Sampling of alternatives for route choice modeling

This paper presents a new paradigm for choice set generation in the context of route choice model estimation. We assume that the choice sets contain all paths connecting each origin–destination pair. Although this is behaviorally questionable, we make this assumption in order to avoid bias in the econometric model. These sets are in general impossible to generate explicitly. Therefore, we propose an importance sampling approach to generate subsets of paths suitable for model estimation. Using only a subset of alternatives requires the path utilities to be corrected according to the sampling protocol in order to obtain unbiased parameter estimates. We derive such a sampling correction for the proposed algorithm.Estimating models based on samples of alternatives is straightforward for some types of models, in particular the multinomial logit (MNL) model. In order to apply MNL for route choice, the utilities should also be corrected to account for the correlation using, for instance, a path size (PS) formulation. We argue that the PS attribute should be computed based on the full choice set. Again, this is not feasible in general, and we propose a new version of the PS attribute derived from the sampling protocol, called Expanded PS.Numerical results based on synthetic data show that models including a sampling correction are remarkably better than the ones that do not. Moreover, the Expanded PS shows good results and outperforms models with the original PS formulation.     

Strategic sampling for large choice sets in estimation and application

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

Implications of Thresholds in Discrete Choice Modelling

Abstract

Individual choices are affected by complex factors and the challenge consists of how to incorporate these factors in order to improve the realism of the modelling work. The presence of limits, cut‐offs or thresholds in the perception and appraisal of both attributes and alternatives is part of the complexity inherent to choice‐making behaviour. The paper considers the existence of thresholds in three contexts: inertia (habit or reluctance to change), minimum perceptible changes in attribute values, and as a mechanism for accepting or rejecting alternatives. It discusses the more relevant approaches in modelling these types of thresholds and analyses their implications in model estimation and forecasting using both synthetic and real databanks. It is clear from the analysis that if thresholds exist but are not considered, the estimated models will be biased and may produce significant errors in prediction. Fortunately, there are practical methods to attack this problem and some are demonstrated.     

Does the choice model method and/or the data matter?

The opportunity to have seven data sets associated with a stated choice experiment that are very similar in content and design is rare, and provides an opportunity to look in detail at the empirical evidence within and between each data set in the context of a range of discrete choice estimation methods, from multinomial logit to latent class to scale multinomial logit to mixed logit, and the most general model, generalized mixed multinomial logit that accounts for preference and scale heterogeneity. Given the problems associated with data from different countries and time periods, we estimate separate models for each data set, obtaining values of travel time savings that are then updated post estimation to a common dollar for comparative purposes. We also pooled all data sets for a scaled MNL model, treating each data set as a set of three separate utility expressions, but linked to the other data sets through scale heterogeneity. This is not behaviourally appropriate with MNL, latent class or mixed logit. The main question investigated is whether there exists greater synergy in the willingness to pay evidence within model form across data sets compared to across model forms within data sets. The evidence suggests that there is a relatively greater convergence of evidence across the choice models, with the exception of generalized mixed logit, after controlling for data set differences; and there is strong evidence to suggest that differences between data sets do matter.     

Environmental repercussions of parking demand management strategies using a constrained logit model

In order to select the correct mobility strategy, individuals’ choice behavior must be studied, and their reactions in response to strategies must be predicted. Upon exploring aspects subject to constraints, our results included walking distance, parking rates, search time and parking availability. We have identified scenarios in which simulation outputs of environmental parking mobility strategies differ significantly when using the Constrained Multi-Nominal Logit (CMNL) when compared with the widely used Multi-Nominal Logit (MNL). With the CMNL model growing in popularity, it is worth considering environmental mobility strategy repercussions in this context with the incorporation of relevant constraints.     

Dominance among alternatives in random utility models

In many discrete choice contexts the actual choice set, including the alternatives effectively perceived and considered by the decision maker, may substantially differ from the universal choice set, including all available alternatives: one of the most relevant examples within transport demand simulation is probably the choice of destination, wherein the universal choice set normally includes hundreds of traffic zones. In these cases, proper simulation of the choice set is crucial for correct simulation of the choice context.In this regard, our paper has two main objectives. The first is to give a general contribution to choice set modelling by extending and applying the concept of dominance among alternatives to the framework of random utility theory. The main result is the definition of a methodology for the generation of new dominance attributes, which can be used in choice set modelling. The second aim is to make a specific contribution to destination choice modelling: dominance attributes are defined from the above methodology and introduced into this choice context, and new spatial variables reproducing better knowledge of zones with a privileged spatial position are also proposed. Methodology and attributes are tested both on synthetic and on real data.     

