Cross-nested Logit Model Research Articles

A practical method to draw from multivariate extreme value distributions

Generating random draws from multivariate extreme value (MEV) distributions plays an important role in the microsimulation of travel behaviors, which can effectively avoid heavy computational burdens from simulation based on calculated probability values, particularly in simulations for a large population or choice behaviors from a large choice set. However, there are few practical and effective methods for drawing from MEV distributions. This paper proposes a simple and computationally efficient approach for drawing from MEV distributions in the nested logit (NL), cross-nested logit (CNL), and paired combinatorial logit (PCL) models. The proposed approach to draw from the MEV distribution for a CNL model provides a new perspective to understand the underlying choice mechanism of the CNL model. To our knowledge, this is the first study to draw from an MEV distribution in the PCL model. Random draws from the proposed approach approximately follow the standard Gumbel distribution, which is the marginal distribution of NL/CNL/PCL models, and approximate correlations among alternatives well. Simulation results of NL/CNL/PCL models show that the proposed approach provides high-level accuracy in recovering model parameters with the overall mean absolute percentage bias being less than 3%. The proposed approach is computationally more efficient than similar ones because it only needs to draw from Gumbel distributions. The proposed approach can be used to simulate NL/CNL/PCL models with a large choice set or a multiple discrete-continuous generalized extreme value model in various application settings such as joint destination-mode choices, time use allocations, etc.

EXPRESS: Constrained Assortment Optimization under the Cross-Nested Logit Model

We study the assortment optimization problem under general linear constraints, where the customer choice behavior is captured by the Cross-Nested Logit model. In this problem, there is a set of products organized into multiple subsets (or nests), where each product can belong to more than one nest. The aim is to find an assortment to offer to customers so that the expected revenue is maximized. We show that, under the Cross-Nested Logit model, the unconstrained assortment problem is NP-hard even when there are only two nests, and the problem is generally NP-hard to approximate to any constant factors. To tackle this challenging problem, we develop a new discretization mechanism to approximate the problem by a linear fractional program with a performance guarantee of [Formula: see text], for any accuracy level ε > 0. We then show that optimal solutions to the approximate problem can be obtained by solving mixed-integer linear programs. We further show that our discretization approach can also be applied to solve a joint assortment optimization and pricing problem, as well as an assortment problem under a mixture of Cross-Nested Logit models to account for multiple classes of customers. Our empirical results on a large number of randomly generated test instances demonstrate that, under a performance guarantee of 90% (i.e., expected revenues are guaranteed to be at least 90% of the optimal revenue), the percentage gaps between the objective values obtained from our approximation methods and the optimal expected revenues are no larger than 1.2%.

Perturbation of Residential Preferences by COVID-19 Shocks in the Greater Toronto Area

This research investigates the immediate effects of the COVID-19 pandemic on residential preferences in the Greater Toronto Area (GTA), Canada, using a stated preference (SP) survey dataset. The study examines changes in relocation preferences and trends in the GTA after the Ontario government lifted the initial lockdown. The obtained choice data is then modeled using a mixed cross-nested logit model to find substitution patterns across regions and dwelling types, as well as explore residents’ preferences for different dwelling characteristics and the accessibility of their residence, including factors such as telecommuting options. The results reveal that the pandemic caused short-term residential dissonance, with residents tending to want to move to lower-density areas to relocate to their preferred dwelling type, emphasizing telecommuting as a key factor influencing residential relocation preferences. Housing qualities were prioritized over accessibility. The study also found heterogeneous behavior among GTA residents with regard to telecommuting as a factor in residential relocation. The study’s findings are relevant for planners and policymakers in anticipating the potential long-term pandemic-induced home relocation decisions and their impact on future household travel behavior, particularly with regard to telecommuting and accessibility.

