Aggregation of common-metric attributes in preference revelation and implications for willingness to pay

There is a growing interest in process heterogeneity in the way that individuals evaluate packages of attributes in real or hypothetical markets and make choices. We consider the role of the relative magnitude of pairs of attributes that are defined on a common metric (e.g., minutes or dollars), to look at the extent to which attributes might be added in preference revelation, in contrast to the commonly adopted single rule of compensatory behaviour. The focus is on a choice model specification that allows for different treatments of pairs of attributes across a sample, in contrast to studies that impose a single rule on all observations, and that does not require supplementary information on whether specific individuals claimed to have added up attributes; rather we structure a non-linear utility function that permits a probabilistic aggregation of each attribute. We translate this into a willingness to pay for travel time-savings for car commuters, in the context of tolling roads in Sydney, and contrast it with the results from the additive model, and a model where self-stated attribute processing information is taken into account. The empirical evidence suggests that mean willingness to pay increases when the addition rule is accounted for. This is a potentially important message for environmental applications where two or more attributes have a common metric.     

Inferring attribute non-attendance from stated choice data: implications for willingness to pay estimates and a warning for stated choice experiment design

There is a growing interest in traveller behaviour research to explore alternative information processing strategies (often referred to as heuristics or rules) adopted by individuals when assessing packages of attributes describing alternatives in a choice set, and making a choice. One popular attribute processing rule relates to attributes not being considered (i.e., being ignored), for all manner of reasons, referred to in the small but growing literature as attribute non-attendance or non-preservation. Researchers have used a mixture of methods to study the role of attribute non-attendance, including supplementary questions on whether each attribute is ignored or not, and methods in which the functional form of the utility expressions defining an alternative can recognise the possibility, up to a probability, of an attribute being ignored. Although supplementary questions are worthy of further consideration, despite the controversy as to the reliability of the response, recent interest has focused on ways to establish the incidence of attribute non-attendance without recourse to such evidence. In this paper we use an existing data set of choice amongst four attributes describing alternative car non-commuting trips, to illustrate the proposed method, and to compare values of travel time savings under each possible combination of non-attendance attributes relative to a model in which all attributes are assumed to be fully attended to. The paper reveals a major concern with the way that attribute levels and ranges are selected in the design of choice experiments, which can induce non-attendance situations where willingness to pay estimates cannot be obtained.     

Identifying preferences for public transport investments under a constrained budget

As urban areas face increasing demands for new transport infrastructure to promote a sustainable future with an increasing reality of constrained government budgets, the debate on whether we should focus on rail or bus-based investments continues unabated in many jurisdictions. Associated with the debate is an emotional (or ideological) bias by communities in favour of one mode, especially rail, which carries much sway at the political level as if there is no budget constraint. This paper presents a stated choice experiment to investigate this context as two unlabelled options described by 20 potential drivers of community preferences for improved public transport, where each choice scenario is conditioned on an estimated construction cost and a total annual transport infrastructure budget for the relevant geographical jurisdiction. This is followed by a labelling of each alternative to reveal whether the option is bus rapid transit (BRT) or light rail (LRT) and to establish whether this additional information influences preference revision. Data is collected in all eight capital cities of Australia in mid 2014. Mixed logit models with heteroscedastic conditioning in terms of the cost of the project infrastructure and whether the alternative is labelled BRT or LRT, provide new evidence on the nature and extent of community modal bias in a budget-constrained choice setting. The conclusions are twofold. On the one hand, if a fully compensatory choice rule is assumed (as is common in all previous modal comparison studies), LRT is predominantly preferred over BRT despite budgetary constraints, similarities in quality of service attributes and the opportunity to choose a greater network coverage for a given construction cost. However, when we allow for attribute non-attendance (a semi-compensatory choice rule), the modal bias is no longer a significant driver of preferences.     

The implications on willingness to pay of respondents ignoring specific attributes

Individuals processing the information in a stated choice experiment are typically assumed to evaluate each and every attribute offered within and between alternatives, and to choose their most preferred alternative. However, it has always been thought that some attributes are ignored in this process for many reasons, including a coping strategy to handle ones perception of the complexity of the choice task. Nonetheless, analysts typically proceed to estimate discrete choice models as if all attributes have influenced the outcome to some degree. The cognitive processes used to evaluate trade-offs are complex with boundaries often placed on the task to assist the respondent. These boundaries can include prioritising attributes and ignoring specific attributes. In this paper we investigate the implications of bounding the information processing task by attribute elimination through ignoring one or more attributes. Using a sample of car commuters in Sydney we estimate mixed logit models that assume all attributes are candidate contributors, and models that assume certain attributes are ignored, the latter based on supplementary information provided by respondents. We compare the value of travel time savings under the alternative attribute processing regimes. Assuming that all attributes are not ignored and duly processed, leads to estimates of parameters which produce significantly different willingness to pay (WTP) to that obtained when the exclusion rule is invoked.     

