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.     

Effects of task complexity and time pressure on activity-travel choices: heteroscedastic logit model and activity-travel simulator experiment

This paper derives, estimates and applies a discrete choice model of activity-travel behaviour that accommodates potential effects of task complexity and time pressure on decision-making. To the best of our knowledge, this is the first time that both factors (task complexity and time pressure) are jointly captured in a discrete choice model. More specifically, our heteroscedastic logit model captures potential impacts of task complexity and time pressure through the scale of the utility of activity-travel options. We collect data using a novel activity-travel simulator experiment that has been specifically designed with the aim of testing our model. Results are in line with expectations, in that higher levels of task complexity and time pressure are found to result in a smaller scale of utility. In other words, higher levels of task complexity and time pressure lead to more random choice behaviour and as a consequence to less pronounced differences in choice probabilities between alternatives. An empirical illustration suggests that choice probability-differences between models that do and those that do not capture these effects, can be very substantial; this in turn suggests that failing to capture the effects of task complexity and time pressure in discrete choice models of activity travel decision-making might lead to serious bias in forecasts of the effects of transport policies.     

Stated choices and benefit estimates in the context of traffic calming schemes: Utility maximization,regret minimization,or both?

This paper proposes a discrete mixture model which assigns individuals, up to a probability, to either a class of random utility (RU) maximizers or a class of random regret (RR) minimizers, on the basis of their sequence of observed choices. Our proposed model advances the state of the art of RU–RR mixture models by (i) adding and simultaneously estimating a membership model which predicts the probability of belonging to a RU or RR class; (ii) adding a layer of random taste heterogeneity within each behavioural class; and (iii) deriving a welfare measure associated with the RU–RR mixture model and consistent with referendum-voting, which is the adequate mechanism of provision for such local public goods. The context of our empirical application is a stated choice experiment concerning traffic calming schemes. We find that the random parameter RU–RR mixture model not only outperforms its fixed coefficient counterpart in terms of fit—as expected—but also in terms of plausibility of membership determinants of behavioural class. In line with psychological theories of regret, we find that, compared to respondents who are familiar with the choice context (i.e. the traffic calming scheme), unfamiliar respondents are more likely to be regret minimizers than utility maximizers.     

Random regret minimization or random utility maximization: an exploratory analysis in the context of automobile fuel choice

Interest in alternative behavioural paradigms to random utility maximization (RUM) has existed ever since the dominance of the RUM formulation. One alternative is known as random regret minimization (RRM), which suggests that when choosing between alternatives, decision makers aim to minimize anticipated regret. Although the idea of regret is not new, its incorporation into the same discrete choice framework of RUM is very recent. This paper is the first to apply the RRM‐model framework to model choice amongst durable goods. Specifically, we estimate and compare the RRM and RUM models in a stated choice context of choosing amongst vehicles fuelled with petrol, diesel and hybrid (associated with specific levels of fuel efficiency and engine capacity). The RRM model is found to achieve a marginally better fit (using a non‐nested test of differences) than its equally parsimonious RUM counterpart. As a second contribution, we derive a formulation for regret‐based elasticities and compare utility‐based and regret‐based elasticities in the context of stated vehicle type choices. We find that in the context of our choice data, mean estimates of elasticities are different for many of the attributes and alternatives. Copyright © 2011 John Wiley & Sons, Ltd.     

The dogit model

This paper presents the dogit model. That model is flexible enough to permit the choice among specific pairs of alternatives to be consistent with the independence from irrelevant alternatives axiom, as in a logit model, but it simultaneously allows the choice among other pairs not to be. Dogit parameters add an “income effect” to the “substitution effect” already built into the logit model; alternatively, they allow for the joint presence of compulsive and discretionary elements in consumer behavior, or for the identification of captive markets. Eventual estimation of the values of the parameters of the dogit model appears simpler than for the probit model.     

