Estimating Media Mix Models with Demand-Marketing Interactions: A Constrained Genetic Algorithm Approach

2026-08-10

AI Summary

This study addresses the limitations of traditional media mix models, which assume independence between marketing effects and demand, thereby failing to capture their dynamic interactions and suffering from estimation bias due to non-identifiable parameters. To overcome these issues, the authors propose a novel multiplicative interaction mechanism between demand and marketing efforts, yielding a model with stronger economic interpretability. They further develop a constrained genetic algorithm framework that incorporates real-world business constraints to effectively resolve parameter non-identifiability. Simulation experiments confirm the unbiasedness of the proposed estimator, while empirical validation on real-world data demonstrates substantially improved parameter estimation accuracy. The approach also enables practical, constraint-aware optimization of marketing budget allocation.

Abstract

This paper proposes a novel extension to Media Mix Modeling (MMM) that introduces a multiplicative interaction between marketing activity and underlying consumer demand. Unlike standard MMM frameworks that assume additive and independent effects of media and baseline demand drivers, our specification allows marketing effectiveness to vary with prevailing demand conditions. However, the proposed structure introduces significant statistical challenges, particularly identifiability issues that can lead to unstable and biased parameter estimates. Using comprehensive simulation studies, we analyze the nature and severity of these identification issues through bias assessment and their implications for statistical inference. To address these issues, we develop a constrained genetic algorithm optimization approach which facilitates robust estimation that simultaneously mitigates biases arising from the aforementioned issues. The proposed approach also offers flexibility to incorporate economically meaningful parameter constraints. Finally, the proposed methodology is applied to real-world data to demonstrate its effectiveness in enhancing estimation accuracy while taking into account additional commercial constraints, facilitating budget allocation decisions.

Problem

• Media Mix Modeling
• Demand-Marketing Interaction
• Identifiability
• Parameter Estimation
• Statistical Bias

Innovation

• Media Mix Modeling
• Demand-Marketing Interaction
• Constrained Genetic Algorithm
• Parameter Identifiability
• Multiplicative Effects