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.     

Discrete choice with spatial correlation: A spatial autoregressive binary probit model with endogenous weight matrix (SARBP-EWM)

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

Novel Methods and the Maximum Likelihood Estimation Technique for Estimating Traffic Critical Gap

Most unsignalised intersection capacity calculation procedures are based on gap acceptance models. Accuracy of critical gap estimation affects accuracy of capacity and delay estimation. Several methods have been published to estimate drivers' sample mean critical gap, the Maximum Likelihood Estimation (MLE) technique regarded as the most accurate. This study assesses three novel methods; Average Central Gap (ACG) method, Strength Weighted Central Gap method (SWCG), and Mode Central Gap method (MCG), against MLE for their fidelity in rendering true sample mean critical gaps. A Monte Carlo event based simulation model was used to draw the maximum rejected gap and accepted gap for each of a sample of 300 drivers across 32 simulation runs. Simulation mean critical gap is varied between 3s and 8s, while offered gap rate is varied between 0.05veh/s and 0.55veh/s. This study affirms that MLE provides a close to perfect fit to simulation mean critical gaps across a broad range of conditions. The MCG method also provides an almost perfect fit and has superior computational simplicity and efficiency to the MLE. The SWCG method performs robustly under high flows; however, poorly under low to moderate flows. Further research is recommended using field traffic data, under a variety of minor stream and major stream flow conditions for a variety of minor stream movement types, to compare critical gap estimates using MLE against MCG. Should the MCG method prove as robust as MLE, serious consideration should be given to its adoption to estimate critical gap parameters in guidelines. Copyright © 2012 John Wiley & Sons, Ltd.     

Statistical estimation of the parameters of Daganzo's gap acceptance model

In a recent article in Transportation Research, Daganzo (1981) described a model of gap acceptance that permits the mean of the gap acceptance function to vary among drivers and permits the duration of the shortest acceptable gap for each driver to vary among gaps. The model contains several constant parameters whose values must be estimated statistically from observations of drivers' behavior. The results of numerical experiments reported by Daganzo (1981) suggested that the values of the parameters cannot be estimated by the method of maximum likelihood, which is the most obvious estimation technique, and Daganzo proposed using a sequential estimation method instead. The sequential method appeared to yield reasonable numerical results. In this paper, it is shown that subject to certain reasonable assumptions concerning the true parameter values and the probability distribution of gap durations, the maximum likelihood method does, in fact, yield consistent estimates of the parameters of Daganzo's model, whereas the sequential method does not. Hence, maximum likelihood is the better estimation method for this model.     

Estimation of a constrained multinomial logit model

Identifying the set of available alternatives in a choice process after considering an individual’s bounds or thresholds is a complex process that, in practice, is commonly simplified by assuming exogenous rules in the choice set formation. The Constrained Multinomial Logit (CMNL) model incorporates thresholds in several attributes as a key endogenous process to define the alternatives choice/rejection mechanism. The model allows for the inclusion of multiple constraints and has a closed form. In this paper, we study the estimation of the CMNL model using the maximum likelihood function, develop a methodology to estimate the model overcoming identification problems by an endogenous partition of the sample, and test the model estimation with both synthetic and real data. The CMNL model appears to be suitable for general applications as it presents a significantly better fit than the MNL model under constrained behaviour and replicates the MNL estimates in the unconstrained case. Using mode choice real data, we found significant differences in the values of times and elasticities between compensatory MNL and semi-compensatory CMNL models, which increase as the thresholds on attributes become active.     

Implementing the maximum likelihood methodology to measure a driver’s critical gap

Most of the capacity calculation procedures for two-way stop-controlled (TWSC) intersections are based on gap acceptance models. Critical gap is one of the major parameters for gap acceptance models. The accuracy of capacity estimation is mainly determined by the accuracy of the critical gap. This paper focuses on the implementation of the maximum likelihood technique to measure a driver’s critical gap using field data. A methodology to define gap events is proposed, so that the accepted gaps and maximum rejected gaps required by the maximum likelihood technique could be obtained. Specific issues regarding multi-lane situations and major street right turn movement are discussed. Special conditions observed during the research are addressed when the proposed method cannot be applied directly, such as the existence of a mid-block refuge area where minor street drivers can seek gaps in a two-stage process, pedestrian blockage, and downstream queue spill back. The proposed method was adopted in measuring critical gap under US conditions during a research project, described by Kyte et al. (1996). ©     

A behavioral choice model of the use of car-sharing and ride-sourcing services

There are a number of disruptive mobility services that are increasingly finding their way into the marketplace. Two key examples of such services are car-sharing services and ride-sourcing services. In an effort to better understand the influence of various exogenous socio-economic and demographic variables on the frequency of use of ride-sourcing and car-sharing services, this paper presents a bivariate ordered probit model estimated on a survey data set derived from the 2014–2015 Puget Sound Regional Travel Study. Model estimation results show that users of these services tend to be young, well-educated, higher-income, working individuals residing in higher-density areas. There are significant interaction effects reflecting the influence of children and the built environment on disruptive mobility service usage. The model developed in this paper provides key insights into factors affecting market penetration of these services, and can be integrated in larger travel forecasting model systems to better predict the adoption and use of mobility-on-demand services.     

