Browsing by Subject "composite marginal likelihood"

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The Composite Marginal Likelihood (CML) Estimation of Panel Ordered-Response Models
(Elsevier, 2013) Paleti, Rajesh; Bhat, Chandra R.
In the context of panel ordered-response structures, the current paper compares the performance of the maximum-simulated likelihood (MSL) inference approach and the composite marginal likelihood (CML) inference approach. The panel structures considered include the pure random coefficients (RC) model with no autoregressive error component, as well as the more general case of random coefficients combined with an autoregressive error component. The ability of the MSL and CML approaches to recover the true parameters is examined using simulated datasets. The results indicate that the performances of the MSL approach (with 150 scrambled and randomized Halton draws) and the simulation-free CML approach are of about the same order in all panel structures in terms of the absolute percentage bias (APB) of the parameters and econometric efficiency. However, the simulation-free CML approach exhibits no convergence problems of the type that affect the MSL approach. At the same time, the CML approach is about 5-12 times faster than the MSL approach for the simple random coefficients panel structure, and about 100 times faster than the MSL approach when an autoregressive error component is added. As the number of random coefficients increases, or if higher order autoregressive error structures are considered, one can expect even higher computational efficiency factors for the CML over the MSL approach. These results are promising for the use of the CML method for the quick, accurate, and practical estimation of panel ordered-response models with flexible and rich stochastic specifications.
Flexible Spatial Dependence Structures for Unordered Multinomial Choice Models: Formulation and Application to Teenagers’ Activity Participation
(Springer, 2012) Sener, Ipek N.; Bhat, Chandra R.
The current paper proposes an approach to accommodate flexible spatial dependency structures in discrete choice models in general, and in unordered multinomial choice models in particular. The approach is applied to examine teenagers’ participation in social and recreational activity episodes, a subject of considerable interest in the transportation, sociology, psychology, and adolescence development fields. The sample for the analysis is drawn from the 2000 San Francisco Bay Area Travel Survey (BATS) as well as other supplementary data sources. The analysis considers the effects of a variety of built environment and demographic variables on teenagers’ activity behavior. In addition, spatial dependence effects (due to common unobserved residential neighborhood characteristics as well as diffusion/interaction effects) are accommodated. The variable effects indicate that parents’ physical activity participation constitutes the most important factor influencing teenagers’ physical activity participation levels, In addition, part-time student status, gender, and seasonal effects are also important determinants of teenagers’ social-recreational activity participation. The analysis also finds strong spatial correlation effects in teenagers’ activity participation behaviors.
A Latent Variable Representation of Count Data Models to Accommodate Spatial and Temporal Dependence: Application to Predicting Crash Frequency at Intersections
(Elsevier, 2012) Castro, Marisol; Paleti, Rajesh; Bhat, Chandra R.
This paper proposes a reformulation of count models as a special case of generalized orderedresponse 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 1,190 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.
The MACML Estimation of the Normally-Mixed Multinomial Logit Model
(2011-01-18) Bhat, Chandra R.
The focus of this paper is to develop a procedure for the Maximum Composite Marginal Likelihood (MACML) estimation of multinomial logit models with normally mixed terms, as would be the case with normally-mixed random coefficient and/or error-component structures.
The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models
(Elsevier, 2011) Bhat, Chandra R.
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 provide s a “blueprint” for the MACML estimation for a wide variety of MNP models.
Model for Children's School Travel Mode Choice: Accounting for Effects of Spatial and Social Interaction
(National Academy of Sciences, 2011) Sidharthan, Raghuprasad; Bhat, Chandra R.; Pendyala, Ram M.; Goulias, Konstadinos G.
Numerous programs aimed at enhancing the choice of bicycle and walk as modes of choice for children's trips to and from school are being implemented by public agencies around the world. Disaggregate choice models capable of accounting for the myriad of factors that influence child school mode choice are needed to accurately forecast the potential impacts of such programs and policies. This paper aims to present a school mode choice model that is capable of capturing the unobserved spatial interaction effects that may potentially influence household decision-making processes when choosing a mode of transportation for children's trips to and from school. For example, households that are geographically clustered close together in a neighborhood may interact or observe one another, and be influenced by each other's actions. In order to overcome the computational intractability associated with estimating a discrete choice model with spatial interaction effects, the paper proposes the use of a maximum approximated composite marginal likelihood (MACML) approach for estimating model parameters. The model is applied to a sample of children residing in Southern California whose households responded to the 2009 National Household Travel Survey in the United States. It is found that spatial correlation effects are statistically significant, and that these effects arise from interactions among households that are geographically close to one another. The findings suggest that public policy programs aimed at enhancing the use of bicycle and walk modes among children may see greater impact if targeted at the local neighborhood level as opposed to a more diffuse regional scale.
