Analyzing the dependences of multi-category purchases on interactions of marketing variables

We extend the usual specification of the multivariate probit model frequently used to analyze multi-category purchase incidence data by introducing interaction effects between marketing variables. Models are estimated by a Markov Chain Monte Carlo simulation method using 24,047 shopping visits made by a random sample of 1500 households in one specific grocery store over a one year period. Our data refer to a total of 25 food and non-food product categories and include socio-demographic household attributes in addition to purchases and marketing variables. Information criteria agree on the superiority of the extended specification. Estimation results demonstrate that many interaction effects are erroneously attributed to the main effects of marketing variables if one applies the usual specification instead. We derive managerial implications with respect to sales revenue by stochastic simulation. If managers base decisions on the usual specification in spite of its worse statistical performance, they run the risk to overestimate sales revenue increases due to sales promotion activities.