An Interproduct Competition Model Incorporating Branding Hierarchy and Product Similarities Using Store-Level Data

We develop and implement a Bayesian semiparametric model of demand under interproduct competition that enables us to assess the respective contributions of brand-SKU (stock keeping unit) hierarchy and interproduct similarity to explaining and predicting demand. To incorporate brand-SKU hierarchy effects, we use Bayesian hierarchical clustering inherent in a nested Dirichlet process to simultaneously partition brands, and SKUs conditional on brands, into groups of "similarity clusters." We examine cluster memberships and postprocess the Markov chain Monte Carlo output to infer cluster properties by accounting for parameter uncertainty. Our proposed approach lends to a spatial competition interpretation in latent attribute space and helps uncover the extent to which competition across SKUs in the latent attribute space is local or global. In a related vein, we discuss the implications of well-defined groups of similar SKUs as subcategory or submarket boundaries in latent attribute space. We empirically test our model using aggregate beer category sales data from a midsize U.S. retail chain. We find that branding hierarchy effects dominate those from product similarity. We find that the model partitions the 15 brands in the data into 4 brand clusters and the 96 SKUs into 25 SKU clusters conditional on brand cluster membership. In estimating a set of models of spatial interproduct competition, we find that SKU competition is more local than global in that only subsets of products compete within groups of comparable products. Finally, we discuss the substantive implications of our results.