presented.     

Empirical test of a constrained choice discrete model: Mode choice in São Paulo,Brazil

This paper examines the properties and empirically tests a model of discrete choice which incorporates probabilistic choice set generation. Denominated the Parametrized Logit Captivity (PLC) model, it is a generalization of the well-known “dogit” specification. The PLC model is shown to be theoretically and empirically more flexible than the latter. Work mode choice data collected in a 1977 O/D survey in São Paulo, Brazil, is used to obtain parameter estimates, as well as to evaluate consumer reaction to a series of perturbations in travel time, travel cost and income, for both the PLC and Multinomial Logit models. Comparisons between the two specifications are made in terms of statistical fit, reasonableness of predictions and differences in predictions across models.     

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.     

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.     

Can mixed logit reveal the actual data generating process? Some implications for environmental assessment

Recent advances in the specification of the utility function of mixed logit models allow the analyst, in principle, to consider a vast variety of individual heterogeneity. Nevertheless, when estimating the model it is common practice to experience severe difficulties in discriminating between different specifications to infer the “true” data generating process. We investigate possible sources for this difficulty focusing on the confounding effects inherent in two basic assumptions of discrete choice model utilities: linearity in the parameters and added error terms. We analyse the role of these assumptions in giving rise to confounding effects and why this increases the difficulty of discriminating among different structures. Finally, we investigate how these problems may affect benefit appraisal using these models. Empirical evidence is provided for two different environmental contexts and a more typical transport context using various kinds of data.     

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.     

Methodological challenges in modelling the choice of mode for a new travel alternative using binary stated choice data – The case of high speed rail in Norway

Binary stated choices between traveller’s current travel mode and a not-yet-existing mode might be used to build a forecasting model with all (current and future) travel alternatives. One challenge with this approach is the identification of the most appropriate inter-alternative error structure of the forecasting model.By critically assessing the practise of translating estimated group scale parameters into nest parameters, we illustrate the inherent limitations of such binary choice data. To overcome some of the problems, we use information from both stated and revealed choice data and propose a model with a cross-nested logit specification, which is estimated on the pooled data set.     

Random utility models with implicit availability/perception of choice alternatives for the simulation of travel demand

Random utility models are undoubtedly the most used models for the simulation of transport demand. These models simulate the choice of a decision-maker among a set of feasible alternatives and their operational use requires that the analyst is able to correctly specify this choice-set for each individual.Some early applications basically ignored this problem by assuming that all decision-makers chose from the same pre-specified choice-set. This assumption may be unrealistic in many practical cases and cause significant misspecification problems (P. Stopher, Transportation Journal of ASCE 106 (1980) 427; H. Williams, J. Ortuzar, Transportation Research B 16 (1982) 167).The problem of choice-set simulation has been dealt within the literature following two basically different approaches:

• •simulating the perception/availability of an alternative implicitly in the choice model,
• •simulating the choice-set generation explicitly in a separate model.

The implicit approach is more convenient from an operational point of view, while the explicit one is more appealing from a theoretical point of view.In this paper, a different approach to the modeling of availability/perception of alternatives in the context of random utility model is proposed. This approach is based on the concept of intermediate degrees of availability/perception of each alternative simulated through a model (or “inclusion function”) which in turn is introduced in the systematic utility of standard random utility models.This model, named implicit availability/perception (IAP), may be differently specified depending on assumptions made on the joint distribution of random residuals and the way in which the average degree of availability/perception is modeled.In this paper, a possible specification of the IAP model, based on the assumption of random residual distributed as i.i. Gumbel and with the average degree of availability/perception modeled as a binomial logit, is proposed.The paper also proposes ML estimation models in two cases: in the first, only information on alternatives choices is available, while in the second, this information is complemented with others on variables related to a latent (i.e., non-observable) alternatives availability/perception degree (e.g., information on car availability of decision-maker i used as an indirect measurement of the unknown and non-observable availability/perception degree of alternative car for decision-maker i in a modal split).The proposed specification is tested on mode choice data; the calibration results are compared with those of a similar logit specification with encouraging results in terms of goodness of fit.     

Estimating “tree” logit models

The existence of the “tree” generalisation of the multinomial logit model, its consistency with theories of “rational” human behaviour, as well as the advantages offered in terms of more realistic modelling by this model form, have all been known for some time. Although a few studies have applied tree logit models, however, applications have been restricted by practical and theoretical difficulties in the estimation of these models, in particular with the sequential estimation that has normally been necessary. This paper presents a new estimation procedure, employing the maximum likelihood criterion, for the estimation of tree logit models. The procedure is based on a simple notation for the tree structure and is believed to be original. It offers the possibility of estimating simultaneously all the parameters of general tree logit structures, without restriction on the number of levels but allowing the user to impose constraints of parameter equality where required. Results are presented indicating both the usefulness of the method in deriving improved models, relative to the more familiar sequential estimations, and its practicality and speed of operation on main-frame, minicomputers and microcomputers.     

