An analysis of airport-choice behaviour using the Mixed Multinomial Logit model

In this paper, we describe part of an ongoing study of airport choice for passengers departing from the San Francisco Bay area. The aim of the present paper is to test for the prevalence of taste heterogeneity across travellers, using the Mixed Multinomial Logit (MMNL) model. Our results indicate the presence of significant levels of heterogeneity in tastes, especially with respect to the sensitivity to access time, characterised by significant (deterministic) variation between groups of travellers (business/leisure, residents/visitors) as well as random variation within groups of travellers. Our analysis reinforces earlier findings showing that business travellers are far less sensitive to fare increases than leisure travellers, and are willing to pay a higher price for decreases in access time (and generally also increases in frequency) than is the case for leisure travellers. Finally, the results show that the random variation between business travellers in terms of sensitivity to access time is more pronounced than that between leisure travellers, as is the case for visitors when compared to residents.

Analysing air-travel choice behaviour in the Greater London area

The analysis of air-passengers’ choices of departure airport in multi-airport regions is a crucial component of transportation planning in many large metropolitan areas, and has been the topic of an increasing number of studies over recent years. In this paper, we advance the state of the art of modelling in this area of research by making use of a Cross-Nested Logit (CNL) structure that allows for the joint representation of inter-alternative correlation along the three choice dimensions of airport, airline and access-mode. The analysis uses data collected in the greater London area, which arguably has the highest levels of inter-airport competition of any multi-airport region; the authors of this paper are not aware of any previous effort to jointly analyse the choice of airport, airline and access-mode in this area. The results of the analysis reveal significant influences on passenger behaviour by access-time, access-cost, flight-frequency and flight-time. A structural comparison of the different models shows that the cross-nested structure offers significant improvements over simple Nested Logit (NL) models, which in turn outperform the Multinomial Logit (MNL) model used as the base model.

Advanced discrete choice models with applications to transport demand

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An alternative method to the scrambled Halton sequence for removing correlation between standard Halton sequences in high dimensions

Halton sequences were first introduced in the 1960s as an alternative to pseudo-random number sequences, with the aim of providing better coverage of the area of integration and negative correlation in the simulated probabilities between observations. This is needed in order to achieve variance reduction when using simulation to approximate an integral that does not have a closed-form expression. Such integrals arise in many areas of regional science, for example in the evaluation and estimation of certain types of discrete choice models. While the performance of standard Halton sequences is very good in low dimensions, problems with correlation have been observed between sequences generated from higher primes. This can cause serious problems in the estimation of models with high-dimensional integrals (e.g., models of aspects of spatial choice, such as route or location). Various methods have been proposed to deal with this; one of the most prominent solutions is the scrambled Halton sequence, which uses special predetermined permutations of the coefficients used in the construction of the standard sequence. In this paper, we conduct a detailed analysis of the ability of scrambled Halton sequences to remove the problematic correlation that exists between standard Halton sequences for high primes in the two-dimensional space. The analysis shows that although the scrambled sequences exhibit a lower degree of overall correlation than the standard sequences, for some choices of primes, correlation remains at an unacceptably high level. This paper then proposes an alternative method, based on the idea of using randomly shuffled versions of the one-dimensional standard Halton sequences in the construction of multi-dimensional sequences. We show that the new shuffled sequences produce a significantly higher reduction in correlation than the scrambled sequences, without loss of quality of coverage. Another substantial advantage of this new method is that it can, without any modifications, be used for any number of dimensions, while the use of the scrambled sequences requires the a-priori computation of a matrix of permutations, which for high dimensional problems could lead to significant runtime disadvantages. Repeated runs of the shuffling algorithm will also produce different sequences in different runs, which nevertheless maintain the same quality of one-dimensional coverage. This is not at all the case for the scrambled sequences. In view of the clear advantages in its ability to remove correlation, combined with its runtime and generalization advantages, this paper recommends that this new algorithm should be preferred to the scrambled Halton sequences when dealing with high correlation between standard Halton sequences.