On the flexibility of using marginal distribution choice models in traffic equilibrium

Traffic equilibrium models are fundamental to the analysis of transportation systems. The stochastic user equilibrium (SUE) model which relaxes the perfect information assumption of the deterministic user equilibrium is one such model. The aim of this paper is to develop a new user equilibrium model, namely the MDM-SUE model, that uses the marginal distribution model (MDM) as the underlying route choice model. In this choice model, the marginal distributions of the path utilities are specified but the joint distribution is not. By focusing on the joint distribution that maximizes expected utility, we show that MDM-SUE exists and is unique under mild assumptions on the marginal distributions. We develop a convex optimization formulation for the MDM-SUE. For specific choices of marginal distributions, the MDM-SUE model recreates the optimization formulation of logit SUE and weibit SUE. Moreover, the model is flexible since it can capture perception variance scaling at the route level and allows for modeling different user preferences by allowing for skewed distributions and heavy tailed distributions. The model can also be generalized to incorporate bounded support distributions and discrete distributions which allows to distinguish between used and unused routes within the SUE framework. We adapt the method of successive averages to develop an efficient approach to compute MDM-SUE traffic flows. In our numerical experiments, we test the ability of MDM-SUE to relax the assumption that the error terms are independently and identically distributed random variables as in the logit models and study the additional modeling flexibility that MDM-SUE provides on small-sized networks as well as on the large network of the city of Winnipeg. The results indicate that the model provides both modeling flexibility and computational tractability in traffic equilibrium.     

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.     

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.     

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.     

Expanding the applicability of random regret minimization for route choice analysis

The discrete choice paradigm of random regret minimization (RRM) has been recently proposed in several choice contexts. In the route choice context, the paradigm has been used to model the choice among three routes and to formulate regret-based stochastic user equilibrium. However, in the same context the RRM literature has not confronted three major challenges: (i) accounting for similarities across alternative routes, (ii) analyzing choice set composition effects on choice probabilities, and (iii) comparing RRM-based models with advanced RUM-based models. This paper looks into RRM-based route choice models from these three perspectives by (i) proposing utility-based and regret-based correction terms to account for similarities across alternatives, (ii) analyzing the variation of choice set probabilities with the choice set composition, and (iii) comparing RRM-based route choice models with C-Logit, Path Size Logit and Paired Combinatorial Logit. The results illustrate the definition of the correction terms within the regret function, the effect of the choice set specificity of RRM-based route choice models, and the positive performance of these models when compared to advanced RUM-based models.     

Modelling parking choices considering user heterogeneity

We examine car driver’s behaviour when choosing a parking place; the alternatives available are free on-street parking, paid on-street parking and parking in an underground multi-storey car park. A mixed logit model, allowing for correlation between random taste parameters and estimated using stated choice data, is used to infer values of time, both when looking for a parking space and for accessing the final destination. Apart from the cost of parking, we found that vehicle age was a key variable when choosing where to park in Spain. We also found that the perception of the parking charge was fairly heterogeneous, depending both on the drivers’ income levels and whether or not they were local residents. Our results can be generalised for personalised policy making related with parking demand management.     

Price-based regulation of oligopolistic markets under discrete choice models of demand

We propose a framework to find optimal price-based policies to regulate markets characterized by oligopolistic competition and in which consumers make a discrete choice among a finite set of alternatives. The framework accommodates general discrete choice models available in the literature in order to capture heterogeneous consumer behavior. In our work, consumers are utility maximizers and are modeled according to random utility theory. Suppliers are modeled as profit maximizers, according to the traditional microeconomic treatment. Market competition is modeled as a non-cooperative game, for which an approximate equilibrium solution is sought. Finally, the regulator can affect the behavior of all other agents by giving subsidies or imposing taxes to consumers. In transport markets, economic instruments might target specific alternatives, to reduce externalities such as congestion or emissions, or specific segments of the population, to achieve social welfare objectives. In public policy, different agents have different individual or social objectives, possibly conflicting, which must be taken into account within a social welfare function. We present a mixed integer optimization model to find optimal policies subject to supplier profit maximization and consumer utility maximization constraints. Then, we propose a model-based heuristic approach based on the fixed-point iteration algorithm that finds an approximate equilibrium solution for the market. Numerical experiments on an intercity travel case study show how the regulator can optimize its decisions under different scenarios.