Modeling heterogeneous parking choice behavior on university campuses

Studies on campus parking indicate more severe problems and a wider range of characteristics than commercial parking because of limited parking places, special conditions, specific policies and enclosed space on university campuses. Heterogeneous characteristics are usually ignored in analyses of campus parking behavior. In this paper, a mixed logit model is applied to analyze parking choice behavior on a campus using data collected from a stated-preference survey of Tongji University, Shanghai, China. The heterogeneity of individuals with various sociodemographic characteristics is evaluated by interaction terms and random parameters. Comparison between the proposed approach and the conditional logit model shows that the results of the mixed logit model are more interpretable because they are not limited by the independence from irrelevant alternatives assumption. Key factors that have considerable effects on campus parking choices are identified and analyzed. Important regularities are also concluded from elasticity analyses. Finally, the campus is divided into two areas according to the walking distance to a new parking lot, and the modeling results show that area-specific policies should be established because the two areas have quite distinct parking choice features.     

A mixed Bayesian network for two-dimensional decision modeling of departure time and mode choice

The modeling of travel decision making has been a popular topic in transportation planning. Previous studies focused on random-utility discrete choice models and machine learning methods. This paper proposes a new modeling approach that utilizes a mixed Bayesian network (BN) for travel decision inference. The authors use a predetermined BN structure and calculate priori and posterior probability distributions of the decision alternatives based on the observed explanatory variables. As a “utility-free” decision inference method, the BN model releases the linear structure in the utility function but assumes the traffic level of service variables follow multivariate Gaussian distribution conditional on the choice variable. A real-world case study is conducted by using the regional travel survey data for a two-dimensional decision modeling of both departure time choice and travel mode choice. The results indicate that a two-dimensional mixed BN provides better accuracy than decision tree models and nested logit models. In addition, one can derive continuous elasticity with respect to each continuous explanatory variable for sensitivity analysis. This new approach addresses a research gap in probabilistic travel decision making modeling as well as two-dimensional travel decision modeling.     

Estimating GEV models with censored data

We examine the problem of estimating parameters for Generalized Extreme Value (GEV) models when one or more alternatives are censored in the sample data, i.e., all decision makers who choose these censored alternatives are excluded from the sample; however, information about the censored alternatives is still available. This problem is common in marketing and revenue management applications, and is essentially an extreme form of choice-based sampling. We review estimators typically used with GEV models, describe why many of these estimators cannot be used for these censored samples, and present two approaches that can be used to estimate parameters associated with censored alternatives. We detail necessary conditions for the identification of parameters associated exclusively with the utility of censored alternatives. These conditions are derived for single-level nested logit, multi-level nested logit and cross-nested logit models. One of the more surprising results shows that alternative specific constants for multiple censored alternatives that belong to the same nest can still be separately identified in nested logit models. Empirical examples based on simulated datasets demonstrate the large-sample consistency of estimators and provide insights into data requirements needed to estimate these models for finite samples.     

Accounting for inertia in modal choices: some new evidence using a RP/SP dataset

Inertia is related with effect that experiences in previous periods may have on the current choice. In particular, it has to do with the tendency to stick with the past choice even when another alternative becomes more appealing. As new situations force individuals to rethink about their choices new preferences may be formed. Thus a learning process begins that relaxes the effect of inertia in the current choice. In this paper we use a mixed dataset of revealed preference (RP)-stated preference (SP) to study the effect of inertia between RP and SP observations and to study if the inertia effect is stable along the SP experiments. Inertia has been studied more extensively with panel datasets, but few investigations have used RP/SP datasets. In this paper we extend previous work in several ways. We test and compare several ways of measuring inertia, including measures that have been proposed for both short and long RP panel datasets. We also explore new measures of inertia to test for the effect of “learning” (in the sense of acquiring experience or getting more familiar with) along the SP experiment and we disentangle this effect from the pure inertia effect. A mixed logit model is used that allows us to account for both systematic and random taste variations in the inertia effect and for correlations among RP and SP observations. Finally we explore the relation between the utility specification (especially in the SP dataset) and the role of inertia in explaining current choices.     

Modeling the modal choice decision process

Most models of modal choice are macroanalytic in nature — focusing on the behavior of large groups of travelers — and have limited explanatory power. Transportation managers need to know more about the decision processes of individual travelers in selecting a mode for a particular trip, if they are to be able to develop strategies for influencing these decisions. A microanalytic model of modal choice is therefore developed in flow-chart form, clarifying the stages in the modal choice decision process for any given trip. Individual consumers are seen as trying to satisfy a particular travel need by first specifying the characteristics of the trip itself and then specifying the “ideal” modal attributes required for this trip. Next, the perceived characteristics of a limited number of modes are evaluated against this “ideal” solution and the consumer is assumed to select that mode which provides the best match. The model explicitly recognizes the impact of psychological variables on modal choice as well as the consumer's need for information if he or she is to evaluate realistically all alternatives.     

Methods of determining choice probability in utility maximising multiple alternative models

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.     

Redefining activity types: Who participates in which leisure activity?

This paper analyzes the activity choices of individuals and the links between socio-demographics, daily schedules and activity attributes using a new activity choice framework. Activities are first clustered into groups based on their salient attributes, such as duration, frequency, flexibility, planning times, and number of involved persons, rather than their functional types (work, leisure and household obligations), using a K-means cluster technique. This led to the creation of several new activity groups such as “long, temporally fixed, personally flexible activities”, “short and flexible activities”. These activity groups form the choice set for the mixed logit activity choice modeling structure developed for the leisure activities in the second part of the paper. The model results reveal the significant relationships between socio-demographics, temporal characteristics, and characteristics of the schedules on leisure activity choice. The results demonstrate how changing demographics and other activities in individuals’ schedules may affect the nature of the leisure activities and present the substitution and complimentary effects that these new activity groups have on one another.