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.     

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.     

Development of destination choice model with pairwise district-level constants using taxi GPS data

In this paper, a destination choice model with pairwise district-level constants is proposed for trip distribution based on a nearly complete OD trip matrix in a region. It is found that the coefficients are weakly identified in a destination choice model with pairwise zone-level constants. Thus, a destination choice model with pairwise district-level constants is then proposed and an iterative algorithm is developed for model estimation. Herein, the “district” means a spatial aggregation of a number of zones. The proposed model is demonstrated through simulation experiments. Then, destination choice models with and without pairwise district-level constants are estimated based on GPS data of taxi passenger trips collected during morning peak hours within the Inner Ring Road of Shanghai, China. The datasets comprise 504,187 trip records and a sample of 10,000 taxi trips for model development. The zones used in the study are actually 961 residents’ committees while the districts are 52 residential districts that are spatial aggregations and upper-level administrative units of residents’ committees. It is found that the estimated value of time dramatically drops after the involvement of district-level constants, indicating that the traditional model tends to overestimate the value of time when ignoring pairwise associations between two zones in trip distribution. The proposed destination choice model can ensure its predicted trip OD matrix to match the observed one at district level. Thus, the proposed model has potential to be widely applied for trip distribution under the situation where a complete OD trip matrix can be observed.     

Feasibility of using time–space prism to represent available opportunities and choice sets for destination choice models in the context of dynamic urban environments

H?gerstrand??s original framework of time geography and the subsequent time?Cspace prism computational methods form the foundation of a new computational method for potential path areas (PPA) in a realistic representation of dynamic urban environments. In this paper the time?Cspace prism framework is used to assess sensitivity of PPA size to different parameters and to build choice sets for regional destination choice models. We explain the implication of different parameters to choice set formation in a step-wise manner and illustrate not only the complexity of the idea and the high computational demand but also behavioral realism. In this context, this paper tests the feasibility of using constraint-based time?Cspace prism to find the choice sets for a large-scale destination choice model, and identifies a variety of implementation issues. Computational demand is estimated based on a household travel survey for the Southern California Association of Government, and the feasibility of using time?Cspace prisms for destination choice models is assessed with different levels of information on the network and destinations available. The implications of time of day effects and flexibility in scheduling on choice set development due to varying level of service on the network and availability of activity opportunities are discussed and numerically assessed.     

Activity-based disaggregate travel demand model system with activity schedules

We present an integrated activity-based discrete choice model system of an individual’s activity and travel schedule, for forecasting urban passenger travel demand. A prototype demonstrates the system concept using a 1991 Boston travel survey and transportation system level of service data. The model system represents a person’s choice of activities and associated travel as an activity pattern overarching a set of tours. A tour is defined as the travel from home to one or more activity locations and back home again. The activity pattern consists of important decisions that provide overall structure for the day’s activities and travel. In the prototype the activity pattern includes (a) the primary – most important – activity of the day, with one alternative being to remain at home for all the day’s activities; (b) the type of tour for the primary activity, including the number, purpose and sequence of activity stops; and (c) the number and purpose of secondary – additional – tours. Tour models include the choice of time of day, destination and mode of travel, and are conditioned by the choice of activity pattern. The choice of activity pattern is influenced by the expected maximum utility derived from the available tour alternatives.     

Analysis of long-distance vacation travel demand in the United States: a multiple discrete–continuous choice framework

This study analyzes the annual vacation destination choices and related time allocation patterns of American households. More specifically, an annual vacation destination choice and time allocation model is formulated to simultaneously predict the different vacation destinations that a household visits in a year, and the time (no. of days) it allocates to each of the visited destinations. The model takes the form of a multiple discrete–continuous extreme value (MDCEV) structure. Further, a variant of the MDCEV model is proposed to reduce the prediction of unrealistically small amounts of vacation time allocation to the chosen destinations. To do so, the continuously non-linear utility functional form in the MDCEV framework is replaced with a combination of a linear and non-linear form. The empirical analysis was performed using the 1995 American Travel Survey data, with the United States divided into 210 alternative destinations. The model estimation results provide several insights into the determinants of households’ vacation destination choice and time allocation patterns. Results suggest that travel times and travel costs to the destinations, and lodging costs, leisure activity opportunities (measured by employment in the leisure industry), length of coastline, and weather conditions at the destinations influence households’ destination choices for vacations. The annual vacation destination choice model developed in this study can be incorporated into a larger national travel modeling framework for predicting the national-level, origin–destination flows for vacation travel.     

