Estimation of multinomial probit-kernel integrated choice and latent variable model: comparison on one sequential and two simultaneous approaches

Integrated choice and latent variable (ICLV) model incorporates latent factors into standard discrete choice model with aim to provide greater explanatory power. Using simulated datasets, this study makes a comparison among three estimation approaches corresponding to the sequential approach and two simultaneous approaches including the maximum simulated likelihood with GHK estimator and maximum approximate composite marginal likelihood (MACML) approach, to evaluate their abilities to recover the underlying parameters of multinomial probit-kernel ICLV model. The results show that both simultaneous approaches outperform the sequential approach in terms of estimates accuracy and efficiency irrespective of the sample sizes, and the MACML approach is the most preferable due to its best performance on recovering true values of parameters with relatively small standard errors, especially when the sample size is large enough.     

A simulation evaluation of the maximum approximate composite marginal likelihood (MACML) estimator for mixed multinomial probit models

This paper evaluates the ability of the maximum approximate composite marginal likelihood (MACML) estimation approach to recover parameters from finite samples in mixed cross-sectional and panel multinomial probit models. Comparisons with the maximum simulated likelihood (MSL) estimation approach are also undertaken. The results indicate that the MACML approach recovers parameters much more accurately than the MSL approach in all model structures and covariance specifications. The MACML inference approach also estimates the parameters efficiently, with the asymptotic standard errors being, in general, only a small proportion of the true values. As importantly, the MACML inference approach takes only a very small fraction of the time needed for MSL estimation. In particular, the results suggest that, for the case of five random coefficients, the MACML approach is about 50 times faster than the MSL for the cross-sectional random coefficients case, about 15 times faster than the MSL for the panel inter-individual random coefficients case, and about 350 times or more faster than the MSL for the panel intra- and inter-individual random coefficients case. As the number of alternatives in the unordered-response model increases, one can expect even higher computational efficiency factors for the MACML over the MSL approach. Further, as should be evident in the panel intra- and inter-individual random coefficients case, the MSL is all but practically infeasible when the mixing structure leads to an explosion in the dimensionality of integration in the likelihood function, but these situations are handled with ease in the MACML approach. It is hoped that the MACML procedure will spawn empirical research into rich model specifications within the context of unordered multinomial choice modeling, including autoregressive random coefficients, dynamics in coefficients, space-time effects, and spatial/social interactions.     

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.     

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.     

The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models

The likelihood functions of multinomial probit (MNP)-based choice models entail the evaluation of analytically-intractable integrals. As a result, such models are usually estimated using maximum simulated likelihood (MSL) techniques. Unfortunately, for many practical situations, the computational cost to ensure good asymptotic MSL estimator properties can be prohibitive and practically infeasible as the number of dimensions of integration rises. In this paper, we introduce a maximum approximate composite marginal likelihood (MACML) estimation approach for MNP models that can be applied using simple optimization software for likelihood estimation. It also represents a conceptually and pedagogically simpler procedure relative to simulation techniques, and has the advantage of substantial computational time efficiency relative to the MSL approach. The paper provides a “blueprint” for the MACML estimation for a wide variety of MNP models.     

Introducing non-normality of latent psychological constructs in choice modeling with an application to bicyclist route choice

In the current paper, we propose the use of a multivariate skew-normal (MSN) distribution function for the latent psychological constructs within the context of an integrated choice and latent variable (ICLV) model system. The multivariate skew-normal (MSN) distribution that we use is tractable, parsimonious in parameters that regulate the distribution and its skewness, and includes the normal distribution as a special interior point case (this allows for testing with the traditional ICLV model). Our procedure to accommodate non-normality in the psychological constructs exploits the latent factor structure of the ICLV model, and is a flexible, yet very efficient approach (through dimension-reduction) to accommodate a multivariate non-normal structure across all indicator and outcome variables in a multivariate system through the specification of a much lower-dimensional multivariate skew-normal distribution for the structural errors. Taste variations (i.e., heterogeneity in sensitivity to response variables) can also be introduced efficiently and in a non-normal fashion through interactions of explanatory variables with the latent variables. The resulting model we develop is suitable for estimation using Bhat’s (2011) maximum approximate composite marginal likelihood (MACML) inference approach. The proposed model is applied to model bicyclists’ route choice behavior using a web-based survey of Texas bicyclists. The results reveal evidence for non-normality in the latent constructs. From a substantive point of view, the results suggest that the most unattractive features of a bicycle route are long travel times (for commuters), heavy motorized traffic volume, absence of a continuous bicycle facility, and high parking occupancy rates and long lengths of parking zones along the route.     

