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A new framework for Marketing Mix Modeling: Addressing Channel Influence Bias and Cross-Channel Effects

Javier Marin

TL;DR

This work tackles spend-driven attribution bias and hidden cross-channel effects in Marketing Mix Modeling by embedding physics-inspired mechanisms into a hierarchical Bayesian framework. It leverages Michaelis-Menten saturation to model shape effects and Boltzmann-type dynamics to quantify funnel cross-channel interactions, with normalization via $\tilde{K_M}$ to obtain investment-independent channel affinity. Validation on synthetic datasets demonstrates competitive predictive accuracy while offering richer interpretation of channel interdependencies and donor channels. The approach has practical implications for more accurate attribution and informed resource allocation in multi-channel campaigns, though it introduces higher model complexity that future work should streamline.

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.

A new framework for Marketing Mix Modeling: Addressing Channel Influence Bias and Cross-Channel Effects

TL;DR

This work tackles spend-driven attribution bias and hidden cross-channel effects in Marketing Mix Modeling by embedding physics-inspired mechanisms into a hierarchical Bayesian framework. It leverages Michaelis-Menten saturation to model shape effects and Boltzmann-type dynamics to quantify funnel cross-channel interactions, with normalization via to obtain investment-independent channel affinity. Validation on synthetic datasets demonstrates competitive predictive accuracy while offering richer interpretation of channel interdependencies and donor channels. The approach has practical implications for more accurate attribution and informed resource allocation in multi-channel campaigns, though it introduces higher model complexity that future work should streamline.

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.
Paper Structure (10 sections, 26 equations, 12 figures, 7 tables)

This paper contains 10 sections, 26 equations, 12 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Hill's equilibrium theory and shape effects
  3. Michaelis–Menten model and the advertising shape effect
  4. Michaelis–Menten model and the advertising shape effect
  5. Michaelis-Menten Stueckelberg equation and behavioural sciences
  6. A hierarchical Bayesian framework for Marketing Mix Modeling
  7. Advertising funnel effects and the Boltzmann kinetic theory
  8. Integration of Michaelis-Menten and Boltzmann Equations in Media Mix Modeling
  9. Validation with data
  10. Conclusions

Figures (12)

  • Figure 1: Hill's model represented for different coefficients values $n$.
  • Figure 2: Michaelis-Menten model curve representation.
  • Figure 3: Michaelis and Menten, Attitudes model and Social Identity model
  • Figure 4: Histogram contour plot comparing total weekly media spend and Brand leads (dataset 1)
  • Figure 5: Michaelis-Menten constant $K_M$ comparison for online and offline channels for dataset 1
  • ...and 7 more figures