Modeling the Influence of Family, Social Context, and Spatial Proximity on Use of Nonmotorized Transport Mode
(National Academy of Sciences, 2011) Ferdous, Nazneen; Pendyala, Ram M.; Bhat, Chandra R.; Konduri Karthik C.
This paper presents a joint model of walking and bicycling activity duration using a hazard based specification that recognizes the interval nature of time reported in activity-travel surveys. The model structure takes the form of a multilevel hazard-based model system that accounts for the range of interactions and spatial effects that might affect walking and bicycling mode use. In addition to the individual-specific factors, family (household-specific) interactions, social group (peer) influences, and spatial clustering effects are also considered as potential factors that contribute to heterogeneity in non-motorized transport mode use behavior. The model system presented is capable of accommodating grouped duration responses often encountered in activity-travel surveys. A composite marginal likelihood estimation approach is adopted to estimate parameters in a computationally tractable manner. The model system is applied to a survey sample drawn from the recent 2009 National Household Travel Survey in the United States. Model results show that there are significant unobserved family-level, social group, and spatial proximity effects that contribute to heterogeneity in walking and bicycling activity duration. The unobserved effects were also found to have a differential impact on bicycling activity duration, thus suggesting the need to treat and model walking and bicycling separately in transportation modeling systems.
On accommodating spatial dependence in bicycle and pedestrian injury counts by severity level
(Elsevier, 2013) Narayanamoorthy, Sriram; Paleti, Rajesh; Bhat, Chandra R.
This paper proposes a new spatial multivariate count model to jointly analyze the traffic crash- related counts of pedestrians and bicyclists by injury severity. The modeling framework is applied to predict injury counts at a Census tract level, based on crash data from Manhattan, New York. The results highlight the need to use a multivariate modeling system for the analysis of injury counts by road-user type and injury severity level, while also accommodating spatial dependence effects in injury counts.
Parental Attitudes Towards Children Walking and Bicycling to School
(Transportation Research Board of the National Academies, 2012) Seraj, Saamiya; Sidharthan, Raghuprasad; Bhat, Chandra R.; Pendyala, Ram M.; Goulias, Konstadinos G.
Recent research suggests that, besides traditional socio-demographic and built environment attributes, the attitudes and perceptions of parents towards walking and bicycling play a crucial role in deciding their children’s mode choice to school. However, very little is known about the factors that shape these parental attitudes towards their children actively commuting to school. The current study aims to investigate this unexplored avenue of research and identify the influences on parental attitudes towards their children walking and bicycling to school, as part of a larger nationwide effort to make children more physically active and combat rising trends of childhood obesity in the US. Through the use of a multivariate ordered response model (a model structure that allows different attitudes to be correlated), the current study analyses five different parental attitudes towards their children walking and bicycling to school, based on data drawn from the California add-on sample of the 2009 National Household Travel Survey. In particular, the subsample from the Los Angeles – Riverside – Orange County area is used in this study to take advantage of a rich set of micro-accessibility measures that are available for this region. It is found that school accessibility, work patterns, current mode use in the household, and sociodemographic characteristics shape parental attitudes towards children walking and bicycling to school. The study findings provide insights on policies, strategies, and campaigns that may help shift parental attitudes to be more favourable towards their children walking and bicycling to school.
A Simulation Evaluation of the Maximum Approximate Composite Marginal Likelihood (MACML) Estimator for Mixed Multinomial Probit Models
(Elsevier, 2011) Bhat, Chandra R.; Sidharthan, Raghuprasad
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 Spatial Generalized Ordered Response Model to Examine Highway Crash Injury Severity
(Elsevier, 2013) Castro, Marisol; Paleti, Rajesh; Bhat, Chandra R.
This paper proposes a flexible econometric structure for injury severity analysis at the level of individual crashes that recognizes the ordinal nature of injury severity categories, allows unobserved heterogeneity in the effects of contributing factors, as well as accommodates spatial dependencies in the injury severity levels experienced in crashes that occur close to one another in space. The modeling framework is applied to analyze the injury severity sustained in crashes occurring on highway road segments in Austin, Texas. The sample is drawn from the Texas Department of Transportation (TxDOT) crash incident files from 2009 and includes a variety of crash characteristics, highway design attributes, driver and vehicle characteristics, and environmental factors. The results from our analysis underscore the value of our proposed model for data fit purposes as well as to accurately estimate variable effects. The most important determinants of injury severity on highways, according to our results, are (1) whether any vehicle occupant is ejected, (2) whether collision type is head-on, (3) whether any vehicle involved in the crash overturned, (4) whether any vehicle occupant is unrestrained by a seat-belt, and (5) whether a commercial truck is involved.