Generalized extreme value (GEV)-based error structures for multiple discrete-continuous choice models

This paper formally derives the class of multiple discrete-continuous generalized extreme value (MDCGEV) models, a general class of multiple discrete-continuous choice models based on generalized extreme value (GEV) error specifications. Specifically, the paper proves the existence of, and derives the general form of, closed-form consumption probability expressions for multiple discrete-continuous choice models with GEV-based error structures. In addition to deriving the general form, the paper derives a compact and readily usable form of consumption probability expressions that can be used to estimate multiple discrete-continuous choice models with general cross-nested error structures.The cross-nested version of the MDCGEV model is applied to analyze household annual expenditure patterns in various transportation-related expenses using data from a Consumer Expenditure Survey in the United States. Model estimation results and predictive log-likelihood based validation tests indicate the superiority of the cross-nested model over the mutually exclusively nested and non-nested model specifications. Further, the cross-nested model was amenable to the accommodation of socio-demographic heterogeneity in inter-alternative covariance across decision-makers through a parameterization of the allocation parameters.     

Sampling of alternatives in Logit Mixture models

Employing a strategy of sampling of alternatives is necessary for various transportation models that have to deal with large choice-sets. In this article, we propose a method to obtain consistent, asymptotically normal and relatively efficient estimators for Logit Mixture models while sampling alternatives. Our method is an extension of previous results for Logit and MEV models. We show that the practical application of the proposed method for Logit Mixture can result in a Naïve approach, in which the kernel is replaced by the usual sampling correction for Logit. We give theoretical support for previous applications of the Naïve approach, showing not only that it yields consistent estimators, but also providing its asymptotic distribution for proper hypothesis testing. We illustrate the proposed method using Monte Carlo experimentation and real data. Results provide further evidence that the Naïve approach is suitable and practical. The article concludes by summarizing the findings of this research, assessing their potential impact, and suggesting extensions of the research in this area.     

Modelling the effects of road pricing on traffic using ERP traffic data

Singapore’s Electronic Road Pricing (ERP) system involves time-variable charges which are intended to spread the morning traffic peak. The charges are revised every three months and thus induce regular motorists to re-think their travel decisions. ERP traffic data, captured by the system, provides a valuable source of information for studying motorists’ travel behaviour. This paper proposes a new modelling methodology for using these data to forecast short-term impacts of rate adjustment on peak period traffic volumes. Separate models are developed for different categories of vehicles which are segmented according to their demand elasticity with respect to road pricing. A method is proposed for estimating the maximum likelihood value of preferred arrival time (PAT) for each vehicle’s arrivals at a particular ERP gantry under different charging conditions. Iterative procedures are used in both model calibration and application. The proposed approach was tested using traffic datasets recorded in 2003 at a gantry located on Singapore’s Central Expressway (CTE). The model calibration and validation show satisfactory results.     

Correcting for endogeneity in behavioral choice models with social influence variables

While psychologists and behavioral economists emphasize the importance of social influences, an outstanding issue is how to capture such influences in behavioral models used to inform urban planning and policy. In this paper we focus on operational models that do not require explicit knowledge of the individual networks of decision makers. We employ a field effect variable to capture social influences, which is calculated as the percent of population in the peer group that has chosen the specific alternative. We define the peer group based on socio-economic status and spatial proximity of residential location. As in behavioral economics and psychology, the concept is that one is influenced by the choices made by one’s peers. However, using such a social influence variable in a behavioral model causes complications because it is likely endogenous; unobserved factors that impact the peer group also influence the decision maker, yielding correlation between the field effect variable and the error. The contribution of this paper is the use of the Berry, Levinsohn, and Pakes (BLP) method to correct the endogeneity in a choice model. The two-stage BLP introduces constants for each peer group to remove the endogeneity from the choice model (where it is difficult to deal with) and insert it into a linear regression model (where endogeneity is relatively easier to deal with). We test the method using a mode choice data set from the Netherlands and readily available software and find there is an upward bias of the field effect parameter when endogeneity is not corrected. The procedure outlined presents a practical and tractable method for incorporating social influences in choice models.     

