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Alan's hierarchical Bayesian model uses information from the whole sample to improve the individual store estimates. He specifies a system of Seemingly Unrelated Regressions (SUR) for each store relating sales of each brand to the price, feature-advertising, and price-promotion of every brand in the same product category. The store-level model also uses lagged sales as a predictor, to account for carryover effects. Each store-level model is viewed as a random draw from a hyper-distribution of parameters.
A unique feature of this model is that rather than shrinking the store-level estimates towards a grand mean across all stores, it defines the mean of the hyper-distribution as a regression on the market characteristics of the particular store. This clever formulation produces a direct link between store-level elasticities and the characteristics of the trade area where it operates. This extension of the Blattberg and George (1991) model will be useful in many other applications both in marketing and other fields. I will focus on this one particular application, and look at some of the assumptions made in applying this innovative approach.
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