Competing methods for representing random taste heterogeneity in discrete choice models

This paper reports the findings of a systematic study using Monte Carlo experiments and a real dataset aimed at comparing the performance of various ways of specifying random taste heterogeneity in a discrete choice model. Specifically, the analysis compares the performance of two recent advanced approaches against a background of four commonly used continuous distribution functions. The first of these two approaches improves on the flexibility of a base distribution by adding in a series approximation using Legendre polynomials. The second approach uses a discrete mixture of multiple continuous distributions. Both approaches allows the researcher to increase the number of parameters as desired. The paper provides a range of evidence on the ability of the various approaches to recover various distributions from data. The two advanced approaches are comparable in terms of the likelihoods achieved, but each has its own advantages and disadvantages.random taste heterogeneity; mixed logit; method of sieves; mixtures of distributions

REFERENCING, GAINS-LOSSES ASYMMETRY AND NON-LINEAR SENSITIVITIES IN COMMUTER DECISIONS: ONE SIZE DOES NOT FIT ALL!

In contrast with expected utility theory, empirical findings indicate that decisionmakers are sensitive to departures from reference points rather than states. Several tests of the reference-dependent preference framework have been carried out in experimental economics, and to a smaller extent in a choice modelling setting, to date. However, these empirical applications have generally focussed on a single behavioural phenomenon using uniform modelling approaches. This paper aims to broaden existing work by presenting a multi-attribute framework, allowing contemporarily for gain-loss asymmetry, non-linearity and testing for several possible reference points. The framework is tested in the context of commuter choices and reveals important gains in model fit and further insights into behaviour compared to standard modelling approaches, including substantial impacts on implied welfare measures.Choice modeling, discrete choice experiment, reference effects, non-linearity, gain/loss deviations, commuting

Treatment of reference alternatives in stated choice surveys for air travel choice behaviour

Stated Choice (SC) surveys are increasingly being used instead of Revealed Preference (RP) surveys for the study of air travel choice behaviour. In many cases, the choice situations presented in these SC surveys are constructed around an observed trip, where this is often included as one of the alternatives. Classically, these RP alternatives have been treated in the same way as the SC alternatives. The applications presented in this paper show that this potentially leads to biased results, and that it is important to recognise the differences in the nature of the two types of alternative. Additionally, the paper discusses issues caused by respondents who consistently prefer the RP alternative over the SC alternatives, a common phenomenon in such SC data

An analysis of parking behaviour using discrete choice models calibrated on SP datasets

Parking policy is an important component of contemporary travel demand management policies. The effectiveness of many parking policy measures depends on influencing parking type choice, so that understanding the factors affecting these choices is of considerable practical importance. Yet, academic interest in this issue has been, at best, intermittent. This paper reports the results of an analysis of parking choice behaviour, based on a stated preference (SP) dataset, collected in various city centre locations in the UK. The analysis advances the state of the art in the analysis of parking choice behaviour by using a mixed multinomial logit (MMNL) model, capable of accommodating random heterogeneity in travellers’ tastes and potential correlation structure induced by repeated observations being made of the same individuals. The results of the analysis indicate that taste heterogeneity is a major factor in parking type choice. Accommodating this heterogeneity leads to significantly different conclusions regarding the influence of substantive factors such as access, search and egress time and on the treatment of potential fines for illegal parking. It also has important effects on the implied willingness to pay for timesavings and on the distribution of this willingness in the population. Our analysis also reveals important differences in parking behaviour across different journey purposes, and the models reveal an important locational effect, in such that the results of the analysis vary substantively across the three locations used in the SP surveys. Finally, the paper also discusses a number of technical issues related to the specification of taste heterogeneity that are of wider significance in the application of the MMNL model.