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.     

Web-based survey design for unravelling semi-compensatory choice in transport and urban planning

The estimation of semi-compensatory models is gaining momentum in transport planning in recent years. However, traditional survey methodologies focus on collecting solely compensatory choice data, which leads to information loss when semi-compensatory models are estimated. The present study proposes a novel web-based survey that enables collecting data about the entire semi-compensatory choice process. The web-based environment allows seamless tracking of semi-compensatory choice protocols without interfering with the natural choice process and without introducing problems related to comprehension bias, narrative inconsistency and misinterpretation of the choice protocols. The procedure is applied to rental apartment choice by students and results shed light on semi-compensatory choice by: (1) demonstrating the importance of choice set formation; (2) unravelling the distribution of threshold selection across the population; (3) revealing the linkage between the viable choice-set and the choice.     

Making use of respondent reported processing information to understand attribute importance: a latent variable scaling approach

In recent years we have seen an explosion of research seeking to understand the role that rules and heuristics might play in improving the predictive capability of discrete choice models, as well as delivering willingness to pay estimates for specific attributes that may (and often do) differ significantly from estimates based on a model specification that assumes all attributes are relevant. This paper adds to that literature in one important way—it explicitly recognises the endogeneity issues raised by typical attribute non-attendance treatments and conditions attribute parameters on underlying unobserved attribute importance ratings. We develop a hybrid model system involving attribute processing and outcome choice models in which latent variables are introduced as explanatory variables in both parts of the model, explaining the answers to attribute processing questions and explaining heterogeneity in marginal sensitivities in the choice model. The resulting empirical model explains how lower latent attribute importance leads to a higher probability of indicating that an attribute was ignored or that it was ranked as less important, as well as increasing the probability of a reduced value for the associated marginal utility coefficient in the choice model. The model does so by treating the answers to information processing questions as dependent rather than explanatory variables, hence avoiding potential risk of endogeneity bias and measurement error.     

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.     

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.     

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.     

Incorporating trip chaining into analysis of destination choice

A model of destination choice is developed in this study employing “prospective utility” of a destination zone as its attraction measure. The prospective utility accounts for future dependency of destination choice and makes possible relevant treatment of interdependent choices in a trip chain. A parameter is included in the model to represent the magnitude of the future dependency. Empirical estimation results show that destination choice is in fact future dependent and coefficients of travel time and zonal attribute variables may be biased if this depedency is not accounted for.     

A non-compensatory choice model incorporating attribute cutoffs

This research proposes an extension to the traditional compensatory utility maximization framework which has guided most theoretical and statistical work in choice modeling applications, including those in transportation demand estimation work. Attribute cutoffs are incorporated into the decision problem formulation; it is then argued on extant empirical evidence that individuals may view these constraints as “soft”. This leads to the formulation of a penalized utility function that allows for constraint violation, but at a cost to the overall evaluation of the good. The proposed model is able to represent fully compensatory, conjunctive and disjunctive choice strategies, as well as combinations thereof. The properties of the proposed theoretical model are examined and discussed. From the theoretical framework, statistical models of choice behavior are easily derived; in their simplest forms, these models can be estimated using existing software. A Stated Preference choice experiment is analyzed using the proposed model, which is found to be highly consistent with observed choices and superior to a structural two-stage choice set formation model.     

Towards a practical method to establish comparable values of travel time savings from stated choice experiments with differing design dimensions

Individual’s process the information in stated choice (SC) experiments in many different ways. In order to accommodate decisions rules that are used in processing information, there is good sense in conditioning the parameterisation of stated choice design attributes on these rules. In particular, rules might be invoked to cope with the dimensionality of the SC design. In this paper, we investigate the impact of rules such as attribute aggregation and reference dependency on preference profiles for specific design attributes, as well as the design specification, as we vary the dimensionality of an SC design. The heteroscedastic extreme value logit model is estimated to identify the role of design dimensionality and attribute processing rules, after accounting for scale differences across sixteen pooled data designs The empirical evidence, drawn from a study in Sydney of car commuter route choice, suggests that accounting for the way that stated choice designs are processed, given their dimensionality, does make a statistically significant difference on measures of willingness to pay, as does accounting for scale differences between pooled data designs. This evidence has practical value in guiding the design of SC experiments and in adjusting results from different SC designs when comparing the evidence. We propose a simple adjustment formula to use in adjusting VTTS from different studies so that they are comparable. From a practical policy perspective, the evidence sends a warning about the risk of undervaluing mean VTTS if the attribute processing rules are not accounted for.     

