An “Agent Based Modeling” Perspective of the Dirichlet Model

Abstract

The Dirichlet is a model of purchase incidence and brand choice that has been used with success since its inception in 1984, and in various incarnations since 1959. Despite its widespread use is sometimes regarded as a “black box” with its workings being inaccessible to a broader audience. This paper demonstrates a method of modelling the behaviour of a population “from the shopper upwards”. We introduce the concept of agent based simulation with respect to this use of The Dirichlet, where “agent rules” operate at the individual level and combine to build a more complete picture. The method has an immediate application in that it allows analysts to investigate behaviour in certain Dirichlet markets where data has not yet been collected. In using the model in this way we also aim to foster a greater understanding of the workings of The Dirichlet. We offer a brief analysis of the fit of the model and a review of the applications for the technique.