Trip chaining propensity and tour mode choice of out-of-home workers: evidence from a mid-sized Canadian city

Suburban development patterns, flexible work hours, and increasing participation in out-of-home activities are making the travel patterns of individuals more complex, and complex trip chaining could be a major barrier to the shift from drive-alone to public transport. This study introduces a cohort-based approach to analyse trip tour behaviors, in order to better understand and model their relationships to socio-demographics, trip attributes, and land use patterns. Specifically, it employs worker population cohorts with homogenous activity patterns to explore differences and similarities in tour frequency, trip chaining, and tour mode choices, all of which are required for travel demand modeling. The paper shows how modeling of these important tour variables may be improved, for integration into an activity-based modeling framework. Using data from the Space–Time Activity Research (STAR) survey for Halifax, Canada, five clusters of workers were identified from their activity travel patterns. These were labeled as extended workers, 8 to 4 workers, shorter work-day workers, 7 to 3 workers, and 9 to 5 workers. The number of home-based tours per day for all clusters were modeled using a Poisson regression model. Trip chaining was then modeled using an Ordered Probit model, and tour mode choice was modeled using a Multinomial logit (MNL) model. Statistical analysis showed that socio-demographic characteristics and tour attributes are significant predictors of travel behavior, consistent with existing literature. Urban form characteristics also have a significant influence on non-workers’ travel behavior and tour complexity. The findings of this study will assist in the future evaluation of transportation projects, and in land-use policymaking.

     

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.     

Time-dependent drivers’ merging behavior model in work zone merging areas

This study investigates the drivers’ merging behavior in work zone merging areas during the entire merging implementation period from the time of starting a merging maneuver to that of completing the maneuver. With the actual work zone merging traffic data, we propose a time-dependent logistic regression model considering the possible time-varying effects of influencing factors, and a standard logistic regression model for the purpose of model comparison. Model comparison results show that the time-dependent model performs better than the standard model because the former can provide higher prediction accuracy. The time-dependent model results show that seven factors exhibit time-varying effects on the drivers’ merging behavior, including merging vehicle speed, through lane lead vehicle speed and through lane lag vehicle speed, longitudinal gap between the merging and lead vehicles, longitudinal gap between the merging and through lane lead vehicles, types of through lane lead and through lane lag vehicles. Interestingly, both the through lane lead vehicle speed and the through lane lag vehicle speed are found to exhibit heterogeneous effects at different times of the merging implementation period. One important finding from this study is that the merging vehicle has a decreasing willingness to take the choice of “complete a merging maneuver” as the elapsed time increases if the through lane lead vehicle is a heavy vehicle.     

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.     

Estimation of link performance functions from incomplete flow data

Despite the pivotal importance of link performance functions to models of transport systems, relatively little work has been done on practical aspects of estimating these functions from observed data. Furthermore it is difficult to find any examples in the literature of estimated urban link performance functions faithfully reproducing theoretical travel time-flow relationships. One reason for the paucity of research in this area is the difficulty and expense of obtaining the requisite data. The increase in automatic collection of traffic flow data goes part way to resolving this problem, but matching such flows to manually recorded travel times can present considerable statistical difficulties in the estimation procedure. This paper considers the estimation of link performance functions from a combination of automatically recorded traffic counts and travel collected by hand, using a non-standard statistical methodology. The study is motivated by a set of data of precisely this type, from the UK city of Leicester.     

Estimation of an integrated driving behavior model

This paper presents the methodology and results of estimation of an integrated driving behavior model that attempts to integrate various driving decisions. The model explains lane changing and acceleration decisions jointly and so, captures inter-dependencies between these behaviors and represents drivers’ planning capabilities. It introduces new models that capture drivers’ choice of a target gap that they intend to use in order to change lanes, and acceleration models that capture drivers’ behavior to facilitate the completion of a desired lane change using the target gap.The parameters of all components of the model are estimated simultaneously with the maximum likelihood method and using detailed vehicle trajectory data collected in a freeway section in Arlington, Virginia. The estimation results are presented and discussed in detail.     

共享单车停放需求影响因素分析和预测研究

为了解决城市共享单车的乱停乱放问题,本文基于北京市的共享单车出行大数据,提出了共享单车停放需求预测的多项Logit模型。首先分析了单车停放需求的影响因素,然后选取了时间、空间及天气方面的12个因素为自变量,通过Wald检验分析了这些因素与停放需求的相关性和显著性,基于多项Logit模型建立了共享单车的停放需求预测模型。结果表明:工作日、时段、商业区、所临道路类型、临近轨交站、高温、下雨、以及风力等级与共享单车停放需求显著相关;构建的预测模型总体预测准确率为77.5%,其中对出现频率最高的低停放需求预测准确率高达86.49%。     

