Robustness of Student link function in multinomial choice models

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 pmbit 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. In particular, this is the first extension of the binary robit to the case of multinomial choices. These models define the choice probability for category j relative to an (interchangeable) reference category. 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 models (GLMs). 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 shown that the travel mode choice is totally deterministic according to the transfer time. In fact, the use of Student link function allow us to detect the total artificial aspect of this famous dataset.