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.     

Stochastic frontier estimation of budgets for Kuhn–Tucker demand systems: Application to activity time-use analysis

We propose a stochastic frontier approach to estimate budgets for the multiple discrete–continuous extreme value (MDCEV) model. The approach is useful when the underlying time and/or money budgets driving a choice situation are unobserved, but the expenditures on the choice alternatives of interest are observed. Several MDCEV applications hitherto used the observed total expenditure on the choice alternatives as the budget to model expenditure allocation among choice alternatives. This does not allow for increases or decreases in the total expenditure due to changes in choice alternative-specific attributes, but only allows a reallocation of the observed total expenditure among different alternatives. The stochastic frontier approach helps address this issue by invoking the notion that consumers operate under latent budgets that can be conceived (and modeled) as the maximum possible expenditure they are willing to incur. The proposed method is applied to analyze the daily out-of-home activity participation and time-use patterns in a survey sample of non-working adults in Florida. First, a stochastic frontier regression is performed on the observed out-of-home activity time expenditure (OH-ATE) to estimate the unobserved out-of-home activity time frontier (OH-ATF). The estimated frontier is interpreted as a subjective limit or maximum possible time individuals can allocate to out-of-home activities and used as the time budget governing out-of-home time-use choices in an MDCEV model. The efficacy of this approach is compared with other approaches for estimating time budgets for the MDCEV model, including: (a) a log-linear regression on the total observed expenditure for out-of-home activities and (b) arbitrarily assumed, constant time budgets for all individuals in the sample. A comparison of predictive accuracy in time-use patterns suggests that the stochastic frontier and log-linear regression approaches perform better than arbitrary assumptions on time budgets. Between the stochastic frontier and log-linear regression approaches, the former results in slightly better predictions of activity participation rates while the latter results in slightly better predictions of activity durations. A comparison of policy simulations demonstrates that the stochastic frontier approach allows for the total out-of-home activity time expenditure to either expand or shrink due to changes in alternative-specific attributes. The log-linear regression approach allows for changes in total time expenditure due to changes in decision-maker attributes, but not due to changes in alternative-specific attributes.     

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.     

Estimation of multinomial probit-kernel integrated choice and latent variable model: comparison on one sequential and two simultaneous approaches

Integrated choice and latent variable (ICLV) model incorporates latent factors into standard discrete choice model with aim to provide greater explanatory power. Using simulated datasets, this study makes a comparison among three estimation approaches corresponding to the sequential approach and two simultaneous approaches including the maximum simulated likelihood with GHK estimator and maximum approximate composite marginal likelihood (MACML) approach, to evaluate their abilities to recover the underlying parameters of multinomial probit-kernel ICLV model. The results show that both simultaneous approaches outperform the sequential approach in terms of estimates accuracy and efficiency irrespective of the sample sizes, and the MACML approach is the most preferable due to its best performance on recovering true values of parameters with relatively small standard errors, especially when the sample size is large enough.     

Forecasting light-duty vehicle demand using alternative-specific constants for endogeneity correction versus calibration

We investigate parameter recovery and forecast accuracy implications of incorporating alternative-specific constants (ASCs) in the utility functions of vehicle choice models. We compare two methods of incorporating ASCs: (1) a maximum likelihood estimator that computes ASCs post-hoc as calibration constants (MLE-C) and (2) a generalized method of moments estimator that uses instrumental variables (GMM-IV) to correct for price endogeneity. In a synthetic study we observe significant coefficient bias with MLE-C when the price-ASC correlation (endogeneity) is large. GMM-IV successfully mitigates this bias given valid instruments but exacerbates the bias given invalid instruments. Despite greater coefficient bias, MLE-C yields better forecasts than GMM-IV with valid instruments in most of the cases examined, including most cases where the price-ASC correlation present in the estimation data is absent in the prediction data. In a market study of U.S. midsize sedan sales from 2002 – 2006 the GMM-IV model predicts the 1-year-forward market better, but the MLE-C model predicts the 5-year-forward market better. Including an ASC in predictions by any of the methods proposed improves share forecasts, and assuming that the ASC of each new vehicle matches that of its closest competitor vehicle yields the best long term forecasts. We find evidence that the instruments most frequently used in the automotive demand literature may be invalid.     

