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.

Abstract For situations in which no assumptions are explicitly made about error distributions, other model assumptions may imply constraints on the form of the residual distribution. This is true of regression models which assume that percentiles are functions of the regressor variable. Hogg (1975) used a procedure based on signs of residuals to fit linear percentile models. Advantages of making (and testing!) explicit parametric assumptions in this context are illustrated using a linear model for scale and location with normal errors. This is applied to the data on professors' salaries discussed by Hogg. Key Words: Parametric percentile regressionPercentile linesRegression models with heterogeneous variance