Sales models are mainly used to analyze markets with a fairly small number of items, obtained after aggregating to the brand level. In practice one may require analyses at a more disaggregate level. For example, brand managers may be interested in a comparison across product attributes. For such an analysis the number of relevant items in the product category make commonly used sales models difficult to use as they would contain too many parameters. In this paper we propose a new model, which allows for the analysis of a market with many items while using only a moderate number of easily interpretable parameters. This is achieved by writing the sales model as a Hierarchical Bayes model. In this way we relate the marketing-mix effectiveness to item characteristics such as brand, package size, package type and shelf position. In this specification we do not have to impose restrictions on the competitive structure, as all items are allowed to have different own and cross elasticities. The parameters in the model are estimated using Markov Chain Monte Carlo techniques. As a by-product this model allows to make predictions of sales levels and marketing-mix effectiveness of new to introduce items or of attribute changes. For example, one can assess the impact of changing the packaging from plastic to glass, on sales and price elasticity. Besides entering and changing products, our model also allows for items to leave the market. We consider the representation, specification and estimation of the model. We apply the model to a ketchup scanner data set with 23 items at the chain level. Our results indicate that the model fits the sales of most items very well.
