Measurement of interactions in non-linear marketing models: The effect of critics' ratings and consumer sentiment on movie demand

In nonlinear models, a typical way to determine the interaction effect between variables is to linearize the model for estimation purpose, add an interaction term, and then use the estimate of the parameter of the interaction term to determine the presence (or absence) and the extent of the interaction effect. In this paper, we show that in many cases such an approach is problematic. By design, non-linear models inherently include interactions, and as a result the interaction coefficient does not capture the full extent and complexity of the interaction effect. After exploring the complexities of interaction effects in non-linear models, we outline methods to estimate and understand the interaction effects in two widely used marketing models. We use 26 years of weekly US movie market data to test the interactions between critics' ratings and consumer sentiment about economic conditions on box office attendance. In addition to finding that movie attendance is counter-cyclical, an expected but not previously documented result, we also show, contrary to popular belief, that critics' ratings have larger impact during economic downturns than during periods of economic expansion.