Development of distress condition index of asphalt pavements using LTPP data through structural equation modeling

Traditional pavement distress index such as the Pavement Condition Index (PCI) developed by U.S. Army Corps of Engineers determines coefficients of distresses based on subjective ratings. This study proposed an asphalt pavement distress condition index based on various types of distress data collected from the Long-Term Pavement Performance (LTPP) database through Structural Equation Modeling (SEM). The SEM method treated the overall distress index as a latent variable while various distresses were treated as endogenous and other influence factors such as age, layer thickness, material type, weather, environment and traffic, were exogenous observed variables. The SEM method modeled the contributions of various distresses as well as the influence of other factors on the overall pavement distress condition. Influences of age, layer thickness, material type, environment and traffic on the latent distress condition were in accordance with previous studies. Compared with previous attempts to model latent pavement condition index utilizing SEM method, more pavement condition measurements and influencing factors were included. Specifically, this study adopted the robust maximum likelihood estimator (MLR) to estimate parameters for non-normally distributed data and derived the explicit expression of latent variables with intercepts. A multiple regression prediction model was built to calculate an overall condition index utilizing those measured distress data. The established pavement distress index prediction model provided a rational estimation of weighting coefficients for each distress type. The prediction model showed that alligator cracking, longitudinal cracking in wheel path, non-wheel path longitudinal cracking, transverse cracking, block cracking, edge cracking, patch and bleeding were significant for the latent pavement distress index.     

A latent segmentation based multiple discrete continuous extreme value model

We examine an alternative method to incorporate potential presence of population heterogeneity within the Multiple Discrete Continuous Extreme Value (MDCEV) model structure. Towards this end, an endogenous segmentation approach is proposed that allocates decision makers probabilistically to various segments as a function of exogenous variables. Within each endogenously determined segment, a segment specific MDCEV model is estimated. This approach provides insights on the various population segments present while evaluating distinct choice regimes for each of these segments. The segmentation approach addresses two concerns: (1) ensures that the parameters are estimated employing the full sample for each segment while using all the population records for model estimation, and (2) provides valuable insights on how the exogenous variables affect segmentation. An Expectation–Maximization algorithm is proposed to address the challenges of estimating the resulting endogenous segmentation based econometric model. A prediction procedure to employ the estimated latent MDCEV models for forecasting is also developed. The proposed model is estimated using data from 2009 National Household Travel Survey (NHTS) for the New York region. The results of the model estimates and prediction exercises illustrate the benefits of employing an endogenous segmentation based MDCEV model. The challenges associated with the estimation of latent MDCEV models are also documented.     

A comprehensive dwelling unit choice model accommodating psychological constructs within a search strategy for consideration set formation

This study adopts a dwelling unit level of analysis and considers a probabilistic choice set generation approach for residential choice modeling. In doing so, we accommodate the fact that housing choices involve both characteristics of the dwelling unit and its location, while also mimicking the search process that underlies housing decisions. In particular, we model a complete range of dwelling unit choices that include tenure type (rent or own), housing type (single family detached, single family attached, or apartment complex), number of bedrooms, number of bathrooms, number of storeys (one or multiple), square footage of the house, lot size, housing costs, density of residential neighborhood, and commute distance. Bhat’s (2015) generalized heterogeneous data model (GHDM) system is used to accommodate the different types of dependent outcomes associated with housing choices, while capturing jointness caused by unobserved factors. The proposed analytic framework is applied to study housing choices using data derived from the 2009 American Housing Survey (AHS), sponsored by the Department of Housing and Urban Development (HUD) and conducted by the U.S. Census Bureau. The results confirm the jointness in housing choices, and indicate the superiority of a choice set formation model relative to a model that assumes the availability of all dwelling unit alternatives in the choice set.     

