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.     

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.     

Embedding risk attitude and decision weights in non-linear logit to accommodate time variability in the value of expected travel time savings

In recent years we have seen important extensions of logit models in behavioural research such as incorporation of preference and scale heterogeneity, attribute processing heuristics, and estimation of willingness to pay (WTP) in WTP space. With rare exception, however, a non-linear treatment of the parameter set to allow for behavioural reality, such as embedded risk attitude and perceptual conditioning of occurrence probabilities attached to specific attributes, is absent. This is especially relevant to the recent focus in travel behaviour research on identifying the willingness to pay for reduced travel time variability, which is the source of estimates of the value of trip reliability that has been shown to take on an increasingly important role in project appraisal. This paper incorporates, in a generalised non-linear (in parameters) logit model, alternative functional forms for perceptual conditioning (known as probability weighting) and risk attitude in the utility function to account for travel time variability, and then derives an empirical estimate of the willingness to pay for trip time variability-embedded travel time savings as an alternative to separate estimates of time savings and trip time reliability. We illustrate the richness of the approach using a stated choice data set for commuter choice between unlabelled attribute packages. Statistically significant risk attitude parameters and parameters underlying decision weights are estimated for multinomial logit and mixed multinomial logit models, along with values of expected travel time savings.     

A theoretical and empirical model of trip chaining behavior

This paper addresses the theoretical and empirical issues involved in modeling complex travel patterns. Existing models have the shortcoming of not representing the interdependencies among trip links in trip chains with multiple non-home stops. A theoretical model based on utility theory and explicitly accounting for the trade-offs involved in the choice of multiple-stop chains is developed. Using this theoretical model, utility maximizing conditions for a household's choice of a daily travel pattern are derived. The optimum travel pattern is described in terms of the number of chairs (tours) traveled on a given day and in terms of the number of stops (sojourns) made on each of those chains. For a given household, the form of the optimum pattern is a function of the transportation expenditures (time, cost) required to reach potential destinations. Constraints on the conditions of optimality due to the limited and discrete nature of travel pattern alternatives are also considered. Parameters of the general utility function were estimated empirically using actual travel data derived from a home interview survey taken in Washington, D.C. The multinomial logit model is used to relate utility scores for the alternative travel patterns to choice probabilities. The resulting parameter estimates agree with theoretical expectations and with empirical results obtained in other studies. In order to demonstrate the empirical and theoretical implications of the model, forecasts for various transportation policies (e.g., gasoline price increases, transit fare reductions), as made by this model and by other less complex models, are compared. The results of these comparisons indicate the need for expanding the scope of existing travel forecasting models to explicit considerations of trip chaining behavior.     

The multinomial logit model revisited: A semi-parametric approach in discrete choice analysis

The multinomial logit model in discrete choice analysis is widely used in transport research. It has long been known that the Gumbel distribution forms the basis of the multinomial logit model. Although the Gumbel distribution is a good approximation in some applications such as route choice problems, it is chosen mainly for mathematical convenience. This can be restrictive in many other scenarios in practice. In this paper we show that the assumption of the Gumbel distribution can be substantially relaxed to include a large class of distributions that is stable with respect to the minimum operation. The distributions in the class allow heteroscedastic variances. We then seek a transformation that stabilizes the heteroscedastic variances. We show that this leads to a semi-parametric choice model which links the linear combination of travel-related attributes to the choice probabilities via an unknown sensitivity function. This sensitivity function reflects the degree of travelers’ sensitivity to the changes in the combined travel cost. The estimation of the semi-parametric choice model is also investigated and empirical studies are used to illustrate the developed method.     

The relationship between land use and intrazonal trip making behaviors: Evidence and implications

This paper addresses the relationship between land use, destination selection, and travel mode choice. Specifically, it focuses on intrazonal trips, a sub-category of trip making where both trip origin and trip destination are contained in the same geographic unit of analysis, using data from the 1994 Household Activity and Travel Diary Survey conducted by Portland Metro. Using multinomial logit and binary logistic models to measure travel mode choice and decision to internalize trips, the evidence supports the conclusions that (1) intrazonal trips characteristics suggest mode choice for these trips might be influenced by urban form, which in turn affects regional trip distribution; (2) there is a threshold effect in the ability of economic diversity/mixed use to alter travel behavior; and (3) greater emphasis to destinations within the area where an individual’s home is located needs to be given in trip distribution models.     

The valuation of commuter travel time savings for car drivers: evaluating alternative model specifications

The empirical valuation of travel time savings is a derivative of the ratio of parameter estimates in a discrete choice model. The most common formulation (multinomial logit) imposes strong restrictions on the profile of the unobserved influences on choice as represented by the random component of a preference function. As we progress our ability to relax these restrictions we open up opportunities to benchmark the values derived from simple (albeit relatively restrictive) models. In this paper we contrast the values of travel time savings derived from multinomial logit and alternative specifications of mixed (or random parameter) logit models. The empirical setting is urban car commuting in six locations in New Zealand. The evidence suggests that less restrictive choice model specifications tend to produce higher estimates of values of time savings compared to the multinomial logit model; however the degree of under-estimation of multinomial logit remains quite variable, depending on the context.     

