Causal identification in MMM
An MMM contribution is a conditional model allocation. Interpreting it as incremental advertising impact requires a defined intervention, outcome, horizon, population and credible counterfactual. A fitted response curve alone does not supply that counterfactual.
Observational assumptions
Media spending can respond to expected demand, promotions, competitor activity or other causes of sales. A regression can therefore associate media with sales even when part of that association reflects treatment assignment.
Controls help only under an appropriate causal structure and measurement contract. Including mediators or colliders can introduce bias. Adstock, saturation, baseline smoothness and priors specify the model; they do not independently establish exchangeability or eliminate unobserved confounding.
A balanced panel or a within transformation does not identify the effect of time-varying confounders. FE and CRE retain their documented statistical and operation contracts. Named RE remains gated.
Experimental evidence and calibration
A properly designed randomised experiment can identify an effect for its assignment mechanism, population and outcome. Assess non-compliance, missing outcomes, interference and the relationship between assignment and exposure. Randomisation alone does not resolve every measurement or transport problem.
A matched-market study is not automatically randomised. If assignment is non-random, its causal interpretation requires the design’s additional assumptions, such as credible controls and an appropriate counterfactual trend. Report the design and uncertainty of each lift estimate before using it as external causal evidence.
ammm’s add_lift_test_measurements(...) adds a calibration likelihood to a
built model. add_cost_per_target_calibration(...) supplies a separate
calibration path. Both remain subject to estimator gates; named FE and CRE do
not support these calibration operations.
EventAdditiveEffect adds a dated component to the model mean. It does not
consume a lift estimate as a calibration likelihood. Use the
Calibration guide for the actual API.
Calibration combines the supplied evidence with the model under an assumed mapping between study and model response. It does not guarantee unbiased attribution for untested channels, dates, geographies or spend ranges.
Choosing an identification design
There is no universal ranking of randomisation, instrumental variables, difference-in-differences, regression discontinuity and observational regression that settles a specific application. Compare their estimands and whether their identifying assumptions are credible in the available data.
State the intervention and source of variation. Explain the assignment or control mechanism, measurement coverage, independent units and threats to identification. Distinguish evidence supporting an assumption, evidence against it and assumptions that the data cannot test.
Prediction and computational checks
R-hat, ESS and divergences assess posterior computation. Prior predictive checks assess implications of the specification. In-sample posterior predictive checks assess reproduction of the fitted observations. Blocked holdout checks assess future prediction under the evaluated conditions.
None of these checks establishes causal identification. Predictively similar models can allocate sales differently across media and baseline. Report that sensitivity rather than treating fit as evidence that attribution is correct.
Planning and recommendations
Budget optimisation depends on marginal response across the candidate spend range, constraints and the objective. A correct ranking of channels at current spend is insufficient. Rankings can change as spend changes, and uncertain curvature can dominate an allocation decision.
A scenario that raises TV spend by 20% is a conditional model calculation. Interpreting its difference as the effect of intervening requires the response curve to remain applicable under that intervention. Evaluate extrapolation, carryover, controls, baseline assumptions and uncertainty over the chosen horizon.
Separate the output classes in reporting.
| Output | Interpretation |
|---|---|
| Observed spend and sales | Data description |
| Posterior contribution, ROAS or scenario difference | Conditional model result |
| Holdout error, coverage or compatible LOO comparison | Predictive evidence |
| Study estimate supported by a credible identification design | Causal evidence for that estimand |
| Proposed allocation or action | Decision recommendation under stated evidence and assumptions |
Report posterior intervals and practical effect thresholds. If an interval includes zero, the estimate is inconclusive as to sign at that threshold. Positive-support priors constrain sign by construction. If causal evidence is absent, describe assumption-dependent scenarios and the additional evidence needed before recommending consequential interventions.