Factors affecting temporal changes in mode choice model parameters

In travel demand forecasting models, parameters are often assumed to be stable over time. The stability of these parameters, however, has been questioned. This study investigates the factors affecting temporal changes in mode choice model parameters using a method proposed by the author that jointly utilises repeated cross-sectional data. In this method, the parameters are assumed to follow functional forms and the parameter changes are modelled endogenously. While the author’s previous studies assumed that all parameters are the same function of the same variable, this study assumes that different parameters are different functions of different variables, including time (year) and macro-economic variables. The paper describes a case study of a journey-to-work mode choice analysis for Nagoya, Japan, that examines 288 combinations of the functional forms and variables. The analysis found that the functions of time had serious over-fitting problems and that parameter changes are more closely related to economic factors.     

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

This paper proposes a reformulation of count models as a special case of generalized ordered-response models in which a single latent continuous variable is partitioned into mutually exclusive intervals. Using this equivalent latent variable-based generalized ordered response framework for count data models, we are then able to gainfully and efficiently introduce temporal and spatial dependencies through the latent continuous variables. Our formulation also allows handling excess zeros in correlated count data, a phenomenon that is commonly found in practice. A composite marginal likelihood inference approach is used to estimate model parameters. The modeling framework is applied to predict crash frequency at urban intersections in Arlington, Texas. The sample is drawn from the Texas Department of Transportation (TxDOT) crash incident files between 2003 and 2009, resulting in 1190 intersection-year observations. The results reveal the presence of intersection-specific time-invariant unobserved components influencing crash propensity and a spatial lag structure to characterize spatial dependence. Roadway configuration, approach roadway functional types, traffic control type, total daily entering traffic volumes and the split of volumes between approaches are all important variables in determining crash frequency at intersections.     

Estimation of an integrated driving behavior model

This paper presents the methodology and results of estimation of an integrated driving behavior model that attempts to integrate various driving decisions. The model explains lane changing and acceleration decisions jointly and so, captures inter-dependencies between these behaviors and represents drivers’ planning capabilities. It introduces new models that capture drivers’ choice of a target gap that they intend to use in order to change lanes, and acceleration models that capture drivers’ behavior to facilitate the completion of a desired lane change using the target gap.The parameters of all components of the model are estimated simultaneously with the maximum likelihood method and using detailed vehicle trajectory data collected in a freeway section in Arlington, Virginia. The estimation results are presented and discussed in detail.     

A multivariate ordered-response model system for adults’ weekday activity episode generation by activity purpose and social context

This paper proposes a multivariate ordered-response system framework to model the interactions in non-work activity episode decisions across household and non-household members at the level of activity generation. Such interactions in activity decisions across household and non-household members are important to consider for accurate activity-travel pattern modeling and policy evaluation. The econometric challenge in estimating a multivariate ordered-response system with a large number of categories is that traditional classical and Bayesian simulation techniques become saddled with convergence problems and imprecision in estimates, and they are also extremely cumbersome if not impractical to implement. We address this estimation problem by resorting to the technique of composite marginal likelihood (CML), an emerging inference approach in the statistics field that is based on the classical frequentist approach, is very simple to estimate, is easy to implement regardless of the number of count outcomes to be modeled jointly, and requires no simulation machinery whatsoever.The empirical analysis in the paper uses data drawn from the 2007 American Time Use Survey (ATUS) and provides important insights into the determinants of adults’ weekday activity episode generation behavior. The results underscore the substantial linkages in the activity episode generation of adults based on activity purpose and accompaniment type. The extent of this linkage varies by individual demographics, household demographics, day of the week, and season of the year. The results also highlight the flexibility of the CML approach to specify and estimate behaviorally rich structures to analyze inter-individual interactions in activity episode generation.     

Statistical estimation of the parameters of Daganzo's gap acceptance model

In a recent article in Transportation Research, Daganzo (1981) described a model of gap acceptance that permits the mean of the gap acceptance function to vary among drivers and permits the duration of the shortest acceptable gap for each driver to vary among gaps. The model contains several constant parameters whose values must be estimated statistically from observations of drivers' behavior. The results of numerical experiments reported by Daganzo (1981) suggested that the values of the parameters cannot be estimated by the method of maximum likelihood, which is the most obvious estimation technique, and Daganzo proposed using a sequential estimation method instead. The sequential method appeared to yield reasonable numerical results. In this paper, it is shown that subject to certain reasonable assumptions concerning the true parameter values and the probability distribution of gap durations, the maximum likelihood method does, in fact, yield consistent estimates of the parameters of Daganzo's model, whereas the sequential method does not. Hence, maximum likelihood is the better estimation method for this model.     

