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.     

Assuring finite moments for willingness to pay in random coefficient models

Random coefficient models such as mixed logit are increasingly being used to allow for random heterogeneity in willingness to pay (WTP) measures. In the most commonly used specifications, the distribution of WTP for an attribute is derived from the distribution of the ratio of individual coefficients. Since the cost coefficient enters the denominator, its distribution plays a major role in the distribution of WTP. Depending on the choice of distribution for the cost coefficient, and its implied range, the distribution of WTP may or may not have finite moments. In this paper, we identify a criterion to determine whether, with a given distribution for the cost coefficient, the distribution of WTP has finite moments. Using this criterion, we show that some popular distributions used for the cost coefficient in random coefficient models, including normal, truncated normal, uniform and triangular, imply infinite moments for the distribution of WTP, even if truncated or bounded at zero. We also point out that relying on simulation approaches to obtain moments of WTP from the estimated distribution of the cost and attribute coefficients can mask the issue by giving finite moments when the true ones are infinite.     

The Signs of the Times: Imposing a Globally Signed Condition on Willingness to Pay Distributions

A feature of recent developments in choice models that enable estimation of the distribution of willingness to pay (WTP) is that the sign of the distribution can change over the range. Behaviourally this often makes little sense for attributes such as travel time on non-discretionary travel, despite a growing recognition of positive utility over some travel time ranges. This can in part be attributed to the analytical distribution that is selected (except the cumbersome lognormal), many of which are unconstrained over the full range. Although a number of analysts have imposed constraints on various distributions for random parameters that can satisfy the single-sign condition, these restrictions are, with rare exception, only satisfied for the mean and the standard deviation estimates of a random parameter. When heterogeneity around the mean and/or heteroscedasticity around the standard deviation is allowed for, however, the constraint condition is often not satisfied. Given the popularity of distributions other than the lognormal, in order to satisfy the sign condition under the most general form of parameterisation, we need to impose a global sign condition. In this paper we show how this might be achieved in the context of the valuation of travel time savings for car commuters choosing amongst an offered set of route-specific travel times and costs. We illustrate the impact of the constraint under a globally constrained Rayleigh distribution for total travel time parameterisation, contrasting the evidence with a multinomial logit model and a range of other distributional assumptions within the mixed logit framework. Discussions with Bill Greene, John Rose, Ken Train and especially Juan de Dios Ortuzar have been invaluable as have the comments of referees.     

Valuing of attributes influencing the attractiveness of suburban train service in Mumbai city: A stated preference approach

The paper presents valuing of qualitative and quantitative travel attributes influencing the attractiveness of suburban train service in Mumbai city, India. A stated preference experiment is designed to capture the data of sub-urban train mode choice behavior. The behavioral data are analyzed using different modeling techniques such as multinomial logit (MNL) and mixed logit (ML). In ML model, the random parameters are assumed to follow constrained triangular distribution, where mean equals its spread. The decomposition of preference heterogeneity around the mean estimate of random parameter is also investigated using ML model. The study shows the influence of headway time and train ride time associated with a particular crowding level (expressed in density of standing passengers/m²) in choosing the sub-urban train mode by calculating their willingness-to-pay (WTP) values and highlights the importance of WTP for addressing policy issues in the reduction of in-vehicle crowding level. The present study documents new findings of the effect of crowding level on train ride time in the context of a developing country and suggests some important directions for future suburban train transport crowding valuation research.     

What do commuters think travel time reliability is worth? Calculating economic value of reducing the frequency and extent of unexpected delays

The measurement of transportation system reliability has become one of the central topics of travel demand studies. A growing literature concerns the measurement of value of travel time reliability which provides a monetary cost of avoiding unpredictable travel time. The goal of this study is to measure commuters’ sensitivities to travel time reliability and their willingness to pay (WTP) to avoid unreliable routes. The preferences are elicited through a pivoted stated preference survey technique. To circumvent the issue of presenting numerical distributions and statistical terms to day-to-day commuters, we use the frequency of delay days as a means of measuring traveler’s sensitivities to travel time reliability. The advantage of using simplified measures to elicit traveler preferences for travel time reliability is that these methods simply compare days with high delay to days with usual travel time. It was found that travelers are not only averse to the amount of unexpected delay but also to the frequency of days with unexpected delays. The paper presents WTP findings for three measures: travel time, frequency embedded travel time, and travel time reliability. The ‘reliability’ increase in WTP for travel time is found to be nearly proportional to the frequency of experiencing unexpected delays. For example, the WTP for mean travel time is calculated at $6.98/h; however, reliability adds $3.27 (about 50 % of $6.98) to avoid unexpected delays ‘5 out of 10 days’. The results of the study would provide valuable inputs to cost-benefit analyses and traffic and revenue studies required for road tolling investment projects.     