Accounting for stochastic variables in discrete choice models

The estimation of discrete choice models requires measuring the attributes describing the alternatives within each individual’s choice set. Even though some attributes are intrinsically stochastic (e.g. travel times) or are subject to non-negligible measurement errors (e.g. waiting times), they are usually assumed fixed and deterministic. Indeed, even an accurate measurement can be biased as it might differ from the original (experienced) value perceived by the individual.Experimental evidence suggests that discrepancies between the values measured by the modeller and experienced by the individuals can lead to incorrect parameter estimates. On the other hand, there is an important trade-off between data quality and collection costs. This paper explores the inclusion of stochastic variables in discrete choice models through an econometric analysis that allows identifying the most suitable specifications. Various model specifications were experimentally tested using synthetic data; comparisons included tests for unbiased parameter estimation and computation of marginal rates of substitution. Model specifications were also tested using a real case databank featuring two travel time measurements, associated with different levels of accuracy.Results show that in most cases an error components model can effectively deal with stochastic variables. A random coefficients model can only effectively deal with stochastic variables when their randomness is directly proportional to the value of the attribute. Another interesting result is the presence of confounding effects that are very difficult, if not impossible, to isolate when more flexible models are used to capture stochastic variations. Due the presence of confounding effects when estimating flexible models, the estimated parameters should be carefully analysed to avoid misinterpretations. Also, as in previous misspecification tests reported in the literature, the Multinomial Logit model proves to be quite robust for estimating marginal rates of substitution, especially when models are estimated with large samples.     

New insights on random regret minimization models

This paper develops new methodological insights on Random Regret Minimization (RRM) models. It starts by showing that the classical RRM model is not scale-invariant, and that – as a result – the degree of regret minimization behavior imposed by the classical RRM model depends crucially on the sizes of the estimated taste parameters in combination with the distribution of attribute-values in the data. Motivated by this insight, this paper makes three methodological contributions: (1) it clarifies how the estimated taste parameters and the decision rule are related to one another; (2) it introduces the notion of “profundity of regret”, and presents a formal measure of this concept; and (3) it proposes two new family members of random regret minimization models: the μRRM model, and the Pure-RRM model. These new methodological insights are illustrated by re-analyzing 10 datasets which have been used to compare linear-additive RUM and classical RRM models in recently published papers. Our re-analyses reveal that the degree of regret minimizing behavior imposed by the classical RRM model is generally very limited. This insight explains the small differences in model fit that have previously been reported in the literature between the classical RRM model and the linear-additive RUM model. Furthermore, we find that on 4 out of 10 datasets the μRRM model improves model fit very substantially as compared to the RUM and the classical RRM model.     

The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models

The likelihood functions of multinomial probit (MNP)-based choice models entail the evaluation of analytically-intractable integrals. As a result, such models are usually estimated using maximum simulated likelihood (MSL) techniques. Unfortunately, for many practical situations, the computational cost to ensure good asymptotic MSL estimator properties can be prohibitive and practically infeasible as the number of dimensions of integration rises. In this paper, we introduce a maximum approximate composite marginal likelihood (MACML) estimation approach for MNP models that can be applied using simple optimization software for likelihood estimation. It also represents a conceptually and pedagogically simpler procedure relative to simulation techniques, and has the advantage of substantial computational time efficiency relative to the MSL approach. The paper provides a “blueprint” for the MACML estimation for a wide variety of MNP models.     

A hyperpath-based network generalized extreme-value model for route choice under uncertainties

Previous route choice studies treated uncertainties as randomness; however, it is argued that other uncertainties exist beyond random effects. As a general modeling framework for route choice under uncertainties, this paper presents a model of route choice that incorporates hyperpath and network generalized extreme-value-based link choice models. Accounting for the travel time uncertainty, numerical studies of specified models within the proposed framework are conducted. The modeling framework may be helpful in various research contexts dealing with both randomness and other non-probabilistic uncertainties that cannot be exactly perceived.     