Analyzing commuter train user behavior: a decision framework for access mode and station choice

The purpose of the current research effort is to develop a framework for a better understanding of commuter train users’ access mode and station choice behavior. Typically, access mode and station choice for commuter train users is modeled as a hierarchical choice with access mode being considered as the first choice in the sequence. The current study proposes a latent segmentation based approach to relax the hierarchy. In particular, this innovative approach simultaneously considers two segments of station and access mode choice behavior: Segment 1—station first and access mode second and Segment 2—access mode first and station second. The allocation to the two segments is achieved through a latent segmentation approach that determines the probability of assigning the individual to either of these segments as a function of socio-demographic variables, level of service (LOS) parameters, trip characteristics, land-use and built environment factors, and station characteristics. The proposed latent segment model is estimated using data from an on-board survey conducted by the Agence Métropolitaine de Transport for commuter train users in Montreal region. The model is employed to investigate the role of socio-demographic variables, LOS parameters, trip characteristics, land-use and built environment factors, and station characteristics on commuter train user behavior. The results indicate that as the distance from the station by active forms of transportation increases, individuals are more likely to select a station first. Young persons, females, car owners, and individuals leaving before 7:30 a.m. have an increased propensity to drive to the commuter train station. The station model indicates that travel time has a significant negative impact on station choice, whereas, presence of parking and increased train frequency encourages use of the stations.     

Modeling the choice continuum: an integrated model of residential location,auto ownership,bicycle ownership,and commute tour mode choice decisions

The integrated modeling of land use and transportation choices involves analyzing a continuum of choices that characterize people’s lifestyles across temporal scales. This includes long-term choices such as residential and work location choices that affect land-use, medium-term choices such as vehicle ownership, and short-term choices such as travel mode choice that affect travel demand. Prior research in this area has been limited by the complexities associated with the development of integrated model systems that combine the long-, medium- and short-term choices into a unified analytical framework. This paper presents an integrated simultaneous multi-dimensional choice model of residential location, auto ownership, bicycle ownership, and commute tour mode choices using a mixed multidimensional choice modeling methodology. Model estimation results using the San Francisco Bay Area highlight a series of interdependencies among the multi-dimensional choice processes. The interdependencies include: (1) self-selection effects due to observed and unobserved factors, where households locate based on lifestyle and mobility preferences, (2) endogeneity effects, where any one choice dimension is not exogenous to another, but is endogenous to the system as a whole, (3) correlated error structures, where common unobserved factors significantly and simultaneously impact multiple choice dimensions, and (4) unobserved heterogeneity, where decision-makers show significant variation in sensitivity to explanatory variables due to unobserved factors. From a policy standpoint, to be able to forecast the “true” causal influence of activity-travel environment changes on residential location, auto/bicycle ownership, and commute mode choices, it is necessary to capture the above-identified interdependencies by jointly modeling the multiple choice dimensions in an integrated framework.     

A gradient boosting logit model to investigate driver’s stop-or-run behavior at signalized intersections using high-resolution traffic data

Driver’s stop-or-run behavior at signalized intersection has become a major concern for the intersection safety. While many studies were undertaken to model and predict drivers’ stop-or-run (SoR) behaviors including Yellow-Light-Running (YLR) and Red-Light-Running (RLR) using traditional statistical regression models, a critical problem for these models is that the relative influences of predictor variables on driver’s SoR behavior could not be evaluated. To address this challenge, this research proposes a new approach which applies a recently developed data mining approach called gradient boosting logit model to handle different types of predictor variables, fit complex nonlinear relationships among variables, and automatically disentangle interaction effects between influential factors using high-resolution traffic and signal event data collected from loop detectors. Particularly, this research will first identify a series of related influential factors including signal timing information, surrounding traffic information, and surrounding drivers’ behaviors using thousands drivers’ decision events including YLR, RLR, and first-to-stop (FSTP) extracted from high-resolution loop detector data from three intersections. Then the research applies the proposed data mining approach to search for the optimal prediction model for each intersection. Furthermore, a comparison was conducted to compare the proposed new method with the traditional statistical regression model. The results show that the gradient boosting logit model has superior performance in terms of prediction accuracy. In contrast to other machine learning methods which usually apply ‘black-box’ procedures, the gradient boosting logit model can identify and rank the relative importance of influential factors on driver’s stop-or-run behavior prediction. This study brings great potential for future practical applications since loops have been widely implemented in many intersections and can collect data in real time. This research is expected to contribute to the improvement of intersection safety significantly.     

