🤖 AI Summary
This paper addresses two critical bottlenecks in marketing mix modeling (MMM): over-attribution to high-investment channels and the difficulty of quantifying cross-channel effects. To this end, we propose a novel hierarchical Bayesian framework integrating concepts from statistical physics and biochemical kinetics. Specifically, we introduce a Michaelis–Menten–type nonlinear response function to model single-channel saturation effects, and derive a Boltzmann-type cross-effect equation grounded in the Maxwell–Boltzmann distribution to enable interpretable modeling of synergistic or inhibitory channel interactions. We further define an investment-invariant, normalized *K*<sub>m</sub> metric to quantify intrinsic channel efficacy and uncover latent channel dependencies via *N*-particle system simulations. Empirical evaluation demonstrates that our approach preserves predictive accuracy while substantially improving attribution reasonableness, accurately identifying key cross-channel dynamics overlooked by conventional models and thereby enhancing strategic resource allocation decisions.
📝 Abstract
This research addresses two fundamental challenges in Marketing Mix Modeling: the tendency of models to over-attribute influence to high-investment channels and the difficulty in quantifying cross-channel effects. We propose integrating the Michaelis-Menten equation and Maxwell-Boltzmann kinetic theory into hierarchical Bayesian models to overcome these limitations. Our approach uses the Michaelis-Menten model to characterize shape effects with spending-independent parameters and Boltzmann-type equations to systematically quantify cross-channel dynamics. Experimental results show that this physics-inspired approach maintains predictive accuracy while providing superior analytical insights into channel effectiveness and interactions. The normalized Michaelis-Menten constant offers an investment-independent measure of channel efficacy, while the N-particle system simulation reveals previously ignored channel interdependencies, enabling more accurate attribution and informed resource allocation decisions.