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.     

Experimental design influences on stated choice outputs: An empirical study in air travel choice

Discrete choice experiments are conducted in the transport field to obtain data for investigating travel behaviour and derived measures such as the value of travel time savings. The multinomial logit (MNL) and other more advanced discrete choice models (e.g., the mixed MNL model) have often been estimated on data from stated choice experiments and applied for planning and policy purposes. Determining efficient underlying experimental designs for these studies has become an increasingly important stream of research, in which the objective is to generate stated choice tasks that maximize the collected information, yielding more reliable parameter estimates. These theoretical advances have not been rigorously tested in practice, such that claims on whether the theoretical efficiency gains translate into practice cannot be made. Using an extensive empirical study of air travel choice behaviour, this paper presents for the first time results of different stated choice experimental design approaches, in which respective estimation results are compared. We show that D-efficient designs keep their promise in lowering standard errors in estimating, thereby requiring smaller sample sizes, ceteris paribus, compared to a more traditional orthogonal design. The parameter estimates found using an orthogonal design or an efficient design turn out to be statistically different in several cases, mainly attributed to more or less dominant alternatives existing in the orthogonal design. Furthermore, we found that small designs with a limited number of choice tasks performs just as good (or even better) than a large design. Finally, we show that theoretically predicted sample sizes using the so-called S-estimates provide a good lower bound. This paper will enable practitioners in better understanding the potential benefits of efficient designs, and enables policy makers to make decisions based on more reliable parameter estimates.     

Identifying a behaviourally relevant choice set from stated choice data

Stated choice experiments are designed optimally in a statistical sense but not necessarily in a behavioural choice making sense. Statistical designs, and consequently model estimation, assume that the set of alternatives offered in the experiment are processed by respondents with a specific processing strategy. Much has been studied about attribute processing using discrete choice methods in travel choice studies, but this paper focuses more broadly on processing of alternatives in the choice set offered in the experiment. This paper is motivated by the primary idea that the distribution of predicted choice probabilities associated with a set of alternatives defining a given choice set might provide strong evidence on the strategies that agents appear to use when choosing a preferred alternative. In an empirical setting of a choice set of size three, four model specifications are considered including a model for the selection of the best alternative in the full choice set and three variants of a best–worst regime. Using state choice data on road pricing reform, the empirical analysis examines which model specification delivers the most accurate prediction of the chosen alternative. The results suggest which alternatives really matter in choice making and hence the alternatives that might be included in a choice set for model specification.     

Modeling park 'n ride and kiss 'n ride as submodal choices

The logit modeling methodology is applied to include transit access mode choices in conjunction with the automobile vs. transit travel choice decision. The practical problems that arise when the choice set expands beyond two alternatives are identified and addressed. In particular, the complexities that must be resolved in order to use ULOGIT or a similar program include the definition of independent choices (the Independence of Irrelevant Alternatives Property (IIA)), a sequential binary or multinomial logit model (MNL) structure, specification and testing of variables, and the potential for transferring the model to new areas for transportation planning purposes. It was found that the available options cannot be reduced to a single modeling strategy. However, the analysis showed certain concepts which can reduce the uncertainties in related applications of the logit model. It was determined that as many independent choices as possible should be hypothesized and tested for inclusion in the model, but the IIA must be carefully considered because it limits the number of choices that can be represented. Although binary calibration techniques are conceptually appealing, the large number of calibrations for studies involving more than three alternatives suggests that the MNL approach is most practical. Application of the MNL model requires that not only must variables be selected that best explain choice, but they must also be placed in the disutility function of the specific mode or modes to which they are most unique. Finally, it was shown that if choice sets and homogeneous market segments are properly defined, the models can be transferred among different urban areas even though the urban areas exhibit different aggregate characteristics. All observations lead to the general conclusion that the logit modeling methodology can now best be advanced with implementation experience.     

