Robustness of Student link function in multinomial choice models

Abstract : The Student distribution has already been used to obtain robust maximum likelihood estimator (MLE) in the framework of binary choice models. But, until recently, only the logit and probit binary models were extended to the case of multinomial choices, resulting in the multinomial logit (MNL) and the multinomial probit (MNP). The recently introduced family of reference models, well defines a multivariate extension of any binary choice model, i.e. for any link function. This paper highlights the robustness of reference models with Student link function, by showing that the influence function is bounded. Inference of the MLE is detailed through the Fisher's scoring algorithm, which is appropriated since reference models belong to the family of generalized linear model (GLM). These models are compared to the MNL on the benchmark dataset of travel mode choice between Sydney and Melbourne. The results obtained on this dataset with reference models are completely different compared with those usually obtained with MNL, nested logit (NL) or MNP that failed to select relevant attributes. It will be showed that the travel mode choice is totally deterministic according to the terminal waiting time. In fact, the use of Student link function allow us to detect the total artificial aspect of this famous dataset.
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https://hal.umontpellier.fr/hal-02385029
Contributeur : Jean Peyhardi <>
Soumis le : jeudi 28 novembre 2019 - 16:05:01
Dernière modification le : samedi 30 novembre 2019 - 01:44:24

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  • HAL Id : hal-02385029, version 1

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Jean Peyhardi. Robustness of Student link function in multinomial choice models. 2019. ⟨hal-02385029⟩

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