Role of car segment and fuel type in the choice of alternative fuel vehicles: A cross-nested logit model for the English market

In this article, we study the role of car segment and fuel type in the choice of alternative fuel vehicles and in the prediction of its market. For this purpose, we propose a joint choice cross-nested logit model to understand the demand for alternative fuel vehicles (AFV) and to study substitutional patterns between fuel types and vehicle segments with a full revealed preference approach, using only publicly available real data at disaggregate (household) level in England. Our results show that, as hypothesised, fuel type choice is not independent from car segment choice. The correlation patterns in the chosen specification reveal that individual car alternatives belonging to the same car segment are strongly correlated, while a weaker correlation exists between alternatives from different segments which share the same fuel type. The results suggest that creating awareness for cleaner fuel alternatives might be more effective if a targeted approach that considers these substitutional patterns is used. From a policy standpoint, while purchase prices play an important role and government policies have been concentrated in reducing the gap between ICE vehicles and AFVs in this dimension, our models stress the relevance of the operating cost variable, suggesting that its effect might also be crucial in the purchase decision.

Modeling joint row- and column-wise correlation in air passenger seat selection: A cross-nested logit approach

Advance seat selection (ASS) fees have gradually become an important revenue generator for the carriers worldwide. In this study, we investigate air passenger seat selection behavior in the ASS service while quantifying spatial correlation structure among seats, which is novel to the literature. Specifically, we employ a Cross-Nested Logit (CNL) model that captures the joint row- and column-wise correlation among seats. The CNL model, together with the Multinomial Logit and Nested Logit models involved as benchmarks, are applied to a rich dataset of 321670 ASS records, extracted from the database of a Chinese regional carrier. The empirical results suggest that the correlation among seats arises from their similarities in both row and column dimensions, with a stronger correlation in the column dimension. And modeling such joint correlation can not only enhance the in-sample model fit, but also facilitate more accurate out-of-sample revenue prediction. Moreover, the utility parameter estimates reveal that passengers exhibit non-linear price sensitivity, representable by a power function with a rational exponent of 0.37. Additionally, passengers display heterogeneous willingness to pay influenced by their flight, booking, and personal characteristics. And seat preferences can be affected by participating in loyalty programs.

A novel modelling approach of integrated taxi and transit mode and route choice using city-scale emerging mobility data

The modelling of mode and route choices of public transport passengers is an essential component of travel demand modelling and transportation planning. Traditionally, choice models are trained using data from revealed and stated preference surveys which are not only cost and time intensive but also suffer from bias due to limitations in sample size. In this article, we present a novel approach utilizing a combination of emerging data sources for non-private modes, namely public transit smart card data, taxi GPS trajectory data, and taxi trips transaction data in order to calibrate an integrated taxi and transit mode and route choice model. We apply our approach for a case study of the taxi and public transport system of Singapore using data sets obtained from the local transport authorities. We solve the first mile and last mile data gaps by overlaying the individual transport nodes against geospatial land use data in order to identify their actual origin and destination points of each journey. To model the behavioural inter-dependencies between the choice of taxi and transit options, we tested a two-level nested logit model and a cross-nested logit model. Along with the commonly included exploratory variables such as in-vehicle travel time, transfer time and number of transfers, our model also incorporates differences in travel cost and separate mode specific constants for peak and off-peak periods. Generic and mode-specific in-vehicle travel time and cost coefficients are tested in the utility functions for the transit and taxi alternatives. Willingness to pay estimates are calculated and compared against similar estimates from Singapore. We also present an application of the model by predicting the mode split between taxi and transit under selected transit and taxi fare change scenarios. Our modelling methodology is highly generalizable and can be applied to other cities with similar data availability.

