Identification of Nonlinear and Time-varying Effects in Marketing Mix Models

Abstract

Recent years have seen a resurgence in interest in marketing mix models (MMMs), which are aggregate-level models of marketing effectiveness. Often these models incorporate nonlinear effects, and either implicitly or explicitly assume that marketing effectiveness varies over time. In this paper, we show that nonlinear and time-varying effects are often not separately identifiable: while certain data patterns may be suggestive of nonlinear effects, such patterns may also emerge under simpler models with time-varying effects. Moreover, these two types of effects often suggest fundamentally different optimal marketing allocations. We examine this identification issue mathematically, describing the conditions under which model conflation is likely to occur. Then, through an analysis of real-world marketing mix datasets and extensive simulations, we show that such conflation is likely widespread in practice, with significant revenue implications. Finally, we recommend measures that practitioners can incorporate when building their MMMs. We show that the standard approach to model selection, evaluating predictive performance on held-out data, fails under conflation, and propose an intervention-based maximal-separation experiment that efficiently identifies the correct model specification in as few as one to two test periods. 

Keywords: marketing mix models, aggregate response models, dynamics, nonlinear models, identification, Bayesian nonparametrics