Using nonparametrics to specify a model to measure the value of travel time

Using a range of nonparametric methods, the paper examines the specification of a model to evaluate the willingness-to-pay (WTP) for travel time changes from binomial choice data from a simple time–cost trading experiment. The analysis favours a model with random WTP as the only source of randomness over a model with fixed WTP which is linear in time and cost and has an additive random error term. Results further indicate that the distribution of log WTP can be described as a sum of a linear index fixing the location of the log WTP distribution and an independent random variable representing unobserved heterogeneity. This formulation is useful for parametric modelling. The index indicates that the WTP varies systematically with income and other individual characteristics. The WTP varies also with the time difference presented in the experiment which is in contradiction of standard utility theory.     

Commuters’ willingness-to-pay for improvement of transfer facilities in and around metro stations – A case study in Kolkata

Although several cities in India are developing the metro system, there are lacunas associated with transfer facilities in and around metro stations. The present work aims to investigate the perception of commuters of Kolkata city, India in terms of their willingness-to-pay (WTP) for improvement of transfer facilities. A stated preference survey instrument was designed to collect choice responses from metro commuters and the database was analysed by developing random parameter logit (RPL) models. The decomposition effects of various socioeconomic and trip characteristics on mean estimates were also investigated in random parameter logit models with heterogeneity. The work indicates significantly high WTP of metro commuters as compared to the average metro fare for improvement of various qualitative attributes of transfer facility such as ‘facility for level change’, ‘visual communication’, ‘pedestrian crossing’, and ‘pedestrian environment’. The WTP values are also found to vary across different groups of commuter formed on the basis of ‘trip purpose’, ‘monthly household income’, ‘station type’ and ‘metro fare’. ‘Work trip’ commuters are found to have higher WTP for improvement of access time, pedestrian environment and use of an escalator over the elevator. On the other hand, ‘high-income group’ commuters have shown higher WTP for improvement of access time, pedestrian crossing, and pedestrian environment. While ‘high fare group’ commuters have higher WTP for access time and pedestrian environment, heterogeneity is also observed in WTP for facility for level change, pedestrian crossing, and pedestrian environment across commuters using different ‘station type’ (underground, at-grade, and elevated). The findings from the study provide a basis for formulating policies for the improvement of transfer facilities in and around metro stations giving due attention to the preference of commuters having different socioeconomic and trip characteristics.     

Quantifying uncertainties in a national forecasting model

Uncertainties related to demand model system outputs is an important issue in travel demand models. This paper focuses on uncertainties arisen from the fact that models are estimated on a sample of the population (and not the whole population). Forecasting systems can be quite complex, and may contain procedures that not easily permit analytically derived statistical measures of uncertainty. In this paper, the possibilities to use computer-intensive numerical methods to compute statistical measures for very complex systems, without being bound to an analytical approach, are explored. Here, the bootstrap method is used to obtain statistical measures of outputs produced by the forecasting system SAMPERS. The SAMPERS system is used by Swedish transport authorities. The bootstrap method is briefly described as well as the procedure of applying bootstrap on the SAMPERS system. Numerical results are presented for selected forecast results at different levels such as total traffic demand, origin–destination demand, train line demand and the demand on specific links. Also, the uncertainty related to the value of time estimate is analysed.     

Valuing reductions in environmental pollution in a residential location context

A stated preference ranking experiment is designed to estimate the willingness-to-pay (WTP) for reducing the amount of atmospheric pollution in a group-based residential location context. Important issues are the proper definition of the context and the variable metric for the environmental attribute. Sample members were asked to rank 10 options arising from variations in the attributes travel time to work and to study, rent of the house and an environmental attribute (the number of days of Alert, in terms of concentration of PM₁₀, at a dwelling’s location). Multinomial logit models based on a consistent microeconomic framework were estimated for various stratifications of the data (income, pollution sensitivity, and type of dwelling currently inhabited). From these subjective values of time and WTP were derived for reductions in the number of days of alert and hence the amount of pollutant concentration at a given location. The WTP came out at about 1% of the family income for reducing one contingence day per year; this is approximately 60% higher than an estimate reported for the city of Edmonton, Canada, but the average PM₁₀ concentration in Santiago is about six times higher.     