     

Stochastic frontier estimation of budgets for Kuhn–Tucker demand systems: Application to activity time-use analysis

We propose a stochastic frontier approach to estimate budgets for the multiple discrete–continuous extreme value (MDCEV) model. The approach is useful when the underlying time and/or money budgets driving a choice situation are unobserved, but the expenditures on the choice alternatives of interest are observed. Several MDCEV applications hitherto used the observed total expenditure on the choice alternatives as the budget to model expenditure allocation among choice alternatives. This does not allow for increases or decreases in the total expenditure due to changes in choice alternative-specific attributes, but only allows a reallocation of the observed total expenditure among different alternatives. The stochastic frontier approach helps address this issue by invoking the notion that consumers operate under latent budgets that can be conceived (and modeled) as the maximum possible expenditure they are willing to incur. The proposed method is applied to analyze the daily out-of-home activity participation and time-use patterns in a survey sample of non-working adults in Florida. First, a stochastic frontier regression is performed on the observed out-of-home activity time expenditure (OH-ATE) to estimate the unobserved out-of-home activity time frontier (OH-ATF). The estimated frontier is interpreted as a subjective limit or maximum possible time individuals can allocate to out-of-home activities and used as the time budget governing out-of-home time-use choices in an MDCEV model. The efficacy of this approach is compared with other approaches for estimating time budgets for the MDCEV model, including: (a) a log-linear regression on the total observed expenditure for out-of-home activities and (b) arbitrarily assumed, constant time budgets for all individuals in the sample. A comparison of predictive accuracy in time-use patterns suggests that the stochastic frontier and log-linear regression approaches perform better than arbitrary assumptions on time budgets. Between the stochastic frontier and log-linear regression approaches, the former results in slightly better predictions of activity participation rates while the latter results in slightly better predictions of activity durations. A comparison of policy simulations demonstrates that the stochastic frontier approach allows for the total out-of-home activity time expenditure to either expand or shrink due to changes in alternative-specific attributes. The log-linear regression approach allows for changes in total time expenditure due to changes in decision-maker attributes, but not due to changes in alternative-specific attributes.     

Accounting for systematic heterogeneity across car commuters in response to multiple TDM policies: case study of Tehran

Modeling commuters’ choice behavior in response to transportation demand management (TDM) helps in predicting the consequences of TDM policies. Although research looking at choice behavior has evolved to investigate preference heterogeneity in response to factors influencing mode choice, as far as we know, no study has considered taste variation across commuters in response to multiple TDM policies. This paper investigates the presence of systematic preference heterogeneity across commuters, in response to the TDM policies that can be explained by their socio-economic or commuting-related characteristics. Analysis is based on results of a stated preference survey developed using a Design of Experiments approach. Five policies were assessed in order to study the impact they had on how commuters chose their mode of transportation. These include increasing parking cost, increasing fuel cost, implementing cordon pricing, reducing transit time and improving access to transit facilities. For the sake of assessing both systematic and random preference heterogeneity across car commuters, a form of the Mixed Multinomial Logit (MMNL) model that identifies sources of heterogeneity and consequently makes the choice models less restrictive in considering both systematic and random preference variation across individuals was developed. The sample includes 366 individuals who regularly commute to their workplace in the city center of Tehran, Iran. The likelihood function value of this model shows a significant improvement compared to the base MNL model, using the same variables. The MMNL model shows that taste variation across the studied commuters results in differences in influences estimated for three policies: increasing parking cost, reducing transit time and improving access to transit. The analysis examines several distributions for random parameters to test the impacts of restricting distributions to allow for only normality. The results confirm the potential to improve model fit with alternative distributions.     