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.     

Testing probabilistic discrete choice models of travel demand by comparing predicted and observed aggregate choice shares

Probabilistic discrete choice models of travel demand often are tested for the presence of specification errors by comparing the models' predictions of aggregate choice shares in population strata with observed shares. A model is rejected as misspecified if the differences between its predictions and the observations are judged too large. This judgement usually is made on intuitive grounds without use of formal statistical methods and, therefore includes no systematic method for distinguishing the effects of specification errors on differences between predictions and observations from those of random sampling errors. This paper represents formal statistical tests for comparing predicted and observed aggregate chioce shares in population strata and reports the results of an investigation of the power of the tests. The test statistics are asymptotically χ² disturbed when the model being tested is correctly specified. The results of the power investigation suggests that greater power is obtained (i.e. there is ability to detect misspecified models) when all of the available data are used for both parameter estimation and specification testing than when the available data are divided into separate estimation and test data sets. Specification tests based on comparisons of predicted and observed aggregate choice shares appear to have less power than do likelihood ratio and likelihood ratio index specification tests when the alternative models required by the latter tests are correctly or approximately correctly specified. However, tests based on comparisons of predicted and observed shares ca have greater power than the other tests when the alternative models are seriouslymisspecified.     

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.     

Linear probit models: Statistical properties and improved estimation methods

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.     

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.     

A simulation evaluation of the maximum approximate composite marginal likelihood (MACML) estimator for mixed multinomial probit models

This paper evaluates the ability of the maximum approximate composite marginal likelihood (MACML) estimation approach to recover parameters from finite samples in mixed cross-sectional and panel multinomial probit models. Comparisons with the maximum simulated likelihood (MSL) estimation approach are also undertaken. The results indicate that the MACML approach recovers parameters much more accurately than the MSL approach in all model structures and covariance specifications. The MACML inference approach also estimates the parameters efficiently, with the asymptotic standard errors being, in general, only a small proportion of the true values. As importantly, the MACML inference approach takes only a very small fraction of the time needed for MSL estimation. In particular, the results suggest that, for the case of five random coefficients, the MACML approach is about 50 times faster than the MSL for the cross-sectional random coefficients case, about 15 times faster than the MSL for the panel inter-individual random coefficients case, and about 350 times or more faster than the MSL for the panel intra- and inter-individual random coefficients case. As the number of alternatives in the unordered-response model increases, one can expect even higher computational efficiency factors for the MACML over the MSL approach. Further, as should be evident in the panel intra- and inter-individual random coefficients case, the MSL is all but practically infeasible when the mixing structure leads to an explosion in the dimensionality of integration in the likelihood function, but these situations are handled with ease in the MACML approach. It is hoped that the MACML procedure will spawn empirical research into rich model specifications within the context of unordered multinomial choice modeling, including autoregressive random coefficients, dynamics in coefficients, space-time effects, and spatial/social interactions.     

Identifying a behaviourally relevant choice set from stated choice data

Stated choice experiments are designed optimally in a statistical sense but not necessarily in a behavioural choice making sense. Statistical designs, and consequently model estimation, assume that the set of alternatives offered in the experiment are processed by respondents with a specific processing strategy. Much has been studied about attribute processing using discrete choice methods in travel choice studies, but this paper focuses more broadly on processing of alternatives in the choice set offered in the experiment. This paper is motivated by the primary idea that the distribution of predicted choice probabilities associated with a set of alternatives defining a given choice set might provide strong evidence on the strategies that agents appear to use when choosing a preferred alternative. In an empirical setting of a choice set of size three, four model specifications are considered including a model for the selection of the best alternative in the full choice set and three variants of a best–worst regime. Using state choice data on road pricing reform, the empirical analysis examines which model specification delivers the most accurate prediction of the chosen alternative. The results suggest which alternatives really matter in choice making and hence the alternatives that might be included in a choice set for model specification.     

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.     

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.     

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.     

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.