A least absolute deviation critical decision path analysis with transport applications

This paper introduces a method that simultaneously analyzes travel variables from stated preferences that are measured under each of several different assumptions. The method uses least absolute deviation estimators and linear programming solutions and is flexible enough to permit inclusion of constraints for ordinal data and latent variables. Travel behavior is characterized by different indicators such as travel time, waiting time, mode choice and departure time. Consideration of different response variables simultaneously as part of a stated preference model requires a reclassification of variables as either endogenous or exogenous. This concept was introduced by the author as structural conjoint analysis earlier. Each endogenous variable may be defined as nominal, ordinal or cardinal and may be either explicitly measured or latent. Current econometric and psychometric techniques cannot accommodate this variety of data. The procedure is essentially a two-stage least absolute deviation simultaneous equation regression. The estimation technique is well known as are the various hypothesis tests. In the method each relationship between endogenous and exogenous variables is formulated separately carefully incorporating assumptions about each type of data. Thus there are different formulations for endogenous variables that are nominal and latent, ordinal and explicit, ordinal and latent, cardinal and explicit and cardinal and latent. Formulations for nominal latent, ordinal explicit and cardinal explicit variables were tested with simulated data for three separate hypothetical problems. Each problem consisted of at least two different types of variables and the technique was found to be able to reproduce the simulation function coefficients in virtually all cases.     

Integration of signal timing estimation model and dynamic traffic assignment in feedback loops: system design and case study

This paper presents an integrated framework for effective coupling of a signal timing estimation model and dynamic traffic assignment (DTA) in feedback loops. There are many challenges in effectively integrating signal timing tools with DTA software systems, such as data availability, exchange format, and system coupling. In this research, a tight coupling between a DTA model with various queue‐based simulation models and a quick estimation method Excel‐based signal control tool is achieved and tested. The presented framework design offers an automated solution for providing realistic signal timing parameters and intersection movement capacity allocation, especially for future year scenarios. The framework was used to design an open‐source data hub for multi‐resolution modeling in analysis, modeling and simulation applications, in which a typical regional planning model can be quickly converted to microscopic traffic simulation and signal optimization models. The coupling design and feedback loops are first demonstrated on a simple network, and we examine the theoretically important questions on the number of iterations required for reaching stable solutions in feedback loops. As shown in our experiment, the current coupled application becomes stable after about 30 iterations, when the capacity and signal timing parameters can quickly converge, while DTA's route switching model predominately determines and typically requires more iterations to reach a stable condition. A real‐world work zone case study illustrates how this application can be used to assess impacts of road construction or traffic incident events that disrupt normal traffic operations and cause route switching on multiple analysis levels. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of household structure and selected travel characteristics on trip chaining

This paper analyzes trip chaining, focusing on how households organize non-work travel. A trip chaining typology is developed using household survey data from Portland, Oregon. Households are organized according to demographic structure, allowing analysis of trip chaining differences among household types. A logit model of the propensity to link non-work trips to the work commute is estimated. A more general model of household allocation of non-work travel among three alternative chain types — work commutes, multi-stop non-work journeys, and unlinked trips — is also developed and estimated. Empirical results indicate that the likelihood of linking work and non-work travel, and the more general organization of non-work travel, varies with respect to household structure and other factors which previous studies have found to be important. The effects of two congestion indicators on trip chaining were mixed: workers who commuted in peak periods were found to have lower propensity to form work/non-work chains, while a more general congestion indicator had no effect on the allocation of non-work trips among alternative chains.