Multicategory Purchase Incidence Models for Partitions of Product Categories

We analyze multicategory purchases of households by means of heterogeneous multivariate probit models that relate to partitions formed from a total of 25 product categories. We investigate both prior and post hoc partitions. We search model structures by a stochastic algorithm and estimate models by Markov chain Monte Carlo simulation. The best model in terms of cross-validated log-likelihood refers to a post hoc partition with two groups; the second-best model considers all categories as one group. Among prior partitions with at least two category groups a five-group model performs best. Effects on average basket value differ for the model with five prior category groups from those for the best-performing model in 40% and 24% of the investigated categories for features and displays, respectively. In addition, the model with five prior category groups also underestimates total sales revenue across all categories by about 28%. Copyright (c) 2016 John Wiley & Sons, Ltd.