Random Covariance Heterogeneity in Discrete Choice Models

The area of discrete choice modelling has developed rapidly in recent years. In particular, continuing refinements of the Generalised Extreme Value (GEV) model family have permitted the representation of increasingly complex patterns of substitution and parallel advances in estimation capability have led to the increased use of model forms requiring simulation in estimation and application. One model form especially, namely the Mixed Multinomial Logit (MMNL) model, is being used ever more widely. Aside from allowing for random variations in tastes across decision-makers in a Random Coefficients Logit (RCL) framework, this model additionally allows for the representation of inter-alternative correlation as well as heteroscedasticity in an Error Components Logit (ECL) framework, enabling the model to approximate any Random Utility model arbitrarily closely. While the various developments discussed above have led to gradual gains in modelling flexibility, little effort has gone into the development of model forms allowing for a representation of heterogeneity across respondents in the correlation structure in place between alternatives. Such correlation heterogeneity is however possibly a crucial factor in the variation of choice-making behaviour across decision-makers, given the potential presence of individual-specific terms in the unobserved part of utility of multiple alternatives. To the authors' knowledge, there has so far only been one application of a model allowing for such heterogeneity, by Bhat (1997). In this Covariance NL model, the logsum parameters themselves are a function of socio-demographic attributes of the decision-makers, such that the correlation heterogeneity is explained with the help of these attributes. While the results by Bhat show the presence of statistically significant levels of covariance heterogeneity, the improvements in terms of model performance are almost negligible. While it is possible to interpret this as a lack of covariance heterogeneity in the data, another explanation is possible. It is clearly imaginable that a major part of the covariance heterogeneity cannot be explained in a deterministic fashion, either due to data limitations, or because of the presence of actual random variation, in a situation analogous to the case of random taste heterogeneity that cannot be explained in a deterministic fashion. In this paper, we propose two different ways of modelling such random variations in the correlation structure across individuals. The first approach is based on the use of an underlying GEV structure, while the second approach consists of an extension of the ECL model. In the former approach, the choice probabilities are given by integration of underlying GEV choice probabilities, such as Nested Logit, over the assumed distribution of the structural parameters. In the most basic specification, the structural parameters are specified as simple random variables, where appropriate choices of statistical distributions and/or mathematical transforms guarantee that the resulting structural parameters fall into the permissible range of values. Several extensions are then discussed in the paper that allow for a mixture of random and deterministic variations in the correlation structure. In an ECL model, correlation across alternatives is introduced with the help of normally distributed error-terms with a mean of zero that are shared by alternatives that are closer substitutes for each other, with the extent of correlation being determined by the estimates of the standard deviations of the error-components. The extension of this model to a structure allowing for random covariance heterogeneity is again divided into two parts. In the first approach, correlation is assumed to vary purely randomly; this is obtained through simple integration over the distribution of the standard deviations of the error-terms, superseding the integration over the distribution of the error-components with a specific draw for the standard deviations. The second extension is similar to the one used in the GEV case, with the standard deviations being composed of a deterministic term and a random term, either as a pure deviation, or in the form of random coefficients in the parameterisation of the distribution of the standard deviations. We next show that our Covariance GEV (CGEV) model generalises all existing GEV model structures, while the Covariance ECL (CECL) model can theoretically approximate all RUM models arbitrarily closely. Although this also means that the CECL model can closely replicate the behaviour of the CGEV model, there are some differences between the two models, which can be related to the differences in the underlying error-structure of the base models (GEV vs ECL). The CECL model has the advantage of implicitly allowing for heteroscedasticity, although this is also possible with the CGEV model, by adding appropriate error-components, leading to an EC-CGEV model. In terms of estimation, the CECL model has a run-time advantage for basic nesting structures, when the number of error-components, and hence dimensions of integration, is low enough not to counter-act the gains made by being based on a more straightforward integrand (MNL vs advanced GEV). However, in more complicated structures, this advantage disappears, in a situation that is analogous to the case of Mixed GEV models compared to ECL models. A final disadvantage of the CECL model structure comes in the form of an additional set of identification conditions. The paper presents applications of these model structures to both cross-sectional and panel datasets from the field of travel behaviour analysis. The applications illustrate the gains in model performance that can be obtained with our proposed structures when compared to models governed by a homogeneous covariance structure assumption. As expected, the gains in performance are more important in the case of data with repeated observations for the same individual, where the notion of individual-specific substitution patterns applies more directly. The applications also confirm the slight differences between the CGEV and CECL models discussed above. The paper concludes with a discussion of how the two structures can be extended to allow for random taste heterogeneity. The resulting models thus allow for random variations in choice behaviour both in the evaluation of measured attributes C as well as the correlation across alternatives in the unobserved utility terms. This further increases the flexibility of the two model structures, and their potential for analysing complex behaviour in transport and other areas of research.

Modelling airport and airline choice behaviour with the use of stated preference survey data

The majority of studies of air travel choice behavior make use of revealed preference (RP) data, generally in the form of survey data collected from departing passengers. While the use of RP data has certain methodological advantages over the use of stated preference (SP) data, major issues arise because of the often low quality of the data relating to the un-chosen alternatives, in terms of explanatory variables as well as availability. As such, studies using RP survey data often fail to recover a meaningful fare coefficient, and are generally not able to offer a treatment of the effects of airline allegiance. In this paper, we make use of SP data for airport and airline choice collected in the US in 2001. The analysis retrieves significant effects relating to factors such as airfare, access time, flight time and airline and airport allegiance, illustrating the advantages of SP data in this context. Additionally, the analysis explores the use of non-linear transforms of the explanatory variables, as well as the treatment of continuous variations in choice behavior across respondents