Constrained nested logit model: formulation and estimation

A model of traveller behaviour should recognise the exogenous and endogenous factors that limit the choice set of users. These factors impose constraints on the decision maker, which constraints may be considered implicitly, as soft constraints imposing thresholds on the perception of changes in attribute values, or explicitly as hard constraints. The purpose of this paper is twofold: (1) To present a constrained nested logit-type choice model to cope with hard constraints. This model is derived from the entropy-maximizing framework. (2) To describe a general framework to deal with (dynamic) non-linear utilities. This approach is based on Reproducing Kernel Hilbert Spaces. The resulting model allows the dynamic aspect and the constraints on the choice process to be represented simultaneously. A novel estimation procedure is introduced in which the utilities are viewed as the parameters of the proposed model instead of attribute weights as in the classical linear models. A discussion on over-specification of the proposed model is presented. This model is applied to a synthetic test problem and to a railway service choice problem in which users choose a service depending on the timetable, ticket price, travel time and seat availability (which imposes capacity constraints). Results show (1) the relevance of incorporating constraints into the choice models, (2) that the constrained models appear to be a better fit than the counterpart unconstrained choice models; and (3) the viability of the approach, in a real case study of railway services on the Madrid–Seville corridor (Spain).     

Daily activity pattern recognition by using support vector machines with multiple classes

The focus of this paper is to learn the daily activity engagement patterns of travelers using Support Vector Machines (SVMs), a modeling approach that is widely used in Artificial intelligence and Machine Learning. It is postulated that an individual’s choice of activities depends not only on socio-demographic characteristics but also on previous activities of individual on the same day. In the paper, Markov Chain models are used to study the sequential choice of activities. The dependencies among activity type, activity sequence and socio-demographic data are captured by employing hidden Markov models. In order to learn model parameters, we use sequential multinomial logit models (MNL) and multiclass Support Vector Machines (K-SVM) with two different dependency structures. In the first dependency structure, it is assumed that type of activity at time ‘t’ depends on the last previous activity and socio-demographic data, whereas in the second structure we assume that activity selection at time ‘t’ depends on all of the individual’s previous activity types on the same day and socio-demographic characteristics. The models are applied to data drawn from a set of California households and a comparison of the accuracy of estimation of activity types and their sequence in the agenda, indicates the superiority of K-SVM models over MNL. Additionally, we show that accuracy in estimating activity patterns increases using different sets of explanatory variables or tuning parameters of the kernel function in K-SVM.     

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.     

An empirical comparison of travel choice models that capture preferences for compromise alternatives

Compromise alternatives have an intermediate performance on each or most attributes rather than having a poor performance on some attributes and a strong performance on others. The relative popularity of compromise alternatives among decision-makers has been convincingly established in a wide range of decision contexts, while being largely ignored in travel behavior research. We discuss three (travel) choice models that capture a potential preference for compromise alternatives. One approach, which is introduced in this paper, involves the construction of a so-called compromise variable which indicates to what extent (i.e., on how many attributes) a given alternative is a compromise alternative in its choice set. Another approach consists of the recently introduced random regret-model form, where the popularity of compromise alternatives emerges endogenously from the regret minimization-based decision rule. A third approach consists of the contextual concavity model, which is known for favoring compromise alternatives by means of a locally concave utility function. Estimation results on a stated route choice dataset show that, in terms of model fit and predictive ability, the contextual concavity and random regret models appear to perform better than the model that contains an added compromise variable.     

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.

     

Covariance, identification, and finite-sample performance of the MSL and Bayes estimators of a logit model with latent attributes

In this paper we discuss the specification, covariance structure, estimation, identification, and point-estimate analysis of a logit model with endogenous latent attributes that avoids problems of inconsistency. We show first that the total error term induced by the stochastic latent attributes is heteroskedastic and nonindependent. In addition, we show that the exact identification conditions support the two-stage analysis found in much current work. Second, we set up a Monte Carlo experiment where we compare the finite-sample performance of the point estimates of two alternative methods of estimation, namely frequentist full information maximum simulated likelihood and Bayesian Metropolis Hastings-within-Gibbs sampling. The Monte Carlo study represents a virtual case of travel mode choice. Even though the two estimation methods we analyze are based on different philosophies, both the frequentist and Bayesian methods provide estimators that are asymptotically equivalent. Our results show that both estimators are feasible and offer comparable results with a large enough sample size. However, the Bayesian point estimates outperform maximum likelihood in terms of accuracy, statistical significance, and efficiency when the sample size is low.     

