Support for Multiplicative Model Specification

[PavanKumarDharmoju]

Hi everyone,

I am currently evaluating Meridian for our organization's MMM implementation and have a question regarding the model specification.

From the documentation (and the ModelSpec class), it appears Meridian relies on a hierarchical additive structure:

$$Y_{g,t} = \text{Intercept}_{g,t} + \text{Controls}_{g,t} + \text{Media}_{g,t}$$

Our primary modeling requirement is to capture inter-channel synergies (e.g., the multiplicative effect where upper-funnel TV spend amplifies lower-funnel Search efficiency), rather than treating channel contributions as strictly independent and additive.

Has anyone in the community or the team successfully implemented this? Specifically:

1. Native Support: Is there a configuration or ModelSpec argument that switches the core equation to a multiplicative form?

2. Log-Log Workaround: If we manually log-transform the Input Data ($Y$ and Media inputs) to force a multiplicative structure, will this break the Budget Optimizer? My concern is that the optimizer's ROI/marginal yield calculations might assume linear additive coefficients and fail to interpret the elasticity coefficients correctly.

3. Interaction Terms: If the model must remain additive, is the recommended best practice to manually engineer interaction features (e.g., creating a TV_x_Search column) and pass them as controls?

Any guidance on the roadmap for multiplicative support or community best practices for modeling synergies would be greatly appreciated.

Thanks!

[cpulavarthi]

Hello @PavanKumarDharmoju,

Thank you for contacting us!

1. Meridian does not support multiplicative media effects.

2. It is not recommended to log-transform the response variable, since this will invalidate all of the post-modeling analysis including budget optimization. Moreover, Meridian's causal estimands (incremental outcome, ROI, optimal budget) are based on changes in expected KPI. A log-transformed response model estimates expected log-KPI. (While it is possible to translate between the two, the translation can be highly sensitive to the assumption of residual normality.)

3. Meridian does not support manually engineered media features. If you include engineered features as controls, the post-modeling analysis will not take into consideration how the engineered features should change under different media counterfactual scenarios. For example, to estimate the TV ROI you need to estimate the expected outcome under the counterfactual scenario where TV execution is set to zero. A TV_x_Search feature should evaluate to zero when TV is set to zero, but Meridian's ROI calculation will only set the "main effect" term to zero.

Do reach out if you have any further questions regarding this.

Google Meridian Support Team