Random utility models with implicit availability/perception of choice alternatives for the simulation of travel demand

Random utility models are undoubtedly the most used models for the simulation of transport demand. These models simulate the choice of a decision-maker among a set of feasible alternatives and their operational use requires that the analyst is able to correctly specify this choice-set for each individual. Some early applications basically ignored this problem by assuming that all decision-makers chose from the same pre-specified choice-set. This assumption may be unrealistic in many practical cases and cause significant misspecification problems. The problem of choice-set simulation has been dealt within the literature following two basically different approaches: (i) simulating the perception/availability of an alternative implicitly in the choice model; (ii) simulating the choice-set generation explicitly in a separate model. The implicit approach is more convenient from an operational point of view, while the explicit one is more appealing from a theoretical point of view. In this paper, a different approach to the modeling of availability/perception of alternatives in the context of random utility model is proposed. This approach is based on the concept of intermediate degrees of availability/perception of each alternative simulated through a model (or ‘inclusion function’) which in turn is introduced in the systematic utility of standard random utility models. This model, named implicit availability/perception (IAP), may be differently specified depending on assumptions made on the joint distribution of random residuals and the way in which the average degree of availability/perception is modeled. In this paper, a possible specification of the IAP model, based on the assumption of random residual distributed as independent, identical Gumbel and with the average degree of availability/perception modeled as a binomial logit, is proposed.