On negative correlation: a comparison between Multinomial Probit and GEV-based discrete choice models

Dong, Han; Ben-Elia, Eran; Cirillo, Cinzia; Toledo, Tomer; Prashker, Joseph N.

doi:10.1080/23249935.2016.1269846

Cited by 4 publications

(3 citation statements)

References 33 publications

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“…As significant t-statistics at the 0.01 level are shown in Tables 1 and 2, all negative covariance elements in covariance matrices of random error terms are correctly estimated, which indicates that the MMNP model can well accommodate various correlated error structures, even with negative correlations. It can perfectly avoid defects in previous MMNP models and mixed GEV models since error terms are assumed to be independent in previous MMNP models [12,13], and negative correlations cannot be accommodated in the mixed GEV models [15], which may lead to bias in model estimation [11].…”

Section: Simulation Resultsmentioning

confidence: 99%

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

Wang

Gan

2022

Journal of Advanced Transportation

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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.

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Section: Simulation Resultsmentioning

confidence: 99%

“…With the increase of random coefficients, the integration will be more complicated with higher dimensions. Besides, GEV estimates are biased when negative correlations appear between choices [11]. However, modelers usually do not know the covariance structure in advance.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Gan

2022

Journal of Advanced Transportation

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“…Note that this constraint on the scale parameters restricts that covariances to be non-negative (this should be clear from the expression in Proposition 2.1). Intuitively, the covariance between two error terms in a nested logit model is the variance of the nest specific error term of the shared nest which can not be negative; see Williams and Ortúzar (1982) for details and Dong et al (2017) for modeling implications. Furthermore by the same proposition, two alternatives are uncorrelated if the smallest partition containing both is the universal set C (or equivalently their youngest common ancestor is the root node).…”

Section: Technical Setup and Foundational Resultsmentioning

confidence: 99%

Learning Structure in Nested Logit Models

Aboutaleb,

Ben-Akiva,

Jaillet

2020

Preprint

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This paper introduces a new data-driven methodology for nested logit structure discovery. Nested logit models allow the modeling of positive correlations between the error terms of the utility specifications of the different alternatives in a discrete choice scenario through the specification of a nesting structure. Current nested logit model estimation practices require an a priori specification of a nesting structure by the modeler. In this we work we optimize over all possible specifications of the nested logit model that are consistent with rational utility maximization. We formulate the problem of learning an optimal nesting structure from the data as a mixed integer nonlinear programming (MINLP) optimization problem and solve it using a variant of the linear outer approximation algorithm. We exploit the tree structure of the problem and utilize the latest advances in integer optimization to bring practical tractability to the optimization problem we introduce. We demonstrate the ability of our algorithm to correctly recover the true nesting structure from synthetic data in a Monte Carlo experiment. In an empirical illustration using a stated preference survey on modes of transportation in the U.S. state of Massachusetts, we use our algorithm to obtain an optimal nesting tree representing the correlations between the unobserved effects of the different travel mode choices. We provide our implementation as a customizable and open-source code base written in the Julia programming language.

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A multinomial probit analysis of shanghai commute mode choice

Wang

Bhat

2022

Transportation

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On negative correlation: a comparison between Multinomial Probit and GEV-based discrete choice models

Cited by 4 publications

References 33 publications

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

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

Learning Structure in Nested Logit Models

A multinomial probit analysis of shanghai commute mode choice

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