A joint model for vehicle type and fuel type choice: evidence from a cross-nested logit study

In the face of growing concerns about greenhouse gas emissions, there is increasing interest in forecasting the likely demand for alternative fuel vehicles. This paper presents an analysis carried out on stated preference survey data on California consumer responses to a joint vehicle type choice and fuel type choice experiment. Our study recognises the fact that this choice process potentially involves high correlations that an analyst may not be able to adequately represent in the modelled utility components. We further hypothesise that a cross-nested logit structure can capture more of the correlation patterns than the standard nested logit model structure in such a multi-dimensional choice process. Our empirical analysis and a brief forecasting exercise produce evidence to support these assertions. The implications of these findings extend beyond the context of the demand for alternative fuel vehicles to the analysis of multi-dimensional choice processes in general. Finally, an extension verifies that further gains can be made by using mixed GEV structures, allowing for random heterogeneity in addition to the flexible correlation structures.     

Random utility models with implicit availability/perception of choice alternatives for the simulation of travel demand

Random utility models are undoubtedly the most used models for the simulation of transport demand. These models simulate the choice of a decision-maker among a set of feasible alternatives and their operational use requires that the analyst is able to correctly specify this choice-set for each individual.Some early applications basically ignored this problem by assuming that all decision-makers chose from the same pre-specified choice-set. This assumption may be unrealistic in many practical cases and cause significant misspecification problems (P. Stopher, Transportation Journal of ASCE 106 (1980) 427; H. Williams, J. Ortuzar, Transportation Research B 16 (1982) 167).The problem of choice-set simulation has been dealt within the literature following two basically different approaches:

• •simulating the perception/availability of an alternative implicitly in the choice model,
• •simulating the choice-set generation explicitly in a separate model.

The implicit approach is more convenient from an operational point of view, while the explicit one is more appealing from a theoretical point of view.In this paper, a different approach to the modeling of availability/perception of alternatives in the context of random utility model is proposed. This approach is based on the concept of intermediate degrees of availability/perception of each alternative simulated through a model (or “inclusion function”) which in turn is introduced in the systematic utility of standard random utility models.This model, named implicit availability/perception (IAP), may be differently specified depending on assumptions made on the joint distribution of random residuals and the way in which the average degree of availability/perception is modeled.In this paper, a possible specification of the IAP model, based on the assumption of random residual distributed as i.i. Gumbel and with the average degree of availability/perception modeled as a binomial logit, is proposed.The paper also proposes ML estimation models in two cases: in the first, only information on alternatives choices is available, while in the second, this information is complemented with others on variables related to a latent (i.e., non-observable) alternatives availability/perception degree (e.g., information on car availability of decision-maker i used as an indirect measurement of the unknown and non-observable availability/perception degree of alternative car for decision-maker i in a modal split).The proposed specification is tested on mode choice data; the calibration results are compared with those of a similar logit specification with encouraging results in terms of goodness of fit.     

A methodological framework for the study of residential location and travel-to-work mode choice under central and suburban employment destination patterns

The aim of this paper is to contribute to the methodological questions that arise from the study of the simultaneous choice of residential location and travel-to-work mode under central and non-central or suburban employment patterns. Geographic information system (GIS) visualisations and network analysis are used to generate a choice set based on the definition of spatially aggregated alternatives. Discrete choice models specified as cross-nested logit (CNL) are estimated for each of the two different types of employment patterns and direct and cross elasticities are presented. The analysis is carried out for the Greater Dublin Area, a metropolitan region that is a recent example of rapid employment suburbanisation and residential sprawl in a European context. A simulation exercise, tracing the extent of mode switching and location switching behaviour is undertaken using the framework developed.     

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.     

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.