Random covariance heterogeneity in discrete choice models

In this paper, we extend the standard discrete choice modelling framework by allowing for random variations in the substitution patterns between alternatives across respondents, leading to increased model flexibility. The paper shows how such a Mixed Covariance model can be specified either with purely random variation or with a mixture of random and deterministic variation. Additionally, the model can be based on an underlying GEV or ECL structure. Finally, the model can be specified as a continuous mixture or as a discrete mixture. An application on Stated Preference data for the choice of departure time and travel mode shows that important gains in model performance can be obtained by allowing for random covariance heterogeneity. Furthermore, the approach leads to significant differences in the implied willingness to pay measures, and the substitution patterns between alternatives.     

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.     

Identifying variations and co-variations in discrete choice models

This study introduces an extended version of a standard multilevel cross-classified logit model which takes co-variations into account, i.e., variations jointly caused by two or more unobserved factors. Whilst focusing on mode choice behavior, this study deals with four different types of variation: spatial variations, inter-individual variations, intra-individual variations and co-variations between inter-individual and spatial variations. Such co-variations represent individual-specific spatial effects, reflecting different responses to the same space among individuals, which may for example be due to differences in their spatial perceptions. In our empirical analysis, we use data from Mobidrive (a continuous six-week travel survey) to clarify the existence of co-variation effects by comparing two models with and without co-variation terms. The results of this analysis indicate that co-variations certainly exist, especially for utility differences in bicycle and public transport use in comparison with car use. We then sequentially introduce four further sets of explanatory variables, examine the sources of behavioral variations and determine what types of influential factors are dominant in mode choice behavior.     

A flexible model structure approach for discrete choice models

Multi-dimensional discrete choice problems are usually estimated by assuming a single-choice hierarchical order for the entire study population or for pre-defined segments representing the behavior of an “average” person and by indicating either limited differences or a variety in choices among the study population. This study develops an integral methodological framework, termed the flexible model structure (FMS), which enhances the application of the discrete choice model by developing an optimization algorithm that segment given data and searches for the best model structure for each segment simultaneously. The approach is demonstrated here through three models that conceptualize the multi-dimensional discrete choice problem. The first two are Nested Logit models with a two-choice dimension of destination and mode; they represent the estimation of a fixed-structure model using pre-segmented data as is mostly common in multi-dimensional discrete choice model implementation. The third model, the FMS, includes a fuzzy segmentation method with weighted variables, as well as a combination of more than one model structure estimated simultaneously. The FMS model significantly improves estimation results, using fewer variables than do segmented NL models, thus supporting the hypothesis that different model structures may best describe the behavior of different groups of people in multi-dimensional choice models. The implementation of FMS involves presenting the travel behavior of an individual as a mix of travel behaviors represented by a number of segments. The choice model for each segment comprises a combination of different choice model structures. The FMS model thus breaks the consensus that an individual belongs to only one segment and that a segment can take only one structure.     

Measuring uncertainty in discrete choice travel demand forecasting models

In transportation projects, uncertainty related to the difference between forecast and actual demand is of major interest for the decision-maker, as it can have a substantial influence on the viability of a project. This paper identifies and quantifies discrete choice model uncertainty, which is present in the model parameters and attributes, and determines its impact on risk taking for decision-making applied to a case study of the High-Speed Rail project in Portugal. The methodology includes bootstrapping for the parameter variation, a postulated triangular distribution for the mode-specific input and a probabilistic graphical model for the socio-economic input variation. In comparison to point estimates, the findings for mode shift results in a wider swing in the system, which constitutes valuable information for decision-makers. The methodology, findings and conclusions presented in this study can be generalized to projects involving similar models.     

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.

     

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.     

