CLOSED-FORM DISCRETE-CHOICE MODELS . IN: HANDBOOK OF TRANSPORT MODELLING

Random utility maximization discrete-choice models are widely used in transportation and other fields to represent the choice of one among a set of mutually exclusive alternatives. The decision-maker, in each case, is assumed to choose the alternative with the highest utility to him or her. The utility to the decision-maker of each alternative is not completely known by the modeler; thus, the modeler represents the utility by a deterministic portion which is a function of the attributes of the alternative, and the characteristics of the decision-maker and an additive random component which represents unknown and/or unobservable components of the decision-maker's utility function. Early development of choice models was based on the assumption that the error terms were multivariate normal and independently and identically type I extreme value (gumbel) distributed. The multivariate normal assumptions leads to the multinomial probit (MNP) model; the independent and identical gumbel assumption leads to the multinomial logit model. The probit model allows complete flexibility in the variance-covariance of a multidimensional normal distribution. The MNL probabilities can be evaluated directly, but the assumption that the error terms are independently and identically distributed across alternative and cases (individuals, households, or choice repetitions) places important limitations on the competitive relationships amount the alternatives. Developments in the structure of discrete-choice models have been directed at either reducing the computational burden associated with the MNP model or increasing the flexibility to extreme value models.