An Inter-Product Competition Model Incorporating Branding Hierarchy and Product Similarities Using Store Level Data
Posted: 19 Jan 2014 Last revised: 8 Feb 2015
Date Written: January 24, 2014
We develop and implement a Bayesian Semi-parametric model of demand under inter-product competition that enables us to assess the respective contributions of branding hierarchy and inter-product similarity to explaining and predicting demand. To incorporate branding 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 post-process the MCMC 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 sub-category or sub-market boundaries in latent attribute space.
We empirically test our model using aggregate beer category sales data from a mid-size US 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 inter-product 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.
Keywords: Competition Modeling, Bayesian Semiparametrics, Nested Dirichlet Process
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