Brand - Price Interactions in Discrete Choice: But Should You?

Choice models are used frequently in marketing to help management make better or more informed product and pricing decisions. The most common statistical model for choice studies is the multinomial logit with heteregeneity via Hierarchcial Bayes (HB). The standard approach is to model main effects for each attribute, but interactions between attributes are also possible. Recently, a company that produces choice modeling software has introduced an automated interaction search feature creating additional buzz for interactions in choice studies. More needs to be known about interactions in the presence of heterogeneity before applying feature interactions willy-nilly. Here we propose a method for testing interaction terms with a special look at brand-price interactions (equivalent to brand specific price effects) that are often recommended in practice. We show that brand specific pricing is unnecessary when using HB estimation and the added terms can lead to devastating model overfit. We provide a general framework for testing interactions. The step-by-step process can be used without a set of dedicated holdout tasks or sample. When evaluating interactions and model specifications more generally, overfit as well as managerial inferences should both be evaluated.