Circumventing the problem of the scale: discrete choice models with multiplicative error terms

This paper is an updated version of the paper \Discrete choice models with multiplicative error terms" by Fosgerau and Bierlaire (2006). We propose a multiplicative speci cation of a discrete choice model that renders choice probabilities independent of the scale of the utility. The scale can thus be random with unspeci ed distribution. The model mostly outperforms the classical additive formulation over a range of stated choice data sets. In some cases, the improvement in likelihood is greater than that obtained from adding observed and unobserved heterogeneity to the additive speci cation. The multiplicative speci cation makes it unnecessary to capture scale heterogeneity and, consequently, yields a signi cant potential for reducing model complexity in the presence of heteroscedasticity. Thus the proposed multiplicative formulation should be a useful supplement to the techniques available for the analysis of discrete choices. There is however a cost to be paid in terms of increased analytical complexity relative to the additive formulations.