Modeling the capacity of multimodal and intermodal urban transportation networks that incorporate emerging travel modes

Given the increasing prevalence of new urban transport modes such as ridesharing, e-hailing, and combined transport, it is essential to evaluate their effects on the capacity of transportation networks. Hence, this paper develops a novel transportation network capacity model to capture the travel behaviors of inter-multimodal mobility in an urban transportation system that incorporates emerging travel modes. The novel model is formulated as a bi-level programming problem, in which the lower-level model is a combined modal split and traffic assignment (CMSTA) problem based on mathematical programming. The CMSTA problem adopts the cross-nested logit model to account for intermodal travel behavior in the modal split phase and the path-sized logit model to account for route overlap in the traffic assignment phase. Moreover, the logit-based trip distribution model is used to capture the dispatch of the e-hailing traffic flow and the matching of ridesharing drivers with passengers. Besides, we consider flow interactions (e.g., cars and buses sharing the same link) in the road network. We customize a solution framework for solving this novel model that adopts the recently developed fast path-based algorithm with the Barzilai–Borwein stepsize strategy to efficiently solve the CMSTA problem, and derive a sensitivity analysis-based (SAB) algorithm to solve the entire bi-level programming problem. The effectiveness of the novel model is verified in numerical experiments that demonstrate the effects of intermodal transportation, e-hailing, and ridesharing on the capacity of a multimodal transportation network.

Mixed Multinomial Probit Model Accommodating Flexible Covariance Structure and Random Taste Variation: An Application to Commute Mode Choice Behavior

This paper developed a mixed multinomial probit (MMNP) model with alternative error specification and random coefficients (for both generic variables and personal attributes) to accommodate flexible covariance structure and taste variation. The MMNP model can be efficiently estimated with analytic approximations of multivariate normal cumulative distribution functions, which avoid defects of simulation-based integration in the mixed multinomial logit (MMNL) model. The integral dimension of the MMNL model increases as random coefficients increase, but it only depends on the number of available alternatives in the MMNP model. Simulation experiments and empirical analysis of Shanghai commuters’ mode choice behavior were undertaken to examine the performance of MMNP models. Both simulation results and empirical results show that MMNP models can well accommodate flexible covariance structures and taste variation reflected through random coefficients being associated with both generic and personal variables. Empirical results indicate that the MMNP model performs better than traditional discrete choice models, such as the multinomial logit, the cross-nested logit, MMNL, and multinomial probit models. Random coefficients of “in-vehicle time of car” and “number of companions” indicate taste heterogeneity and the identifiability of random coefficients associated with both generic and personal attributes. Pairwise positive correlations between car/taxi, bus/metro, and bus/bus and metro are to be expected. However, the positive correlation between the car and metro modes may be unique to the Chinese city, Shanghai, because of the developed metro system. Unequal error variances reflect heterogeneities in unspecified factors in commute modes’ utilities. The MMNP model will offer an alternative efficient way to accommodate taste heterogeneity and flexible error covariance structure in discrete choice models. Compared with the MMNL model, the MMNP model can accommodate more random coefficients without increasing computational complexity.

A variational autoencoder approach for choice set generation and implicit perception of alternatives in choice modeling

Choice set generation is a challenging task, since the consideration set is generally unknown to the modelers, and the full choice set could be too large to be enumerated. The proposed variational autoencoder approach (VAE) is motivated by the idea that the chosen alternatives must belong to the consideration set. The proposed VAE method explicitly considers maximizing the likelihood of including the chosen alternatives in the choice set and inferring the underlying generation process. This paper derives the generalized extreme value (GEV) model with implicit availability/perception (IAP) of alternatives, for bridging the VAE with choice modeling. Specifically, the cross-nested logit (CNL) model with IAP is derived as an example of IAP-GEV models. The IAP approach assumes each alternative is associated with an implicit degree of availability/perception (likelihood in the context of VAE) to be included in the choice set. The VAE approach for route choice set generation is illustrated in a toy network. Simulation experiments show that the proposed method could reproduce the pre-defined true values. We further exemplify the VAE approach using a real dataset. The IAP-CNL model estimated has the best performance in terms of goodness-of-fit and prediction performance, compared to multinomial logit models and conventional choice set generation methods.