Testing probabilistic discrete choice models of travel demand by comparing predicted and observed aggregate choice shares

Probabilistic discrete choice models of travel demand often are tested for the presence of specification errors by comparing the models' predictions of aggregate choice shares in population strata with observed shares. A model is rejected as misspecified if the differences between its predictions and the observations are judged too large. This judgement usually is made on intuitive grounds without use of formal statistical methods and, therefore includes no systematic method for distinguishing the effects of specification errors on differences between predictions and observations from those of random sampling errors. This paper represents formal statistical tests for comparing predicted and observed aggregate chioce shares in population strata and reports the results of an investigation of the power of the tests. The test statistics are asymptotically χ² disturbed when the model being tested is correctly specified. The results of the power investigation suggests that greater power is obtained (i.e. there is ability to detect misspecified models) when all of the available data are used for both parameter estimation and specification testing than when the available data are divided into separate estimation and test data sets. Specification tests based on comparisons of predicted and observed aggregate choice shares appear to have less power than do likelihood ratio and likelihood ratio index specification tests when the alternative models required by the latter tests are correctly or approximately correctly specified. However, tests based on comparisons of predicted and observed shares ca have greater power than the other tests when the alternative models are seriouslymisspecified.     

Analysis of equilibrium automobile holdings in Israel with aggregate discrete choice models

Models of household vehicle ownership decisions do not suffice as a basis for forecasting the size and composition of aggregate vehicle holdings. Forecasting applications require that such models be imbedded in systems describing the operation of the automobile market. This paper presents a new model of short run equilibrium in the automobile market. The short run is a period within which new car designs and prices are fixed but used car prices adjust competitively to market forces. The magnitude and mix of new car sales, the extent of used car scrappage and the composition of used car holdings are determined in equilibrium with used car prices. An econometric version of the market model has been estimated on Israeli data and applied to analyze the impact of vehicle tax policy on automobile holdings in Israel. The paper describes this application.     

Development of an indicator to assess the spatial fit of discrete choice models

Discrete choice models are increasingly implemented using geographical data. When this is the case, it may not be sufficient to project market shares accurately, but also to correctly replicate the spatial pattern of choices. Analysts might then be interested in assessing the results of a model’s fit relative to the spatial distribution of the observed responses. While canonical approaches exist for the exploratory spatial analysis of continuous variables, similar tools have not been widely implemented for discrete choice models, where the variable of interest is categorical. For this reason, despite recent progress with spatial models for discrete outcomes, there is still not a simple and intuitive tool to assess the quality of the spatial fit of a discrete choice model. The objective of this paper is to introduce a new indicator of spatial fit that can be applied to the results of discrete choice models. Utility of the indicator is explored by means of numerical experiments and then demonstrated by means of a case study of vehicle ownership in Montreal, Canada.     

Estimating heterogeneity of car travelers on mode shifting behavior based on discrete choice models

In order to understand the mode shift behavior of car travelers and relieve traffic congestion, a Stated Preference survey has been conducted in the city of Ji'nan in China to analyze bus choice behavior and the heterogeneity of car travelers. Several discrete choice models, including multinomial logit, mixed logit and latent class model (LCM) are developed based on these survey data. A comparative analysis indicates that the LCM has the highest precision and is more suitable to analyze the heterogeneity of car travelers. The LCM divides car travelers into three classes. Different classes have different sets of influencing factors in the model. Policy recommendations are also proposed for those classes to promote bus shift from car travelers based on the model results. Finally, sensitivity analysis on parking fees and fuel cost is carried out on the LCMs under different bus service levels. Car travelers have different sensitivities to the influencing factors. The conclusions indicate that the LCM can reflect the heterogeneity and preferences of car travelers and can be used to understand how to shift the behavior of car travelers and make more effective traffic policy.     

Exploring the feasibility of classification trees versus ordinal discrete choice models for analyzing crash severity

