To control for how Walmart and grocery stores can price products differently, and carry more or fewer competing products, the researchers looked at relative shares of brand types. For example, instead of looking solely at how well Charmin toilet paper (a premium brand) and Angel Soft toilet paper (a value brand) performed in various store formats, they looked at how premium and value toilet-paper brands performed relative to each other at the different stores.
They find that shoppers are influenced by several factors. By considering assortment in addition to pricing, retailers can increase sales in particular products and better determine what products sell best in their stores.