Estimating bike-share trips using station level data

Bicycle sharing systems (BSS) have increased in number rapidly since 2007. The potential benefits of BSS, mainly sustainability, health and equity, have encouraged their adoption through support and promotion by mayors in Europe and North America alike. In most cases municipal governments desire their BSS to be successful and, with few exceptions, state them as being so. New technological improvements have dramatically simplified the use and enforcement of bicycle return, resulting in the widespread adoption of BSS. Unfortunately little evaluation of the effectiveness of differently distributed and managed BSS has taken place. Comparing BSS systems quantitatively is challenging due to the limited data made available. The metrics of success presented by municipalities are often too general or incomparable to others making relative evaluations of BSS success arduous. This paper presents multiple methodologies allowing the estimation of the number of daily trips, the most significant measure of BSS usage, based on data that is commonly available, the number of bicycles available at a station over time. Results provide model coefficients as well as trip count estimates for select cities. Of four spatial and temporal aggregate models the day level aggregation is found to be most effective for estimation. In addition to trip estimation this work provides a rigorous formalization of station level data and the ability to distinguish spatio-temporal rebalancing quantities as well as new characteristics of BSS station use.     

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.     

Development of an indicator to assess the spatial fit of discrete choice models

Discrete choice models are increasingly implemented using geographical data. When this is the case, it may not be sufficient to project market shares accurately, but also to correctly replicate the spatial pattern of choices. Analysts might then be interested in assessing the results of a model’s fit relative to the spatial distribution of the observed responses. While canonical approaches exist for the exploratory spatial analysis of continuous variables, similar tools have not been widely implemented for discrete choice models, where the variable of interest is categorical. For this reason, despite recent progress with spatial models for discrete outcomes, there is still not a simple and intuitive tool to assess the quality of the spatial fit of a discrete choice model. The objective of this paper is to introduce a new indicator of spatial fit that can be applied to the results of discrete choice models. Utility of the indicator is explored by means of numerical experiments and then demonstrated by means of a case study of vehicle ownership in Montreal, Canada.     

Development of crash prediction models with individual vehicular data

Typical engineering research on traffic safety focuses on identifying either dangerous locations or contributing factors through a post-crash analysis using aggregated traffic flow data and crash records. A recent development of transportation engineering technologies provides ample opportunities to enhance freeway traffic safety using individual vehicular information. However, little research has been conducted regarding methodologies to utilize and link such technologies to traffic safety analysis. Moreover, traffic safety research has not benefited from the use of hurdle-type models that might treat excessive zeros more properly than zero-inflated models.This study developed a new surrogate measure, unsafe following condition (UFC), to estimate traffic crash likelihood by using individual vehicular information and applied it to basic sections of interstate highways in Virginia. Individual vehicular data and crash data were used in the development of statistical crash prediction models including hurdle models. The results showed that an aggregated UFC measure was effective in predicting traffic crash occurrence, and the hurdle Poisson model outperformed other count data models in a certain case.     

Assessment of schedule-based and frequency-based assignment models for strategic and operational planning of high-speed rail services

Despite some substantial limitations in the simulation of low-frequency scheduled services, frequency-based (FB) assignment models are by far the most widely used in practice. They are less expensive to build and less demanding from the computational viewpoint with respect to schedule-based (SB) models, as they require neither explicit simulation of the timetable (on the supply side), nor segmentation of OD matrices by desired departure/arrival time (on the demand side).The objective of this paper is to assess to what extent the lack of modeling capabilities of FB models is acceptable, and, on the other hand, the cases in which such approximations are substantial and more detailed SB models are needed. This is a first attempt to shed light on the trade-off between (frequency-based) model inaccuracy and (scheduled-based) model development costs in the field of long-distance (e.g. High-speed Rail, HSR) service modeling.To this aim, we considered two modeling specifications estimated using mixed Revealed Preferences (RP) and Stated Preferences (SP) surveys and validated with respect to the same case study. Starting from an observed (baseline) scenario, we artificially altered the demand distributions (uniform vs. time-varying demand) and the supply configuration (i.e. train departure times), and analyzed the differences in modal split estimates and flows on individual trains, using the two different model specifications.It resulted that when the demand distribution is uniform within the period of analysis, such differences are significant only when departure times of trains are strongly unevenly spaced in time. In such cases, the difference in modal shares, using FB w.r.t. SB, is in the range of [0%, +5%] meaning that FB models tend to overestimate HSR modal shares. When the demand distribution is not uniform, the difference in modal shares, using FB w.r.t. SB, is in the range of [−10%, +10%] meaning that FB models can overestimate or underestimate HSR modal shares, depending on timetable settings with respect to travelers’ desired departure times. The differences in on-board train flow estimates are more substantial in both cases of uniform and not uniform demand distribution.     