Willingness to pay for public transportation options for improving the quality of life of the rural elderly

Transportation for the rural elderly is an increasing concern as baby boomers age and young people continue to exit rural communities. When the elderly are no longer able to drive, they rely on alternative forms of transportation, including public transportation systems. Currently, such systems are usually not good substitutes for driving a private car, especially in rural areas. Because expanded rural transportation systems would likely be funded by taxpayers, an understanding of their preferences and willingness to pay (WTP) for non-medical transportation options is essential. To help understand WTP and preferences, a choice experiment survey was administered to taxpayers in three counties (Atascosa, Polk, and Parker) in Texas. Results indicate taxpayers’ value transportation services for the elderly and are willing to support them. They value more flexible options over base levels of the attributes presented, but they may not always prefer the most flexible options. Respondents’ WTP for the same transportation attribute was similar across counties, but differences in socio-demographic coefficients suggest that transportation systems may need to be customized to meet local needs. Furthermore, county residents’ WTP may not cover the cost of desired improvements to the transportation systems.     

Estimating the willingness to pay and value of risk reduction for car occupants in the road environment

In recent years there has been a re-focus on the valuation of a statistical life from the ex post or human capital method to an ex ante willingness to pay (WTP) approach. This is in part a recognition that we may have been undervaluing the cost of fatalities and injuries to society associated with crashes, but also a strong belief in the need to focus on establishing the amount, ex ante, that individuals are willing to pay to reduce the risk of exposure to circumstances that might lead to death or degree of injury on the road network. This study has developed a framework in which to identify the degree of preference heterogeneity in willingness to pay by individuals who are drivers or passengers in cars to avoid being killed or injured. A stated choice experiment approach is developed. The empirical setting is a choice of route for a particular trip that a sample of individuals periodically undertakes in Australia. The particular trip is described in enough detail to provide the respondent with a familiar market environment, providing all the relevant background information required for making a decision. Mixed logit models are estimated to obtain the marginal (dis)utilities associated with each influence on the choice amongst the attribute packages offered in the stated choice scenarios. These estimates are used to obtain the WTP distributions for fatality and injury avoidance, which are then aggregated to obtain estimates of the value of risk reduction (VRR), of which the fatality class is also known as the value of a statistical life (VSL).     

Experience as a conditioning effect on choice: Does it matter whether it is exogenous or endogenous?

Previous choice studies have proposed a way to condition the utility of each alternative in a choice set on experience with the alternatives accumulated over previous periods, defined either as a mode used or not in a most recent trip, or the mode chosen in their most recent trip and the number of similar one-way trips made during the last week. The paper found that the overall statistical performance of the mixed logit model improved significantly, suggesting that this conditioning idea has merit. Experience was treated as an exogenous influence linked to the scale of the random component, and to that extent it captures some amount of the heterogeneity in unobserved effects, purging them of potential endogeneity. The current paper continues to investigate the matter of endogeneity versus exogeneity. The proposed approach implements the control function method through the experience conditioning feature in a choice model. We develop two choice models, both using stated preference data. The paper extends the received contribution in that we allow for the endogenous variable to have an impact on the attributes through a two stage method, called the Multiple Indicator Solution, originally implemented in a different context and for a single (quality) attribute, in which stage two is the popular control function method. In the first stage, the entire utility expression associated with all observed attributes is conditioned on the prior experience with an alternative. Hence, we are capturing possible correlates associated with each and every attribute and not just one selected attribute. We find evidence of potential endogeneity. The purging exercise however, results in both statistical similarities and differences in time and cost choice elasticities and mean estimates of the value of travel time savings. We are able to identify a very practical method to correct for possible endogeneity under experience conditioning that will encourage researchers and practitioners to use such an approach in more advanced non-linear discrete choice models as a matter of routine.

     

Modeling discrete choice behavior using concepts from fuzzy set theory,approximate reasoning and neural networks

Models of discrete choice analysis are usually based on the random utility framework. They assume that decision makers make decisions that maximize their utility. Alternative formulations of the problem have also been proposed in the literature. These approaches model the decision makers’ perceptions of the attributes of the various alternatives using fuzzy sets and linguistic variables, and the decision process itself, using concepts from approximate reasoning and fuzzy control. The underlying assumption is that decision makers use a few simple rules that relate their vague perceptions of the various attributes to their preferences towards the available alternatives. The paper extends this approach by incorporating rule weights, which capture the importance of a particular rule in the decision process. It also presents an approach for calibrating the weights using concepts from neural networks. A case study, involving mode choice, is used to demonstrate the potential of the approach and compare it to alternative formulations and methodologies.     

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.