The multinomial logit model revisited: A semi-parametric approach in discrete choice analysis

Li, Baibing

doi:10.1016/j.trb.2010.09.007

Cited by 65 publications

(37 citation statements)

References 17 publications

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“…A more advanced non-parametric approach could be used in the multivariate method to overcome this limitation, where the bounded Pareto distribution is replaced with an unspecified underlying distribution function. In addition, the logit model for pedestrians' choice bebavior (accept or not accept a gap) could be restrictive in some applications, and hence it can be replaced with a more general semi-parametric model developed in Li (2011) in future research.…”

Section: Discussionmentioning

confidence: 99%

“…In terms of statistical inference, we note that although logit model (7) has the standard form of multinomial discrete choice models reflecting pedestrians' individual decision-making (see, e.g., Train, 2009;Li, 2011), vector cannot be estimated solely based on model (6) because the pedestrian type is not directly observable in practice.…”

Section: A Bilevel Multivariate Modelmentioning

confidence: 99%

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A bilevel model for multivariate risk analysis of pedestrians’ crossing behavior at signalized intersections

2014

Transportation Research Part B: Methodological

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Pedestrians who cross streets during the red-man phase of traffic light signals expose themselves to safety and health hazards and hence are considered to be at risk. Pedestrians' street-crossing behavior is in general the outcome of interaction between pedestrians and vehicles: the gaps between vehicles provide an opportunity for pedestrians to cross the street, and pedestrians may or may not accept the street-crossing risk during the red-man phase. In this paper, we propose a multivariate method to investigate pedestrians' risk exposure associated with unsafe crossings. The proposed method consists of two hierarchically interconnected generalized linear models that characterize two different facets of the unsafe crossing behavior. It gauges pedestrians' attitudes toward risk-taking and also measures the impact of potential risk factors on pedestrians' intended waiting times during the red-man phase of the traffic lights. A Bayesian approach with the data augmentation method is used to draw statistical inference for the parameters associated with risk exposure. The proposed method is illustrated using field traffic data.

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Section: Discussionmentioning

confidence: 99%

Section: A Bilevel Multivariate Modelmentioning

confidence: 99%

A bilevel model for multivariate risk analysis of pedestrians’ crossing behavior at signalized intersections

2014

Transportation Research Part B: Methodological

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“…Unlike the binary, closed-form, asymmetric models discussed above-where the functional form of P (y i1 = 1 | V i1 , V i2 ) is assumed outrightthe multinomial, asymmetric models created by transportation researchers come from assuming various distributions for the error terms in the utility equations for each alternative. In particular, multinomial, asymmetric choice models have been derived by transportation researchers by assuming Weibull (Castillo et al, 2008;Fosgerau and Bierlaire, 2009), Rayleigh (Li, 2011), Type II Generalized Logistic (Li, 2011), Pareto (Li, 2011;Mattsson et al, 2014), Exponential (Li, 2011), and Fréchet (Mattsson et al, 2014) distributions for the utilities of one's alternatives. In each of these cases, the resulting multinomial choice model is asymmetric.…”

Section: Literature Reviewmentioning

confidence: 99%

Asymmetric, closed-form, finite-parameter models of multinomial choice

Brathwaite

Walker

2018

Journal of Choice Modelling

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Class imbalance, where there are great differences between the number of observations associated with particular discrete outcomes, is common within transportation and other fields. In the statistics literature, one explanation for class imbalance that has been hypothesized is an asymmetric (rather than the typically symmetric) choice probability function. Unfortunately, few relatively simple models exist for testing this hypothesis in transportation settings-settings that are inherently multinomial. Our paper fills this gap.In particular, we address the following questions: "how can one construct asymmetric, closed-form, finite-parameter models of multinomial choice" and "how do such models compare against commonly used symmetric models?" Methodologically, we introduce (1) a new class of closed-form, finite-parameter, multinomial choice models, (2) a procedure for using these models to extend existing binary choice models to the multinomial setting, and (3) a procedure for creating new binary choice models (both symmetric and asymmetric). Together, our contributions allow us to create new asymmetric, closed-form, finite-parameter multinomial choice models. We demonstrate our methods by developing four new asymmetric, multinomial choice models. Empirically, most of our models strongly dominate the multinomial logit (MNL) model in terms of in-sample and out-of-sample log-likelihoods. Moreover, analyzing two policy applications, we find practical differences between the MNL and our new asymmetric models. Our results suggest that while asymmetric models may not always outperform symmetric ones, asymmetric choice models are worth testing because they might have better statistical performance and entail substantively different policy and financial implications when compared with traditional symmetric models, such as the MNL. 4 The probability equation of open-form models contain analytically intractable integrals or infinite sums. 5 Models with an infinite number of parameters are known as non-parametric or semi-parametric models.

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“…Fosgerau and Bierlaire (2009) considered a multiplicative error term and derived a closed-form model similar to the weibit model of Castillo et al (2008). Li (2011) extended the logit and weibit models for other distributions and offered other alternative error distributions for discrete-choice models. Chen (2013, 2014) proposed a stochastic user equilibrium model with a weibit route choice.…”

Section: Introductionmentioning

confidence: 99%

Unified closed-form expression of logit and weibit and its extension to a transportation network equilibrium assignment

Nakayama

Chikaraishi

2015

Transportation Research Part B: Methodological

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a b s t r a c tThis study proposes a generalized multinomial logit model that allows heteroscedastic variance and flexible utility function shape. The novelty of our approach is that the model is theoretically derived by applying a generalized extreme-value distribution to the random component of utility, while retaining its closed-form expression. In addition, the weibit model, in which the random utility is assumed to follow the Weibull distribution, is a special case of the proposed model. This is achieved by utilizing the q-generalization method developed in Tsallis statistics. Then, our generalized logit model is incorporated into a transportation network equilibrium model. The network equilibrium model with a generalized logit route choice is formulated as an optimization problem for uncongested networks. The objective function includes Tsallis entropy, a type of generalized entropy. The generalization of the Gumbel and Weibull distributions, logit and weibit models, and network equilibrium model are formulated within a unified framework with q-generalization or Tsallis statistics.

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The multinomial logit model revisited: A semi-parametric approach in discrete choice analysis

Cited by 65 publications

References 17 publications

A bilevel model for multivariate risk analysis of pedestrians’ crossing behavior at signalized intersections

A bilevel model for multivariate risk analysis of pedestrians’ crossing behavior at signalized intersections

Asymmetric, closed-form, finite-parameter models of multinomial choice

Unified closed-form expression of logit and weibit and its extension to a transportation network equilibrium assignment

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