Further evidence on the temporal stability of disaggregate travel demand models

Current evidence on the transferability of disaggregate travel demand models is inconclusive. Adding to this body of research, the present analysis focuses upon the temporal characteristics of work trip behavior in the San Francisco Bay Area. Using before and after data sets associated with the BART Impact Travel Study, multinomial logit models of work trip modal choice are estimated. The results indicate that the general form and the coefficient estimates of a pre BART model are transferable in time. Moreover, when updated to reflect BART's presence, the model's predictive success and its implied elasticity measures are generally accurate, relative to those implied by reestimating the entire model on post BART data. Finally, as economic theory would predict, elasticity measures of the service related variables were found to increase over time.     

Development of railway station choice models to improve the representation of station catchments in rail demand models

ABSTRACT

This paper describes the development of railway station choice models suitable for defining probabilistic station catchments. These catchments can then be incorporated into the aggregate demand models typically used to forecast demand for new rail stations. Revealed preference passenger survey data obtained from the Welsh and Scottish Governments was used for model calibration. Techniques were developed to identify trip origins and destinations from incomplete address information and to automatically validate reported trips. A bespoke trip planner was used to derive mode-specific station access variables and train leg measures. The results from a number of multinomial logit and random parameter (mixed) logit models are presented and their predictive performance assessed. The models were found to have substantially superior predictive accuracy compared to the base model (which assumes the nearest station has a probability of one), indicating that their incorporation into passenger demand forecasting methods has the potential to significantly improve model predictive performance.     

Trip chaining as a barrier to the propensity to use public transport

Trip chaining is a growing phenomenon in travel and activity behaviour. Individuals increasingly seek out opportunities to minimise the amount of travel required as part of activity fulfilment, given the competing demands on time budgets and their valuation of travel time savings. This search for ways of fulfilling (more) activities with less travel input has produced a number of responses, one of which is trip chaining. A particularly important policy implication of trip chaining is the potential barrier it creates in attracting car users to switch to public transport. This paper seeks to improve our understanding of trip chaining as a barrier to public transport use. A series of discrete choice models are estimated to identify the role that socio-economic and demographic characteristics of households have on the propensity to undertake trip chains of varying degrees of simplicity/complexity that involve use of the car or public transport with an embedded commuting or non-commuting primary purpose. Multinomial logit, nested logit and random parameter logit models are developed and contrasted to establish the gains in relaxing the strict conditions of the multinomial logit model.     

Development of destination choice models for pedestrian travel

Most research on walking behavior has focused on mode choice or walk trip frequency. In contrast, this study is one of the first to analyze and model the destination choice behaviors of pedestrians within an entire region. Using about 4500 walk trips from a 2011 household travel survey in the Portland, Oregon, region, we estimated multinomial logit pedestrian destination choice models for six trip purposes. Independent variables included terms for impedance (walk trip distance), size (employment by type, households), supportive pedestrian environments (parks, a pedestrian index of the environment variable called PIE), barriers to walking (terrain, industrial-type employment), and traveler characteristics. Unique to this study was the use of small-scale destination zone alternatives. Distance was a significant deterrent to pedestrian destination choice, and people in carless or childless households were less sensitive to distance for some purposes. Employment (especially retail) was a strong attractor: doubling the number of jobs nearly doubled the odds of choosing a destination for home-based shopping walk trips. More attractive pedestrian environments were also positively associated with pedestrian destination choice after controlling for other factors. These results shed light on determinants of pedestrian destination choice behaviors, and sensitivities in the models highlight potential policy-levers to increase walking activity. In addition, the destination choice models can be applied in practice within existing regional travel demand models or as pedestrian planning tools to evaluate land use and transportation policy and investment scenarios.     

Factors influencing destination choice for the urban grocery shopping trip

Destination choice for the urban grocery shopping trip is hypothesized to be determined by three factors: the individual's perception of the destination, the individual's accessibility to the destination and the relative number of opportunities to exercise any particular choice. Results of a multinomial logit model estimation support this hypothesis and provide useful information concerning the role of urban form in this destination choice situation. It is determined that accessibility is the primary aspect influencing destination choice and that its effect is nonlinear.On leave 1977-78 from State University of New York at Buffalo, Buffalo, New York 14214.     

