A Product Choice Model with Marketing, Filtering and Purchase Feedback

A household's purchase history provides evidence about three interrelated phenomena, product loyalty, marketing response and purchase feedback. First, most households display underlying product preferences or loyalties, in the sense of habitual purchase. However, marketing activities are likely to influence brand choice. Finally, throughfeedback of experience with purchased products, prior preferences may be reinforced and new ones introduced. The three phenomena are intertwined. For example, if a product is bought under promotional conditions, one can ask whether the household made the purchase because of an underlying preference or because of the promotion. The formulation presented here seeks to untangle these effects. Our model assumes that, on a given purchase occasion, a household's probabilities for choosing products follow a Dirichlet distribution. Initially, the Dirichlet reflects the heterogeneity of preferences across the household population. The parameters of the Dirichlet are modeled as functions of marketing variables. After each purchase the standard update of parameters for a Dirichlet-multinomial process provides new information about underlyin