Sales Modeling and Local Factor Decomposition for Optimal Investment Decisions in MMM: A Monte Carlo Simulation Study

Abstract: Media Mix Models (MMM) are used to understand drivers behind key performance indicators and to measure the effectiveness of media channels. The key metric to report causal impacts of media investments on sales is return on investment (ROI). The shape of ROI-curves crucially impacts optimal allocation. Different modeling and decomposition approaches are scrutinized in an effort to estimate such response patterns. OLS, SVR, GAM and TVEM models in combination with WFD, ALE and SHAP decomposition are employed. TVEM allows the marketer to pool data, thereby leveraging larger samples despite potential structural changes. The different methodologies are tested and compared in a Monte Carlo study and in a virtual MMM environment: AMSS is a micro-founded demand model which is calibrated to real data. We find that an information criterion can be used as a proxy for the goodness of ROI-curve fit. Additive models should be combined with SHAP whereas ALE produces better estimates for multiplicative models. A bias-variance trade-off can be observed with additive models producing lower bias but higher variance. The multiplicative power model specification yields the most consistent estimates. TVEM is able to slightly reduce the variance of estimates and is not very sensitive to the degree of dynamic change. Strong funnel effects impose a challenge for all approaches. SVR is among the best performing methodologies when media channels are considered individually. GAM is overall the most balanced approach. We believe that our testing environment is a valid tool to be explored in further research.