A cross-median crash (CMC) is one of the most severe types of crashes in which a vehicle crosses the median and sometimes collides with opposing traffic. A study of severity of CMCs in the state of Wisconsin was conducted by Lu et al. in 2010. Discrete choice models, namely ordinal logit and probit models were used to analyze factors related to the severity of CMCs. Separate models were developed for single and multi-vehicle CMCs. Although 25 different crash, roadway, and geometric variables were used, only 3 variables were found to be statistically significant which were alcohol usage, posted speed, and road conditions. The objective of this research was to explore the feasibility of GUIDE Classification Tree method to analyze the severity of CMCs to discover if any additional information could be revealed.A dataset of CMCs in the state of Wisconsin between 2001 and 2007, used in the study by Lu et al. was used to develop three different GUIDE Classification Trees. Additionally, the effects of variable types (continuous or discrete), misclassification costs, and tree pruning characteristics on models results were also explored. The results were directly compared with discrete choice models developed in the study by Lu et al. showing that the GUIDE Classification Trees revealed new variables (median width and traffic volume) that affect CMC severity and provided useful insight on the data. The results of this research suggest that the use of Classification Tree analysis should at least be considered in conjunction with regression-based crash models to better understand factors affecting crashes. Classification Tree models were able to reveal additional information about the dependent variable and offer advantages with respect to multicollinearity and variable redundancy issues.     

Fundamentals of discrete multimodal choice modelling

Abstract

In this paper an overview is given of the most relevant issues relating to the application of multimodal choice models, with particular emphasis on disaggregate modal split models. The paper considers questions of data, such as type of data, alternative sampling strategies and problems of measurement; and modelling issues, such as model specification and estimation, including a good presentation of the statistical techniques'available. The paper also addresses the aggregation problem, which lies at the heart of one of today's most hotly contested debates: whether to use aggregate or disaggregate models for policy analysis, and in which circumstances.     

Allowing for heterogeneous decision rules in discrete choice models: an approach and four case studies

The study of respondent heterogeneity is one of the main areas of research in the field of choice modelling. The general emphasis is on variations across respondents in relative taste parameters while maintaining the assumption of homogeneous utility maximising decision rules. While recent work has allowed for differences in the utility specification across respondents in the context of looking at heterogeneous information processing strategies, the underlying assumption that all respondents employ the same choice paradigm remains. This is despite evidence in the literature that different paradigms work differently well on given datasets. In this article, we argue that such differences may in fact extend to respondents within a single dataset. We accommodate these differences in a latent class model, where individual classes make use of different underlying paradigms. We present four applications using three different datasets, showing mixtures between “standard” random utility maximisation models and lexicography based models, models with multiple reference points, elimination by aspects models and random regret minimisation models. In each of the case studies, the behavioural mixing model obtains significant gains in fit over the base structure where all respondents are hypothesised to use the same rule. The findings offer important further insights into the behavioural patterns of respondents. There is also evidence that what is retrieved as taste heterogeneity in standard models may in fact be heterogeneity in decision rules.     

About attitudes and perceptions: finding the proper way to consider latent variables in discrete choice models

We provide an in-depth theoretical discussion about the differences between individual-specific latent constructs (representing attitudes, for example, but also other characteristics such as values or personality traits) and alternative-specific latent constructs (that may represent perceptions) affecting the choice-making process of individuals; we also carry out an empirical exercise to analyze their effects. This discussion is of importance, as the majority of papers considering attitudinal latent variables just take these as attributes affecting directly the utility of a certain alternative, while systematic taste variations are rarely considered and perceptions are mostly ignored. The results of our case study show that perceptions may indeed affect the decision making process and that they are able to capture a significant part of the variability that is normally explained by alternative specific constants. Furthermore, our results indicate that attitudes may be a reason for systematic taste variations, and that a proper categorization of latent variables, in accordance with underlying theory, may outperform the customary assumption of linearity.     

Generation of synthetic datasets for discrete choice analysis

Despite the widespread use of synthetic data in discrete choice analysis, little is known about how the methodology used to generate synthetic datasets influences the properties of parameter estimates and the validity of results based on these estimates. That is, there are two potential sources of biases when using synthetic discrete choice data: (1) bias due to the method used to generate the dataset; and, (2) bias due to parameter estimation. The primary objective of this study is to examine bias due to the underlying data generation method. This study compares three methods for generating synthetic datasets and uses design of experiments and analysis of variance methods to investigate the ability to recover estimates for “true” logsum parameters for nested logit models. The method that uses nested logit probabilities to generate the chosen alternative results in unbiased parameter estimates. The method that is based on Gumbel error component approximations reveals that while the error components themselves are unbiased, subtle empirical identification problems can arise when these error components are combined with synthetically generated utility functions. The method that is based on normal error component approximations reveals that all logsum coefficients are biased upwards; the bias dramatically increases for those nests that have a low choice frequency and is most pronounced for those nests with high correlations among alternatives. Based on the results of the analysis, several recommendations for the generation of synthetic datasets for discrete choice analyses are provided.     