A meta-model of vehicle ownership choice parameters

This paper builds a meta-model of vehicle ownership choice parameters to predict how their values might vary across extended periods as a function of macroeconomic variables. Multinomial logit models of vehicle ownership are estimated from repeated cross-sectional data between 1971 and 1996 for large urban centers in Ontario. Three specifications are tested: a varying constants (VC) model where the alternative specific constants are allowed to vary each year; a varying scales (VS) model where the scale parameter varies instead; and a varying scales and constants model. The estimated parameters are then regressed on macroeconomic variables (e.g., employment rate, gas prices, etc.). The regressions yield good fit and statistically significant results, suggesting that changes in the macroeconomic environment influence household decision making over time, and that macroeconomic information could potentially help predict how model parameters evolve. This implies that the common assumption of holding parameters constant across forecast horizons could potentially be relaxed. Furthermore, using a separate validation dataset, the predictive power of the VC and VS models outperform conventional approaches providing further evidence that pooling data from multiple periods could also produce more robust models.     

Measuring the impacts of weather variability on home-based trip chaining behaviour: a focus on spatial heterogeneity

Using the 2011 Swedish national travel survey data, this paper explores the influence of weather characteristics on individuals’ home-based trip chaining complexity. A series of panel mixed ordered Probit models are estimated to examine the influence of individual/household social demographics, land use characteristics, and weather characteristics on individuals’ home-based trip chaining complexity. A thermal index, the universal thermal climate index (UTCI), is used in this study instead of using directly measured weather variables in order to better approximate the effects of the thermal environment. The effects of UTCI are segmented into different seasons to account for the seasonal difference of UTCI effects. Moreover, a spatial expansion method is applied to allow the impacts of UTCI to vary across geographical locations, as individuals in different regions have different weather/climate adaptions. The effects of weather are examined in subsistence, routine, and discretionary trip chains. The results reveal that the ‘ground covered with snow’ condition is the most influential factor on the number of trips chained per trip chain among all other weather factors. The variation of UTCI significantly influences trip chaining complexity in autumn but not in spring and winter. The routine trip chains are found to be most elastic towards the variation of UTCI. The marginal effects of UTCI on the expected number of trips per routine trip chain have considerable spatial variations, while these spatial trends of UTCI effects are found to be not consistent over seasons.     

Short-term travel time prediction

Effective prediction of travel times is central to many advanced traveler information and transportation management systems. In this paper we propose a method to predict freeway travel times using a linear model in which the coefficients vary as smooth functions of the departure time. The method is straightforward to implement, computationally efficient and applicable to widely available freeway sensor data.We demonstrate the effectiveness of the proposed method by applying the method to two real-life loop detector data sets. The first data set––on I-880––is relatively small in scale, but very high in quality, containing information from probe vehicles and double loop detectors. On this data set the prediction error ranges from 5% for a trip leaving immediately to 10% for a trip leaving 30 min or more in the future. Having obtained encouraging results from the small data set, we move on to apply the method to a data set on a much larger spatial scale, from Caltrans District 12 in Los Angeles. On this data set, our errors range from about 8% at zero lag to 13% at a time lag of 30 min or more. We also investigate several extensions to the original method in the context of this larger data set.     

Maneuvers of motorcycles in queues at signalized intersections

The maneuvering models of motorcycles in previous studies often considered motorcycles' traveling in terms of movements in a physical static lane and not in terms of dynamic virtual lane‐based movements. For that reason, these models are not able to imitate motorcyclists' behavior well. This paper proposes a maneuverability model framework for motorcycles in queues at signalized intersections with considering the dynamic motorcycle's lane. The model includes (i) a dynamic motorcycle's lane to identify the current, left, and right lanes of the subject motorcycle, (ii) a threshold distance to determine when a motorcyclist starts to consider maneuvering, (iii) a lane selection model to identify the lane preferred by a motorcyclist, and (iv) a gap acceptance model to describe whether or not the lead and lag gaps are acceptable for maneuvering. The model framework captures the variation across the motorcyclist population and over time observations. The models were applied to Hanoi and Hochiminh city, Vietnam, based on microscopic data collected from video images. All of the parameters were estimated using the maximum likelihood method with the statistical estimation software GAUSS. The results show that 77.88% of the observed maneuvers – either staying in the current lane or turning left or right – could be modeled correctly by the proposed models. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling measurement errors and missing initial values in freeway dynamic origin–destination estimation systems

Most existing dynamic origin–destination (O–D) estimation approaches are grounded on the assumption that a reliable initial O–D set is available and traffic volume data from detectors are accurate. However, in most traffic systems, both types of critical information are either not available or subjected to some level of measurement errors such as traffic counts and speed measurement from sensors. To contend with those critical issues, this study presents two robust algorithms, one for estimation of an initial O–D set and the other for tackling the input measurement errors with an extended estimation algorithm. The core concept of the initial O–D estimation algorithm is to decompose the target network in a number of sub-networks based on proposed rules, and then execute the estimation of the initial O–D set iteratively with the observable information at the first time interval. To contend with the inevitable detector measurement error, this study proposes an interval-based estimation algorithm that converts each model input data as an interval with its boundaries being set based on some prior knowledge. The performance of both proposed algorithms has been tested with a simulated system, the I-95 freeway corridor between I-495 and I-695, and the results are quite promising.