Strategic sampling for large choice sets in estimation and application

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

Microscopic decision model for pedestrian route choice at signalized crosswalks

In this paper, two‐tier mathematical models were developed to simulate the microscopic pedestrian decision‐making process of route choice at signalized crosswalks. In the first tier, a discrete choice model was proposed to predict the choices of walking direction. In the second tier, an exponential model was calibrated to determine the step size in the chosen direction. First, a utility function was defined in the first‐tier model to describe the change of utility in response to deviation from a pedestrian's target direction and the conflicting effects of neighboring pedestrians. A mixed logit model was adopted to estimate the effects of the explanatory variables on the pedestrians' decisions. Compared with the standard multinomial logit model, it was shown that the mixed logit model could accommodate the heterogeneity. The repeated observations for each pedestrian were grouped as panel data to ensure that the parameters remained constant for individual pedestrians but varied among the pedestrians. The mixed logit model with panel data was found to effectively address inter‐pedestrian heterogeneity and resulted in a better fit than the standard multinomial logit model. Second, an exponential model in the second tier was proposed to further determine the step size of individual pedestrians in the chosen direction; it indicates the change in walking speed in response to the presence of other pedestrians. Finally, validation was conducted on an independent set of observation data in Hong Kong. The pedestrians' routes and destinations were predicted with the two‐tier models. Compared with the tracked trajectories, the average error between the predicted destinations and the observed destinations was within an acceptable margin. Copyright © 2016 John Wiley & Sons, Ltd.     

Influences on commuter trip departure time decisions in Singapore

This paper provides empirical evidence to support the widely held view that institutional factors such as official work start times and staggered working hours are powerful policy tools in traffic management and in influencing travel behaviour. This approach is to be preferred over continued investment in infrastructure given the scarcity of land in Singapore. A more efficient use of existing infrastructure could be achieved by spreading peak travel. Full utilisation of the Mass Rapid Transit will depend on changing the commuter's perception on multi mode travel in addition to using public transport. While many studies have been carried out on modal choice, research on commuter trip departure decisions have been few and remain largely least understood. This paper employs multinomial logit and simultaneous nested logit analysis to model the choice of departure time (using household data collected in Singapore in 1983). Preliminary findings show that schedule delay, travel cost, and journey time to be important influences on commuter's choice of trip departure time to work. Some difficulties are highlighted and suggestions for further research are made.     

Assessing traveler responsiveness to land and location based accessibility and mobility solutions

In this paper, a joint multinomial logit (MNL) model of residential location and vehicle availability choice is formulated and estimated using a sample of households from the San Francisco, CA area Metropolitan Transportation Commission's 1990 household travel survey. Subsequently, models of travel intensity (number of daily household trips and vehicle-miles traveled) are estimated as a function of household characteristics and of attributes derived from the joint residential location and auto availability choice model (number of vehicles, percent land developed). A policy test shows that reducing the cost of locating in the densest areas of the metropolitan area is likely to have only marginal impact on vehicle availability and household trip making.     

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.     

The role of accessibility in basic transportation choice behavior

Accessibility measures reflect the level of service provided by transportation systems to various locations. Basic transportation choice behavior is defined to include those decisions of how many automobiles to own and how many trips to which destinations to make by automobile and by public transit. Here, these decisions are assumed to be made jointly by urban households and are conditional upon residential location decisions. It is the purpose of this paper to explore the role of accessibility as a causal factor in such basic transportation choice behavior.An economic utility theory model of choice behavior is postulated in which the benefits from making trips to specific destinations are reflected by measures of destination attraction. Through determination of utility-maximizing trip frequencies, indirect utility functions are developed which include accessibility concepts. Behavioral implications of these concepts are proposed and contrasts are drawn to accessibility measures used in conventional segregated models of trip distribution, modal choice, and automobile ownership.Sensitivity analyses of alternative empirical definitions of accessibility in the choice model are conducted using data from the Detroit Regional Transportation and Land Use Study — covering counties in southeastern Michigan. These analyses employ a multinomial logit estimation technique and focus on definitions of trip attraction. Results of these analyses indicate that more complicated attraction measures can be replaced by measures involving the proportion of either urban area population or urban area employment within a traffic analysis zone. Also, evidence is found that decision-makers in the case study area consider trips of up to 60 or even 90 minutes duration when evaluating accessibilities offered by alternative public and private transportation systems.     

An investigation of commuting trip timing and mode choice in the Greater Toronto Area: Application of a joint discrete-continuous model

The trip timing and mode choice are two critical decisions of individual commuters mostly define peak period traffic congestion in urban areas. Due to the increasing evidence in many North American cities that the duration of the congested peak travelling periods is expanding (peak spreading), it becomes necessary and natural to investigate these two commuting decisions jointly. In addition to being considered jointly with mode choice decisions, trip timing must also be modelled as a continuous variable in order to precisely capture peak spreading trends in a policy sensitive transportation demand model. However, in the literature to date, these two fundamental decisions have largely been treated separately or in some cases as integrated discrete decisions for joint investigation. In this paper, a discrete-continuous econometric model is used to investigate the joint decisions of trip timing and mode choice for commuting trips in the Greater Toronto Area (GTA). The joint model, with a multinomial logit model for mode choice and a continuous time hazard model for trip timing, allows for unrestricted correlation between the unobserved factors influencing these two decisions. Models are estimated by occupation groups using 2001 travel survey data for the GTA. Across all occupation groups, strong correlations between unobserved factors influencing mode choice and trip timing are found. Furthermore, the estimated model proves that it sufficiently captures the peak spreading phenomenon and is capable of being applied within the activity-based travel demand model framework.