Discrete choice models with q-product random utilities

Chikaraishi, Makoto; Nakayama, Shinichi

doi:10.1016/j.trb.2016.08.013

Cited by 23 publications

(4 citation statements)

References 31 publications

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“…When a violation of the standard Gumbel distribution assumption is found, alternative modelling approaches may be explored to overcome the ill-effects. Adopting an alternative parametric distribution for random utilities may prove to be a solution; for example, the Weibull or logistic distribution recently proposed in the literature[ 24 , 25 ] could serve as appropriate distributional assumptions on the random error term. In addition, a generalized multinomial logit model or a discrete-continuous choice model that allows heteroscedastic variance may also prove to be superior to the standard MNL and MDCEV model[ 26 , 27 ].…”

Section: Literature Reviewmentioning

confidence: 99%

On the development of a semi-nonparametric generalized multinomial logit model for travel-related choices

Wang

Pendyala

et al. 2017

PLoS ONE

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A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimation. The proposed method is applied to model commute mode choice among four alternatives (auto, transit, bicycle and walk) using travel behavior data from Argau, Switzerland. Comparisons between the multinomial logit model and the proposed semi-nonparametric model show that violations of the standard Gumbel distribution assumption lead to considerable inconsistency in parameter estimates and model inferences.

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Section: Literature Reviewmentioning

confidence: 99%

On the development of a semi-nonparametric generalized multinomial logit model for travel-related choices

Wang

Pendyala

et al. 2017

PLoS ONE

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“…Xu et al 2015formulate a Hybrid closed-form route choice model to alleviate the contrasting scaling issues of MNL and MNW by simultaneously considering absolute cost difference and relative cost difference, and is extended to include a path size correction factor to capture the correlation between routes. Chikaraishi & Nakayama (2016) extend concepts from the q-Generalised Logit model (Nakayama & Chikaraishi, 2015) to introduce a q-Product Logit model in which the relationship between the deterministic and random components of utilities can be either additive, multiplicative, or inbetween, depending on the value of the parameter q, where MNL and MNW are special cases of the model. A q-Product Nested Logit model is presented to capture correlation, where the CNL model is a special case, as well as a nested equivalent of the Weibit model.…”

Section: Introductionmentioning

confidence: 99%

Path Size Logit route choice models: Issues with current models, a new internally consistent approach, and parameter estimation on a large-scale network with GPS data

Duncan

Watling

Connors

et al. 2020

Transportation Research Part B: Methodological

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Path Size Logit route choice models attempt to capture the correlation between routes by including correction terms within the route utility functions. This provides a convenient closed-form solution for implementation in traffic network models. The path size terms measure distinctiveness of routes; a route is penalised based on the number of other routes sharing its links, and the costs of those shared links. Typically, real road networks have many very long routes that should be considered unrealistic. Such unrealistic routes are problematic for the Path Size Logit (PSL) model because they negatively impact the choice probabilities of realistic routes when links are shared. The Generalised Path Size Logit (GPSL) model attempts to address this problem by weighting the contributions of routes to path size terms according to the ratio of route travel costs. However, the GPSL model is not internally consistent in how it defines routes as being unrealistic: the path size terms consider only travel cost, whereas the route choice probability relation considers disutility including the correction term. To solve these challenges, this paper formulates a new internally consistent Adaptive Path Size Logit (APSL) model wherein routes contribute to path size terms according to the ratio of route choice probabilities, ensuring that routes defined as unrealistic by the path size terms, are exactly those with very low choice probabilities. The APSL route choice probability relation is an implicit function, naturally expressed as a fixed-point problem. A proof is provided for the guaranteed existence of solutions, as well as conditions for the uniqueness of solutions. A Maximum Likelihood Estimation procedure is given for estimating the APSL model with tracked route observation data, and this procedure is investigated in a simulation study where it is shown it is generally possible to reproduce assumed true parameters. APSL is then estimated using real tracked route GPS data on a large-scale network, and results are compared with other PSL models.

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“…In recent years, researchers have explored various departures from standard kernel error distributions (see Paleti, 2019, for a review). These advancements include negative exponential (Alptekinoglu and Semple, 2016), negative Weibull (Castillo et al, 2008), generalised exponential (Fosgerau and Bierlaire, 2009) and q-generalised reverse Gumbel (Chikaraishi and Nakayama, 2016) kernel error distributions, additive combinations of Gumbel and exponential error terms (Del Castillo, 2016), a class of asymmetric distributions (Brathwaite and Walker, 2018), copulas with Gumbel marginals (Del Castillo, 2020). However, these extensions do not aim at enhancing the robustness of choice models.…”

Section: Introductionmentioning

confidence: 99%

Robust discrete choice models with t-distributed kernel errors

Krueger¹,

Bierlaire²,

Gasos³

et al. 2020

Preprint

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Models that are robust to aberrant choice behaviour have received limited attention in discrete choice analysis. In this paper, we analyse two robust alternatives to the multinomial probit (MNP) model.Both alternative models belong to the family of robit models, whose kernel error distributions are heavy-tailed t-distributions. The first model is the multinomial robit (MNR) model in which a generic degrees of freedom parameter controls the heavy-tailedness of the kernel error distribution. The second alternative, the generalised multinomial robit (Gen-MNR) model, has not been studied in the literature before and is more flexible than MNR, as it allows for alternative-specific marginal heavy-tailedness of the kernel error distribution. For both models, we devise scalable and gradient-free Bayes estimators. We compare MNP, MNR and Gen-MNR in a simulation study and a case study on transport mode choice behaviour. We find that both MNR and Gen-MNR deliver significantly better in-sample fit and out-of-sample predictive accuracy than MNP. Gen-MNR outperforms MNR due to its more flexible kernel error distribution. Also, Gen-MNR gives more reasonable elasticity estimates than MNP and MNR, in particular regarding the demand for under-represented alternatives in a class-imbalanced dataset.

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Discrete choice models with q-product random utilities

Cited by 23 publications

References 31 publications

On the development of a semi-nonparametric generalized multinomial logit model for travel-related choices

On the development of a semi-nonparametric generalized multinomial logit model for travel-related choices

Path Size Logit route choice models: Issues with current models, a new internally consistent approach, and parameter estimation on a large-scale network with GPS data

Robust discrete choice models with t-distributed kernel errors

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