New York, Abu Dhabi, London or Stay at Home? Using a Cross-Nested Logit Model to Identify Complex Substitution Patterns in Migration

The question of how people revise their decisions about whether to emigrate, and where to, when facing changes in the global environment is of critical importance in migration literature. We propose a cross-nested logit (CNL) approach to generalize the way deviations from the IIA (independence from irrelevant alternatives)) hypothesis can be tested and exploited in migration studies. Compared with the widely used logit model, the structure of a CNL model allows for more sophisticated substitution patterns between destinations. To illustrate the relevance of our approach, we provide a case study using migration aspiration data from India. We demonstrate that the CNL approach outperforms standard competing approaches in terms of quality of fit, has stronger predictive power, implies stronger heterogeneity in responses to shocks, and highlights complex and intuitive substitution patterns between all possible alternatives. In particular, we shed light on the low degree of substitutability between the home and foreign alternatives as well as on the subgroups of countries that are considered by potential Indian movers as highly or poorly substitutable.

Doubly generalized logit: A closed-form discrete choice model system with multivariate generalized extreme value distributed utilities

In this study, we generalize our previous q-generalized multinomial logit model (Nakayama & Chikaraishi, 2015), in which the heteroscedastic variance and flexible shape of the utility distribution are considered, by allowing for statistical dependency of alternatives. This is achieved by introducing the q-generalization of McFadden’s multivariate Gumbel distribution. Thus, the logit model is doubly generalized; 1) each utility follows the generalized extreme value distribution that includes the Gumbel, Weibull, and Fréchet distributions; and 2) the utility distribution is multivariate, and therefore, a nested or cross-nested structure and dependency of alternatives are allowed. The proposed doubly generalized logit model system allows for deriving new closed-form discrete choice models such as the q-generalized nested logit model and q-generalized cross-nested logit (CNL) model. Furthermore, the model system includes conventional logit models such as the multinomial logit, nested logit, and CNL models as special cases as well as the new generalized logit models, while retaining a closed-form expression. We empirically confirm that the goodness-of-fit of the proposed model could be substantially better compared to that of the conventional models in some cases, though the degree of improvements varies across cases.

A copula-based continuous cross-nested logit model for tour scheduling in activity-based travel demand models

This paper introduces a multi-dimensional continuous activity scheduling choice modeling framework. The paper is focused on modeling the joint choice of arrival to an activity and departure from the activity. Each of the choices is modeled in continuous time using the continuous cross-nested logit model. The continuous cross-nested logit model is able to capture various types of correlation between alternatives in continuous time. In addition to the correlation between alternatives, this paper uses copula to capture the correlation between the two dependent choices of arrival to an activity and departure from the activity. Copula can model the correlation structure without knowing the actual bivariate distribution function. With its multidimensionality and ability to capture different sorts of correlations and model demand in fine time resolution, the introduced framework can provide a sufficient tool for the time-of-day component of various travel demand models.

New York, Abu Dhabi, London or Stay at Home? Using a Cross-Nested Logit Model to Identify Complex

The question of how people revise their decisions about whether to emigrate, and where to, when facing changes in the global environment is of critical importance in migration literature. We propose a cross-nested logit (CNL) approach to generalize the way deviations from the IIA (independence from irrelevant alternatives)) hypothesis can be tested and exploited in migration studies. Compared with the widely used logit model, the structure of a CNL model allows for more sophisticated substitution patterns between destinations. To illustrate the relevance of our approach, we provide a case study using migration aspiration data from India. We demonstrate that the CNL approach outperforms standard competing approaches in terms of quality of fit, has stronger predictive power, implies stronger heterogeneity in responses to shocks, and highlights complex and intuitive substitution patterns between all possible alternatives. In particular, we shed light on the low degree of substitutability between the home and foreign alternatives as well as on the subgroups of countries that are considered by potential Indian movers as highly or poorly substitutable.