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.     

On accommodating spatial interactions in a Generalized Heterogeneous Data Model (GHDM) of mixed types of dependent variables

We develop an econometric framework for incorporating spatial dependence in integrated model systems of latent variables and multidimensional mixed data outcomes. The framework combines Bhat's Generalized Heterogeneous Data Model (GHDM) with a spatial (social) formulation to parsimoniously introduce spatial (social) dependencies through latent constructs. The applicability of the spatial GHDM framework is demonstrated through an empirical analysis of spatial dependencies in a multidimensional mixed data bundle comprising a variety of household choices – household commute distance, residential location (density) choice, vehicle ownership, parents’ commute mode choice, and children's school mode choice – along with other measurement variables for two latent constructs – parent's safety concerns about children walking/biking to school and active lifestyle propensity. The GHDM framework identifies an intricate web of causal relationships and endogeneity among the endogenous variables. Furthermore, the spatial (social) version of the GHDM model reveals a high level of spatial (social) dependency in the latent active lifestyle propensity of different households and moderate level of spatial dependency in parents’ safety concerns. Ignoring spatial (social) dependencies in the empirical model results in inferior data fit, potential bias and statistical insignificance of the parameters corresponding to nominal variables, and underestimation of policy impacts.     

A note on the consistent aggregation of nested logit demand functions

The present paper derives a set of rules allowing for the consistent aggregation of nested logit travel demand functions across origin and destination zones. Presented aggregation rules are derived for the case when the mode choice is performed conditional on destination choice. The derivation is based on the principles of consistency between aggregate and disaggregate travel demand models introduced by Sweet as well as upon the sampling theory.     

A review on travel behaviour modelling in dynamic traffic simulation models for evacuations

Dynamic traffic simulation models are frequently used to support decisions when planning an evacuation. This contribution reviews the different (mathematical) model formulations underlying these traffic simulation models used in evacuation studies and the behavioural assumptions that are made. The appropriateness of these behavioural assumptions is elaborated on in light of the current consensus on evacuation travel behaviour, based on the view from the social sciences as well as empirical studies on evacuation behaviour. The focus lies on how travellers’ decisions are predicted through simulation regarding the choice to evacuate, departure time choice, destination choice, and route choice. For the evacuation participation and departure time choice we argue in favour of the simultaneous approach to dynamic evacuation demand prediction using the repeated binary logit model. For the destination choice we show how further research is needed to generalize the current preliminary findings on the location-type specific destination choice models. For the evacuation route choice we argue in favour of hybrid route choice models that enable both following instructed routes and en-route switches. Within each of these discussions, we point at current limitations and make corresponding suggestions on promising future research directions.     

Demand and welfare effects in recreational travel models: Accounting for substitution between number of trips and days to stay

In this paper we present a non-linear demand system for households’ joint choice of number of trips and days to spend at a destination. The approach, which facilitates welfare analysis of exogenous policy and price changes, is used empirically to study the effects of an increased CO₂ tax. In particular, we focus on the effect of including substitution between households choice of the number of trips and days to spend at a destination in the welfare analysis. The analysis reveals that the equivalent variation (EV) measure, for the count data demand system, can be seen as an upper bound for the households welfare loss. Approximating the welfare loss by the change in consumer surplus, accounting for the positive effect from longer stays, imposes a lower bound on the households welfare loss. The difference in the estimated loss measures, from the considered CO₂ tax reform, is about 20%. This emphasizes the importance of accounting for substitutions toward longer stays in travel demand policy evaluations.     

On the existence of stationary states in general road networks

Our daily driving experience and empirical observations suggest that traffic patterns in a road network are relatively stationary during peak periods. In numerous transportation network studies, there has been an implicit conjecture that stationary states exist in a network when origin demands, route choice proportions, and destination supplies are constant. In this study, we first rigorously formulate the conjecture within the framework of a network kinematic wave theory with an invariant junction model. After defining stationary states, we derive a system of algebraic equations in 3-tuples of stationary link flow-rates, demands, and supplies. We then introduce a new definition of junction critical demand levels based on effective demands and supplies. With a map in critical demand levels, we show that its fixed points and, therefore, stationary states exist with the help of Brouwer’s fixed point theorem. For two simple road networks, we show that the map is well-defined and can be used to solve stationary states with a brute-force method. Finally we summarize the study and present some future extensions and applications.     

