A Multiplicative Concept for Random Utility

Abstract

The paper introduces a new type of random utility model. Here the random term is formulated as a multiplicative factor to express the random effects of the utility together with deterministic utility aspects. Some arguments are given why this multiplicative approach is preferable over the additive solution which is more common in transportation planning. It is shown using the Weibull distribution, that this concept can be transformed into rather simple equations for the probability of the selection of different modes by individual travellers. More mathematical derivations show that the new concept has close relations to the Logit model. It can, however, provide one more degree of freedom and thus, better flexibility to adjust the model to reality. Also with other assumptions for the random utility term, like the lognormal distribution, this basic concept can be developed. For the model, a method of parameter calibration based on individual traveller’s decisions by maximum likelihood has been developed. The whole concept is demonstrated with real world data to demonstrate its usability.