Estimating a model of dynamic activity generation based on one-day observations: Method and results

In this paper we develop and explore an approach to estimate dynamic models of activity generation on one-day travel-diary data. Dynamic models predict multi-day activity patterns of individuals taking into account dynamic needs as well as day-varying preferences and time-budgets. We formulate an ordered-logit model of dynamic activity-agenda-formation decisions and show how one-day observation probabilities can be derived from the model as a function of the model’s parameters and, with that, how parameters can be estimated using standard loglikelihood estimation. A scale parameter cannot be identified because information on within-person variability is lacking in one-day data. An application of the method to data from a national travel survey illustrates the method. A test on simulated data indicates that, given a pre-set scale, the parameters can be identified and that estimates are robust for a source of heterogeneity not captured in the model. This result indicates that dynamic activity-based models of the kind considered here can be estimated from data that are less costly to collect and that support the large sample sizes typically required for travel-demand modeling. We conclude therefore that the proposed approach opens up a way to develop large-scale dynamic activity-based models of travel demand.     

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.     

Well-being and activity-based models

We present empirical and theoretical analyses to investigate the relationship between happiness (or subjective well-being) and activity participation and develop a framework for using well-being data to enhance activity-based travel demand models. The overriding hypothesis is that activities are planned and undertaken to satisfy needs so as to maintain or enhance subjective well-being. The empirical analysis consists of the development of a structural equations exploratory model of activity participation and happiness using data from a cross-sectional survey of a sample of commuters. The model reveals significant correlations between happiness and behavior for different types of activities: higher propensity of activity participation is associated with greater activity happiness and greater satisfaction with travel to the activity. The theoretical analysis consists of the development of a modeling framework and measures for the incorporation of well-being within activity-based travel demand models. The motivation is that activity pattern models have been specified in ad-hoc ways in practice as a function of mobility, lifestyle, and accessibility variables. We postulate that well-being is the ultimate goal of activity patterns which are driven by needs and propose two extensions of activity pattern models. The first extension consists of the use of well-being measures as indicators of the utility of activity patterns (in addition to the usual choice indicators) within a random utility modeling framework. The second extension models conceptually the behavioral process of activity generation based on needs satisfaction. We present an example of an operational activity pattern model and propose well-being measures for enhancing it.     

Reprint of: Modelling the impact of traffic incidents on travel time reliability

Traffic incidents are recognised as one of the key sources of non-recurrent congestion that often leads to reduction in travel time reliability (TTR), a key metric of roadway performance. A method is proposed here to quantify the impacts of traffic incidents on TTR on freeways. The method uses historical data to establish recurrent speed profiles and identifies non-recurrent congestion based on their negative impacts on speeds. The locations and times of incidents are used to identify incidents among non-recurrent congestion events. Buffer time is employed to measure TTR. Extra buffer time is defined as the extra delay caused by traffic incidents. This reliability measure indicates how much extra travel time is required by travellers to arrive at their destination on time with 95% certainty in the case of an incident, over and above the travel time that would have been required under recurrent conditions. An extra buffer time index (EBTI) is defined as the ratio of extra buffer time to recurrent travel time, with zero being the best case (no delay). A Tobit model is used to identify and quantify factors that affect EBTI using a selected freeway segment in the Southeast Queensland, Australia network. Both fixed and random parameter Tobit specifications are tested. The estimation results reveal that models with random parameters offer a superior statistical fit for all types of incidents, suggesting the presence of unobserved heterogeneity across segments. What factors influence EBTI depends on the type of incident. In addition, changes in TTR as a result of traffic incidents are related to the characteristics of the incidents (multiple vehicles involved, incident duration, major incidents, etc.) and traffic characteristics.     

Dynamic travel mode searching and switching analysis considering hidden model preference and behavioral decision processes

This paper proposes a conceptual framework to model the travel mode searching and switching dynamics. The proposed approach is structurally different from existing mode choice models in the way that a non-homogeneous hidden Markov model (HMM) has been constructed and estimated to model the dynamic mode srching process. In the proposed model, each hidden state represents the latent modal preference of each traveler. The empirical application suggests that the states can be interpreted as car loving and carpool/transit loving, respectively. At each time period, transitions between the states are functions of time-varying covariates such as travel time and travel cost of the habitual modes. The level-of-service (LOS) changes are believed to have an enduring impact by shifting travelers to a different state. While longitudinal data is not readily available, the paper develops an easy-to-implement memory-recall survey to collect required process data for the empirical estimation. Bayesian estimation and Markov chain Monte Carlo method have been applied to implement full Bayesian inference. As demonstrated in the paper, the estimated HMM is reasonably sensitive to mode-specific LOS changes and can capture individual and system dynamics. Once applied with travel demand and/or traffic simulation models, the proposed model can describe time-dependent multimodal behavior responses to various planning/policy stimuli.     