New York, Abu Dhabi, London or Stay at Home? Using a Cross-Nested Logit Model to Identify Complex Substitution Patterns in Migration

The question of how people revise their decisions about whether to emigrate, and where to, when facing changes in the global environment is of critical importance in migration literature. We propose a cross-nested logit (CNL) approach to generalize the way deviations from the IIA (independence from irrelevant alternatives)) hypothesis can be tested and exploited in migration studies. Compared with the widely used logit model, the structure of a CNL model allows for more sophisticated substitution patterns between destinations. To illustrate the relevance of our approach, we provide a case study using migration aspiration data from India. We demonstrate that the CNL approach outperforms standard competing approaches in terms of quality of fit, has stronger predictive power, implies stronger heterogeneity in responses to shocks, and highlights complex and intuitive substitution patterns between all possible alternatives. In particular, we shed light on the low degree of substitutability between the home and foreign alternatives as well as on the subgroups of countries that are considered by potential Indian movers as highly or poorly substitutable.

Will autonomous vehicles change residential location and vehicle ownership? Glimpses from Georgia

Many studies have begun investigating possible transportation landscapes in the autonomous vehicle (AV) era, but empirical results on longer-term decisions are limited. We address this gap using data collected from a survey designed and implemented for Georgia residents in 2017–2018. Focusing on a hypothetical all-AV future, this section of the survey included questions regarding advantages/disadvantages of AVs, short-term mode choice impacts, medium-term impacts on activity patterns, and long-term behavioral changes – specifically, whether/how AVs will influence individuals to change residential location and the number of cars in the household. We hypothesize that AVs could act in concert with attitudinal preferences to stimulate changes in these long-term decisions, and that some medium-term activity changes triggered by AVs could motivate people to relocate their residence or shed household vehicles. We applied exploratory factor analysis to measure the perceived likelihood that AVs would prompt various medium-term changes. We then included some of those measures, among other variables, in a cross-nested logit (CNL) model of the choice of the residential location/vehicle ownership bundle. Although more than half of respondents expected “no change” in their bundle, we found that younger, lower income, pro-suburban, and pro-non-car-mode individuals were more likely to anticipate changing their selections. In addition, some expected medium-term impacts of AVs influenced changes in these longer-term choices. We further applied the CNL model to two population segments (Atlanta and non-Atlanta-region residents). We found notable improvement in goodness of fit and different effects of factors across segments, signifying the existence of geography-related taste heterogeneity.

A joint choice decision model of intra-household interaction-based motorcycle mode and departure time in Yogyakarta, Indonesia

The motorcycle-based joint trip between family members in a household becomes a common phenomenon in responding to unreliable public transport. This study aims to model the joint choice decision between intra-household interaction-based joint trip using motorcycle and departure time. With the data collected from 416 workers using the motorcycles in Yogyakarta, Indonesia, a cross-nested logit model was developed to explore the individual and household characteristics, work-and travel-related characteristics influencing household-based joint trip and departure time. The model result reveals that motorcyclists are more likely to change their departure time rather than an intra-household-based joint trip. Motorcyclists departing on a peak hour have a lower elasticity due to the alteration of travel time and travel cost than motorcyclists leaving on an off-peak hour. In a case of the off-peak departure time, motorcyclists leaving home to work by driving alone are more elastic for a change of travel cost than motorcyclists departing to work with their family member.

Multiclass traffic assignment model for mixed traffic flow of human-driven vehicles and connected and autonomous vehicles

Compared to existing human-driven vehicles (HDVs), connected and autonomous vehicles (CAVs) offer users the potential for reduced value of time, enhanced quality of travel experience, and seamless situational awareness and connectivity. Hence, CAV users can differ in their route choice behavior compared to HDV users, leading to mixed traffic flows that can significantly deviate from the single-class HDV traffic pattern. However, due to the lack of quantitative models, there is limited knowledge on the evolution of mixed traffic flows in a traffic network. To partly bridge this gap, this study proposes a multiclass traffic assignment model, where HDV users and CAV users follow different route choice principles, characterized by the cross-nested logit (CNL) model and user equilibrium (UE) model, respectively. The CNL model captures HDV users’ uncertainty associated with limited knowledge of traffic conditions while overcoming the route overlap issue of logit-based stochastic user equilibrium. The UE model characterizes the CAV's capability for acquiring accurate information on traffic conditions. In addition, the multiclass model can capture the characteristics of mixed traffic flow such as the difference in value of time between HDVs and CAVs and the asymmetry in their driving interactions, thereby enhancing behavioral realism in the modeling. The study develops a new solution algorithm labeled RSRS-MSRA, in which a route-swapping based strategy is embedded with a self-regulated step size choice technique, to solve the proposed model efficiently. Sensitivity analysis of the proposed model is performed to gain insights into the effects of perturbations on the mixed traffic equilibrium, which facilitates the estimation of equilibrium traffic flow and identification of critical elements under expected or unexpected events. The study results can assist transportation decision-makers to design effective planning and operational strategies to leverage the advantages of CAVs and manage traffic congestion under mixed traffic flows.

