Analysis of multi-category purchase incidence decisions using IRI market basket data

Empirical studies in Marketing have typically characterized a household's purchase incidence decision, i.e. the household's decision of whether or not to buy a product on a given shopping visit, as being independent of the household's purchase incidence decisions in other product categories. These decisions, however, tend to be related both because product categories serve as complements (e.g. bacon and eggs) or substitutes (e.g. colas and orange juices) in addressing the household's consumption needs, and because product categories vie with each other in attracting the household's limited shopping budget. Existing empirical studies have either ignored such inter-relationships altogether or have accounted for them in a limited way by modeling household purchases in pairs of complementary product categories. Given the recent availability of IRI market basket data, which tracks purchases of panelists in several product categories over time, and the new computational Bayesian methods developed in Albert and Chib (1993) and Chib and Greenberg (1998), estimating high-dimensional multi-category models is now possible. This paper exploits these developments to fit an appropriate panel data multivariate probit model to household-level contemporaneous purchases in twelve product categories, with the descriptive goal of isolating correlations amongst various product categories within the household's shopping basket. We provide an empirical scheme to endogenously determine the degree of complementarity and substitutability among product categories within a household's shopping basket, providing full details of the methodology. Our main findings are that existing purchase incidence models underestimate the magnitude of cross-category correlations and overestimate the effectiveness of the marketing mix, and that ignoring unobserved heterogeneity across households overestimates cross-category correlations and underestimate the effectiveness of the marketing mix.