Global versus localised attitudinal responses in discrete choice

Despite the increasing popularity of including attitudinal and perceptual indicators within discrete choice models, debate endures as to whether there exists a causative relationship between attitudes and behaviour, resulting in what has been termed the attitude behaviour gap. In attempt to understand its origins, attitudes have been categorised as global or localised according to whether or not they are related to a specific time, context and action. Under this framework, global attitudes (GA) typically result in poor predictions of specific overt behaviours, whilst attitudes toward behaviour, or localised attitudes (LA), tend to be better predictors of actual outcomes. Also, attitude strength, measured as the accessibility in memory, plays a determinant role in reducing the gap between attitudes and behaviour, with “memory-based” attitudes having a better prediction of overt behaviours than short-term attitudes constructed “on the spot”. The specific focus of the current paper is to examine the temporal stability and the nature of attitudes, being it critical to transportation planning and research considering the controversial link between attitudes and behaviour. An in depth analysis of the different types of attitudes towards satisfaction for train trips reveals that GAs and LAs provide moderately different outcomes. Also, a memory effect has been found, suggesting the connection between attitudes created on the spot and those stored in memory. Further, both GAs and LAs impact significantly on individual preferences. Finally, the omission of LAs, which are rarely employed within transport literature, may potentially lead to inconsistent estimates, as their contribution in explaining the choice will be absorbed by the error term.

     

Effectiveness of en route traffic information in developing countries using conventional discrete choice and neural‐network models

Providing commuters with traffic information or advising them of alternative routes during traffic incidents can alleviate congestion. For decades, advanced traveler information services (ATIS) have been devised and dedicated to this role. ATIS comprises a wide variety of technologies across the world, including radio traffic information (RTI) advisory service. RTI is common in both developed and developing countries. Although extensive literature and evaluation results of ATISs and RTI are available in developed countries, little attention has been devoted to that in developing countries. This work provides a modeling platform to study drivers' response to en route traffic information provided by Radio‐Payam broadcasting service in Tehran, the capital city of the developing country of Iran. The results are compared with counterpart cases in developed countries. Past studies and this study have employed conventional discrete models for drivers' response, such as ordered logit and ordered probit. This work evaluates the accuracy level of these conventional models in comparison with a developed neural‐network (NN) model, because it has been widely proven that NN models are highly precise. It has also been found that, apart from reliability, the conventional models are within an acceptable level of prediction accuracy compared with the NN models. The results show a high degree of similarities between the case of Tehran and its counterparts in the developing countries. The results also deliver some insights on how to improve or better implement the ATIS technologies. Copyright © 2012 John Wiley & Sons, Ltd.     

Specification tests for probabilistic choice models

Probabilistic choice models, such as logit and probit models, are highly sensitive to a variety of specification errors, including the use of incorrect functional forms for the systematic component of the utility function, incorrect specification of the probability distribution of the random component of the utility function, and incorrect specification of the choice set. Specification errors can cause large forecasting errors, so it is of considerable importance to have means of testing for the presence of these errors. A number of tests based on the likelihood ratio statistic have been developed. These tests and available information on their power are summarized in this paper. The likelihood ratio test can entail considerable computational diffuculty, owing to the need to evaluate the likelihood function for both the null and alternative hypotheses. Substantial gains in computational efficiency can be achieved through the use of a test that requires evaluating the likelihood function only for the null hypothesis. A Lagrangian multiplier test that has this property is described, and numerical examples of its computational properties are given.An important disadvantage of conventional specification tests is that they do not permit comparisons of models that belong to different parametric families in order to determine which model best explains the available data. Thus, these tests cannot be used to compare models whose utility functions have substantially different functional forms or models that are based on different behavioral paradigms. Several methods for dealing with this problem, including the construction of hybrid models and the Cox test of separate families of hypotheses, are described.