A Tour-Based Mode Choice Model for Commuters in Indonesia

With the advent of activity-based modelling, transport planners’ focus has shifted from isolated trips to tours. Tours are series of interconnected trips that start and finish at home. There are different types of tours; we focus on two: hwh (start at home; go to work; and then go back home) and hw+wh (where + represents a non-work activity). Tour types introduce a new dimension to the traditional problem of travel mode choice, as the mode choice might be influenced by the type of tour. This study attempts to measure and compare the relationship between tour type and mode choice using three different modelling approaches: Multinomial Logit (MNL); Nested Logit (NL) and Cross-Nested Logit (CNL). We compare each approach using secondary data from a larger survey: 24-h daily activity patterns of 420 commuters between Bekasi and Jakarta; one of the busiest commuting routes in Indonesia. Among other results, we found that gender and income significantly influence commuter’s choice of mode and that reducing travel time and cost can increase the ridership of public transport. Furthermore, the NL and CNL models showed significant improvement over the simpler MNL when grouping the alternatives based on tour types. This points to a significant influence of the tour type on the mode choice. Policy recommendations to increase traveler’s wellbeing are also formulated.

Optimizing EV-based P&R subsidy policies for commuting corridor based on cross-nested logit model

The promotion of electric vehicles (EVs) is restricted by cruising range limitation and charging station deficiency. Given the mature development of Park and Ride (P&R) mode, which is used in many cities worldwide to attract more travelers to use public transit, a new travel mode, i.e., EV-based P&R is introduced as an alternative for commuters’ daily travel. This seems quite attractive to expand the use of EVs and further increase their market share. This paper aims to investigate the impact of EV-based P&R introduction on travel mode choice along commuting corridor, and further aid in the optimal subsidy policies decision for the government. A bi-level model is proposed to model the presented problem. The lower level describes commuters’ joint mode and transfer choice behavior through a cross-nested logit (CNL) model, while the upper level minimizes the system cost. A genetic algorithm is developed to solve the formulated model with a partial linearization algorithm for solving the lower level model. And a numerical example is then used to demonstrate the effectiveness of the methodology and illustrate how the network flow pattern reshapes due to the introduction of EVs into the P&R mode and the change of corresponding subsidy policies. As the results show, improving the EV hardware, applying the intelligent supporting service system, developing new technologies for EV fast charging, appropriately improving the parking space capacity, and increasing the parking fee of transfer stations near the central business district (CBD) are all helpful to save the social cost and promote the usage of EVs.

Integrating automated vehicles into macroscopic travel demand models

Abstract The development of vehicles with increasing levels of automation will change transport supply and is likely to influence travel demand. The paper looks at ways of integrating characteristics of AV and AV-related mobility services in traditional macroscopic travel demand models based on the four-stage algorithm. It suggests a framework for (1) modelling impacts of AV on network performance and capacity, for (2) modelling impacts of AV on travel demand and for (3) modelling impacts of vehiclesharing systems on empty trips and the bundling of ridesharing trips. To model capacity three approaches are described quantifying capacity in passenger car units, in vehicle units and in time units. For mode choice approaches with a Multinomial Logit model, a Nested Logit model and a Cross-Nested Logit model are compared.