A behavioral housing search model: Two-stage hazard-based and multinomial logit approach to choice-set formation and location selection

Residential location search has become an important topic to both practitioners and researchers as more detailed and disaggregate land-use and transportation demand models are developed which require information on individual household location decisions. The housing search process starts with an alternative formation and screening stage. At this level households evaluate all potential alternatives based on their lifestyle, preferences, and utilities to form a manageable choice set with a limited number of plausible alternatives. Then the final residential location is selected among these alternatives. This two-stage decision making process can be used for both aggregate zone-level selection as well as searching disaggregate parcel or building-based housing markets for potential dwellings. In this paper a zonal level household housing search model is developed. Initially, a household specific choice set is drawn from the entire possible alternatives in the area based on the average household work distance to each alternative. Following the choice set formation step, a discrete choice model is utilized for modeling the final residential zone selection of the household. A hazard-based model is used for the choice set formation module while the final choice selection is modeled using a multinomial logit formulation with a deterministic sample correction factor. The approach presented in the paper provides a remedy for the large choice set problem typically faced in housing search models.     

The joint estimation of respondent-reported certainty and acceptability with choice

In the stated choice literature, increasing attention has been paid to methods that seek to close the gap between the choices from these experiments and the choices experienced in the real world. Attempts to produce model estimates that are truer to real market behaviours are especially important for transportation, where many important policy decisions rely on such experiments. A recent approach that has emerged makes use of a certainty index whereby respondents report how certain they are about each choice they make. Additional literature also posits that when making decisions, people first identify an acceptable set of alternatives (alternative acceptability) such that a consideration set if formed and it is from this reduced set that the ultimate choice is made. This paper presents two models that jointly estimates choice and choice certainty and choice and alternative acceptability. This joint estimation allows the modeller to overcome potential endogeneity that may exist between these responses. In comparing choices of differing certainty, surprisingly little difference in marginal sensitivities are found. This is not the case in the alternative acceptability models however. An important finding of this research is that what could be interpreted as preference heterogeneity may in fact be more closely linked to scale. The ramifications of these results on future research are discussed.     

Implicit choice set generation in discrete choice models: Application to household auto ownership decisions

Latent choice set models that account for probabilistic consideration of choice alternatives during decision making have long existed. The Manski model that assumes a two-stage representation of decision making has served as the standard workhorse model for discrete choice modeling with latent choice sets. However, estimation of the Manski model is not always feasible because evaluation of the likelihood function in the Manski model requires enumeration of all possible choice sets leading to explosion for moderate and large choice sets. In this study, we propose a new group of implicit choice set generation models that can approximate the Manski model while retaining linear complexity with respect to the choice set size. We examined the performance of the models proposed in this study using synthetic data. The simulation results indicate that the approximations proposed in this study perform considerably well in terms of replicating the Manski model parameters. We subsequently used these implicit choice set models to understand latent choice set considerations in household auto ownership decisions of resident population in the Southern California region. The empirical results confirm our hypothesis that certain segments of households may only consider a subset of auto ownership levels while making decisions regarding the number of cars to own. The results not only underscore the importance of using latent choice models for modeling household auto ownership decisions but also demonstrate the applicability of the approximations proposed in this study to estimate these latent choice set models.     

A non-compensatory model of transportation behavior based on sequential consideration of attributes

The proposed model of travel choice behavior is based upon an assumption that individuals compare their choice alternatives on a series of attributes ordered in terms of importance; they eliminate from consideration those alternatives which do not meet their expectation on one or more of the characteristics. The process is repeated with adjusted levels of expectation until only one alternative remains. The model thus incorporates a number of psychological decision axioms which have seldom been applied in models aimed at providing transportation planners with useful information from consumer survey data.Estimates of parameters defining distributions of expectation levels in a population of travelers are generated using a nonlinear optimization technique. The technique is demonstrated to provide estimates which replicate well the choices of travelers in two different contexts: choice of hypothetical concepts of small urban vehicles and choice of destination for shopping trips within an urban area.