A hybrid-choice latent-class model for the analysis of the effects of weather on cycling demand

In this paper we analyze demand for cycling using a discrete choice model with latent variables and a discrete heterogeneity distribution for the taste parameters. More specifically, we use a hybrid choice model where latent variables not only enter into utility but also inform assignment to latent classes. Using a discrete choice experiment we analyze the effects of weather (temperature, rain, and snow), cycling time, slope, cycling facilities (bike lanes), and traffic on cycling decisions by members of Cornell University (in an area with cold and snowy winters and hilly topography). We show that cyclists can be separated into two segments based on a latent factor that summarizes cycling skills and experience. Specifically, cyclists with more skills and experience are less affected by adverse weather conditions. By deriving the median of the ratio of the marginal rate of substitution for the two classes, we show that rain deters cyclists with lower skills from bicycling 2.5 times more strongly than those with better cycling skills. The median effects also show that snow is almost 4 times more deterrent to the class of less experienced cyclists. We also model the effect of external restrictions (accidents, crime, mechanical problems) and physical condition as latent factors affecting cycling choices.     

Door-to-door travel times in RP departure time choice models: An approximation method using GPS data

A common way to determine values of travel time and schedule delay is to estimate departure time choice models, using stated preference (SP) or revealed preference (RP) data. The latter are used less frequently, mainly because of the difficulties to collect the data required for the model estimation. One main requirement is knowledge of the (expected) travel times for both chosen and unchosen departure time alternatives. As the availability of such data is limited, most RP-based scheduling models only take into account travel times on trip segments rather than door-to-door travel times, or use very rough measures of door-to-door travel times. We show that ignoring the temporal and spatial variation of travel times, and, in particular, the correlation of travel times across links may lead to biased estimates of the value of time (VOT). To approximate door-to-door travel times for which no complete measurement is possible, we develop a method that relates travel times on links with continuous speed measurements to travel times on links where relatively infrequent GPS-based speed measurements are available. We use geographically weighted regression to estimate the location-specific relation between the speeds on these two types of links, which is then used for travel time prediction at different locations, days, and times of the day. This method is not only useful for the approximation of door-to-door travel times in departure time choice models, but is generally relevant for predicting travel times in situations where continuous speed measurements can be enriched with GPS data.     

Estimating heterogeneity of car travelers on mode shifting behavior based on discrete choice models

In order to understand the mode shift behavior of car travelers and relieve traffic congestion, a Stated Preference survey has been conducted in the city of Ji'nan in China to analyze bus choice behavior and the heterogeneity of car travelers. Several discrete choice models, including multinomial logit, mixed logit and latent class model (LCM) are developed based on these survey data. A comparative analysis indicates that the LCM has the highest precision and is more suitable to analyze the heterogeneity of car travelers. The LCM divides car travelers into three classes. Different classes have different sets of influencing factors in the model. Policy recommendations are also proposed for those classes to promote bus shift from car travelers based on the model results. Finally, sensitivity analysis on parking fees and fuel cost is carried out on the LCMs under different bus service levels. Car travelers have different sensitivities to the influencing factors. The conclusions indicate that the LCM can reflect the heterogeneity and preferences of car travelers and can be used to understand how to shift the behavior of car travelers and make more effective traffic policy.     

Modelling route choice behaviour in multi-modal transport networks

The paper presents new findings on the influence of multi-modal trip attributes on the quality and competitiveness of inter-urban multi-modal train alternatives. The analysis covers the entire trip from origin to destination, including access and egress legs to and from the train network. The focus is on preferences for different feeder modes, railway station types and train service types as well as on the relative influence of time elements and transfer penalties. Data from dedicated surveys are used including individual objective choice sets of 235 multi-modal homebound trips in which train is the main transport mode. The observed trips have origins and destinations within the Rotterdam–Dordrecht region in The Netherlands with an average total trip time of 50 minutes. Hierarchical Nested Logit models are estimated to take account of unobserved similarities between alternatives at the home-end and the activity-end of the trip respectively, resulting in two-level nesting structures which differentiate between intercity (IC) and non-intercity railway station types at the upper level and between transit and private access modes at the lower level. In order to reflect the multi-dimensional structure of the data a more advanced so-called Multi-Nested GEV model according to the Principles of Differentiation has been estimated which significantly improves the explanatory power and stresses the importance of the home-end of the multi-modal trip.     