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 link travel time functions for heterogeneous traffic flows on freeways

Oversized vehicles, such as trucks, significantly contribute to traffic delays on freeways. Heterogeneous traffic populations, that is, those consisting of multiple vehicles types, can exhibit more complicated travel behaviors in the operating speed and performance, depending on the traffic volume as well as the proportions of vehicle types. In order to estimate the component travel time functions for heterogeneous traffic flows on a freeway, this study develops a microscopic traffic‐simulation based four‐step method. A piecewise continuous function is proposed for each vehicle type and its parameters are estimated using the traffic data generated by a microscopic traffic simulation model. The illustrated experiments based on VISSIM model indicate that (i) in addition to traffic volume, traffic composition has significant influence on the travel time of vehicles and (ii) the respective estimations for travel time of heterogeneous flows could greatly improve their estimation accuracy. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Analysing Demand for Suburban Trips: A Mixed RP/SP Model with Latent Variables and Interaction Effects

We analyse mode choice behaviour for suburban trips in the Grand Canary island using mixed revealed preference (RP)/stated preference (SP) information. The SP choice experiment allowed for interactions among the main policy variables: travel cost, travel time and frequency, and also to test the influence of latent variables such as comfort. It also led to discuss additional requirements on the size and sign of the estimated model parameters, to assess model quality when interactions are present. The RP survey produced data on actual trip behaviour and was used to adapt the SP choice experiment. During the specification searches we detected the presence of income effect and were able to derive willingness-to-pay measures, such as the subjective value of time, which varied among individuals. We also studied the systematic heterogeneity in individual tastes through the specification of models allowing for interactions between level-of-service and socio-economic variables. We concluded examining the sensitivity of travellers’ behaviour to various policy scenarios. In particular, it seems that contrary to political opinion, in a crowded island policies penalising the use of the private car seem to have a far greater impact in terms of bus patronage than policies implying direct improvements to the public transport service.     

Travel time variability and airport accessibility

We analyze the cost of access travel time variability for air travelers. Reliable access to airports is important since the cost of missing a flight is likely to be high. First, the determinants of the preferred arrival times at airports are analyzed. Second, the willingness to pay (WTP) for reductions in access travel time, early and late arrival time at the airport, and the probability to miss a flight are estimated, using a stated choice experiment. The results indicate that the WTPs are relatively high. Third, a model is developed to calculate the cost of variable travel times for representative air travelers going by car, taking into account travel time cost, scheduling cost and the cost of missing a flight using empirical travel time data. In this model, the value of reliability for air travelers is derived taking “anticipating departure time choice” into account, meaning that travelers determine their departure time from home optimally. Results of the numerical exercise show that the cost of access travel time variability for business travelers are between 0% and 30% of total access travel cost, and for non-business travelers between 0% and 25%. These numbers depend strongly on the time of the day.     

Are we ready to embrace connected and self-driving vehicles? A case study of Texans

While connected, highly automated, and autonomous vehicles (CAVs) will eventually hit the roads, their success and market penetration rates depend largely on public opinions regarding benefits, concerns, and adoption of these technologies. Additionally, the introduction of these technologies is accompanied by uncertainties in their effects on the carsharing market and land use patterns, and raises the need for tolling policies to appease the travel demand induced due to the increased convenience. To these ends, this study surveyed 1088 respondents across Texas to understand their opinions about smart vehicle technologies and related decisions. The key summary statistics indicate that Texans are willing to pay (WTP) $2910, $4607, $7589, and $127 for Level 2, Level 3, and Level 4 automation and connectivity, respectively, on average. Moreover, affordability and equipment failure are Texans’ top two concerns regarding AVs. This study also estimates interval regression and ordered probit models to understand the multivariate correlation between explanatory variables, such as demographics, built-environment attributes, travel patterns, and crash histories, and response variables, including willingness to pay for CAV technologies, adoption rates of shared AVs at different pricing points, home location shift decisions, adoption timing of automation technologies, and opinions about various tolling policies. The practically significant relationships indicate that more experienced licensed drivers and older people associate lower WTP values with all new vehicle technologies. Such parameter estimates help not only in forecasting long-term adoption of CAV technologies, but also help transportation planners in understanding the characteristics of regions with high or low future-year CAV adoption levels, and subsequently, develop smart strategies in respective regions.