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.     

A new estimation approach for the multiple discrete–continuous probit (MDCP) choice model

This paper develops a blueprint (complete with matrix notation) to apply Bhat’s (2011) Maximum Approximate Composite Marginal Likelihood (MACML) inference approach for the estimation of cross-sectional as well as panel multiple discrete–continuous probit (MDCP) models. A simulation exercise is undertaken to evaluate the ability of the proposed approach to recover parameters from a cross-sectional MDCP model. The results show that the MACML approach does very well in recovering parameters, as well as appears to accurately capture the curvature of the Hessian of the log-likelihood function. The paper also demonstrates the application of the proposed approach through a study of individuals’ recreational (i.e., long distance leisure) choice among alternative destination locations and the number of trips to each recreational destination location, using data drawn from the 2004 to 2005 Michigan statewide household travel survey.     

A nested recursive logit model for route choice analysis

We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modeled as a sequence of link choices and the model does not require any sampling of choice sets. Furthermore, the model can be consistently estimated and efficiently used for prediction.A key challenge lies in the computation of the value functions, i.e. the expected maximum utility from any position in the network to a destination. The value functions are the solution to a system of non-linear equations. We propose an iterative method with dynamic accuracy that allows to efficiently solve these systems.We report estimation results and a cross-validation study for a real network. The results show that the NRL model yields sensible parameter estimates and the fit is significantly better than the RL model. Moreover, the NRL model outperforms the RL model in terms of prediction.     

Flow-based accessibility measurement: The Place Rank approach

In this paper, we empirically test the viability of a flow-based approach as an alternative to transport accessibility measurement. To track where commuters travel from and to (but not commute times), we use transactional smartcard data from residents in Singapore to construct the (daily) spatial network of trips generated. We use the Place Rank method to demonstrate the viability of the flow-based approach to study accessibility. We compute the Place Rank of each of 44 planning areas in Singapore. Interestingly, even though the spatial network is constructed using only origin–destination information, we find that the travel time of the trips out of each planning area generally decreases as the area’s Place Rank increases. The same is also the case for in-vehicle time, number of transfers in the network and transfer time. This shows that a flow-based approach can be used to measure the notion of accessibility, which is traditionally assessed using travel time information in the system. We also compare Place Rank with other indicators, namely, bus stop density, eigenvector centrality, clustering coefficient and typographical coefficient to evaluate an area’s accessibility. The results show that these indicators are not as effective as the Place Rank method.     

Differences in probability weighting for individual travelers: a managed lane choice application

Using a 2012 stated preference survey based on a traveler’s most recent actual trip, this study predicts traveler choices between general purpose lanes and managed lanes for a freeway in Houston, Texas. The choice model incorporates probability weighting for risky travel times. The results indicate significant improvement in predicative power over a model that excludes weighting, confirming non-linearity in the probability weighting function. The maximum value of time (VOT) measures calculated in this study are lower than estimated in many previous route choice studies. This highlights the importance of incorporating individual weights for travel risks. Travelers’ underweighting of travel time risks would help explain the lower VOTs found in our study because respondents consider route choice decision-making as a gamble, but assign their own probabilities of occurrence to arriving at their destination on time, late, or early. We find that traveler groups are heterogeneous and the different weights developed for different groups of travelers can be used to better understand their probabilities. Segmentation analysis indicates that Age may serve to proxy the effects of more experience over time, or changing driving abilities, or changes in one’s sense of optimism or pessimism at different ages. Gender and Income also play a role in how the objective probabilities presented to respondents were translated into subjective probabilities.     

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.     

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.     

Analysis of parking cruising behaviour and parking location choice

ABSTRACT

This paper explores car drivers’ cruising behaviour and location choice for curb parking in areas with insufficient parking space based on a survey of car drivers in Beijing, China. Preliminary analysis of the data show that car drivers’ cruising behaviour is closely related to their parking duration and parking location. A multinomial probit (MNP) model is used to analyse cruising behaviour and the results show that the closer to the destination car drivers are, the more likely they choose to park on the curb. The adjacent locations are the basis of car drivers’ sequential parking decisions at different locations. The research results provide a better understanding of cruising behaviour for parking and recommendations for reducing cruising for parking. The provision of parking information can help regulate the parking demand distribution.