Modelling mode choice for freight transport using advanced choice experiments

In this paper we use advanced choice modelling techniques to analyse demand for freight transport in a context of modal choice. To this end, a stated preference (SP) survey was conducted in order to estimate freight shipper preferences for the main attributes that define the service offered by the different transport modes. From a methodological point of view, we focus on two critical issues in the construction of efficient choice experiments. Firstly, in obtaining good quality prior information about the parameters; and secondly, in the improved quality of the experimental data by tailoring a specific efficient design for every respondent in the sample.With these data, different mixed logit models incorporating panel correlation effects and accounting for systematic and random taste heterogeneity are estimated. For the best model specification we obtain the willingness to pay for improving the level of service and the elasticity of the choice probabilities for the different attributes. Our model provide interesting results that can be used to analyse the potential diversion of traffic from road (the current option) to alternative modes, rail or maritime, as well as to help in the obtaining of the modal distribution of commercial traffic between Spain and the European Union, currently passing through the Pyrenees.     

Estimating vehicle miles traveled combined with ITS data

‘Vehicle miles traveled’ (VMT) is an important performance measure for highway systems. Currently, VMT [or ‘annual average daily traffic’ (AADT)] is estimated from a combination of permanent counting stations and short-term counts done at specified locations as part of the Highway Performance Monitoring System (HPMS) mandated by the US Federal Highway Administration. However, on some roadway sections, Intelligent Transportation Systems (ITS) such as detectors and cameras also produce traffic data. The question addressed in this paper is whether and under what conditions ITS systems data could be used instead of HPMS short-term counts (called ‘coverage counts’)? This paper develops a methodology for determining a threshold number of missing daily traffic counts, or alternatively, the number of valid ITS data observations needed, in order to confidently replace the HPMS coverage counts with ITS data.

Because ITS counts, coverage counts, and actual ground counts (e.g. continuous counts) cannot be found coexisting on a roadway section, it is hard to compare them directly. In this paper, the Monte Carlo simulation method is employed to generate synthetic ITS counts and coverage counts from a set of relatively complete traffic counts collected at a continuous count station. Comparisons are made between simulated ITS counts, coverage counts, and actual ground counts. The simulation results indicate that when there are<330 daily traffic counts missing in a set of ITS counts in a year, that is, when there are at least 35 days of valid data, ITS counts can be used to derive a better AADT than using coverage counts. This result is applied to calculate the VMT for the Hampton Roads region in Virginia. The comparison between the VMTs derived with using and not using the threshold number indicates that these two VMTs are significantly different.     

Development of destination choice model with pairwise district-level constants using taxi GPS data

In this paper, a destination choice model with pairwise district-level constants is proposed for trip distribution based on a nearly complete OD trip matrix in a region. It is found that the coefficients are weakly identified in a destination choice model with pairwise zone-level constants. Thus, a destination choice model with pairwise district-level constants is then proposed and an iterative algorithm is developed for model estimation. Herein, the “district” means a spatial aggregation of a number of zones. The proposed model is demonstrated through simulation experiments. Then, destination choice models with and without pairwise district-level constants are estimated based on GPS data of taxi passenger trips collected during morning peak hours within the Inner Ring Road of Shanghai, China. The datasets comprise 504,187 trip records and a sample of 10,000 taxi trips for model development. The zones used in the study are actually 961 residents’ committees while the districts are 52 residential districts that are spatial aggregations and upper-level administrative units of residents’ committees. It is found that the estimated value of time dramatically drops after the involvement of district-level constants, indicating that the traditional model tends to overestimate the value of time when ignoring pairwise associations between two zones in trip distribution. The proposed destination choice model can ensure its predicted trip OD matrix to match the observed one at district level. Thus, the proposed model has potential to be widely applied for trip distribution under the situation where a complete OD trip matrix can be observed.