Discrete choice models with q-product random utilities

While most existing closed-form discrete choice models can be regarded as special cases of McFadden's generalized extreme value model, recently, alternative frameworks of McFadden's generalized extreme value model, which maintain closed-form expressions, have been proposed; these include the weibit model, which uses the Weibull distribution for its random component. In this paper, we develop a generalized closed-form discrete choice model which include both logit and weibit models as special cases, by introducing the q-product random utility, in which the relationship between the systematic component and the random component can be either additive, multiplicative, or in-between, depending on the value of the parameter q. We show that, when imposing the Gumbel distribution on its error component (instead of assuming the additive case as the logit model), the parameter q depicts decision maker's risk attitude in the sense of the Arrow–Pratt measure of relative risk aversion, which would be a behavioral foundation of the model. We also show that the model can be straightforwardly extended to incorporate statistical dependence across alternatives. The performance of the proposed model is examined by using two case studies; one on travel-route choices and the other on transport-mode choices.