OMEN: Identifiability, Inductive Bias, and Mechanistic Modeling in Marketing Mix Models
Abstract
Marketing Mix Modeling (MMM) is widely used to guide large-scale marketing investment decisions, yet practitioners routinely observe instability, implausible elasticities, and contradictory budget recommendations across model implementations. We argue that the primary explanation is structural: the separable, additive factorization used by most MMMs conflicts with actual marketing system dynamics, leading to non-identifiability under realistic conditions. We compare OMEN, a mechanistic and nonlinear MMM, against two widely used open-source baselines using a synthetic, agent-based marketing environment with known causal ground truth. Across ten independently generated datasets, OMEN exhibits substantially lower error in recovering true incremental contributions, sharply reduced baseline leakage into media attribution, higher peak-lift fidelity during high-demand periods, and markedly lower optimization regret under counterfactual budget shifts.
Key findings
Structural, not statistical failure. The dominant source of MMM failure is not noise, insufficient data, or imperfect regularization — it is structural misalignment between the model's hypothesis class and the causal structure of real marketing systems.
Non-identifiability persists asymptotically. When spend is correlated with demand (as it always is in practice), separable MMMs become under-identified. No amount of data, regularization, or hyperparameter tuning can make a misspecified MMM reliable.
Seven structural constraints. We identify seven empirically motivated constraints that marketing systems exhibit — funnel directionality, nonstationary efficiency, memory and latency, flexible response shapes, cross-channel interaction, exogenous modulation, and non-universal saturation — that separable models cannot represent.
OMEN as a latent dynamical system. Rather than decomposing observed outcomes into baseline and additive channel effects, OMEN models marketing as a system evolving over time. Baseline demand and marketing effects emerge jointly from system dynamics rather than being specified independently.
Substantially lower attribution error. Across ten synthetic datasets, OMEN achieves a mean RMSE of approximately 31,000 on true incremental contributions versus approximately 110,000 (Baseline A) and 99,000 (Baseline B).
Reduced baseline leakage. OMEN shows significantly lower leakage of baseline structure (trend, seasonality, holidays) into media attribution, with paired t-tests confirming the improvement across all baseline components.
Higher peak-lift fidelity. During high-demand periods where decision stakes are highest, OMEN achieves sMAPE of approximately 0.277 versus 0.559 (Baseline A) and 1.058 (Baseline B).
Lower optimization regret. Mean optimization regret during peak periods is 5.6% for OMEN versus 32.2% (Baseline A) and 45.1% (Baseline B). In a Black Friday/Cyber Monday simulation, Baseline A recommends overspending by 81% while OMEN deviates from the optimum by approximately 1%.
Implications
For practitioners, unstable or implausible attribution outputs should not be interpreted as tuning failures — they are often indicators that the model class lacks the representational capacity to capture the system being measured. Progress in MMM will depend less on incremental algorithmic refinement and more on rethinking the structural assumptions that define the problem.