Identification and evidence
Separate model estimation from causal identification. A precise posterior can reflect restrictive priors and functional forms even when the observations do not distinguish plausible causal explanations.
Define what is being estimated
Name the intervention, outcome, population and horizon. A channel-off contrast holding other inputs fixed differs from a total effect that allows downstream channels to respond. If search activity is partly caused by another channel, holding search fixed changes the estimand. Controlling for a mediator can remove part of the effect of interest; conditioning on a collider can introduce bias.
Observational causal interpretation requires a defensible assignment and adjustment argument, sufficient support for the proposed intervention, reliable measurement and suitable assumptions about spillovers and response stability. A directed acyclic graph records those assumptions; software cannot establish them from a supplied graph. Price, promotions and media budgets can respond to anticipated demand, so their observed associations need not be intervention effects.
Variation and panel models
There is no universal minimum number of weeks. Look for independent changes in transformed exposure, spend levels spanning the relevant response range, and variation remaining after controls and seasonal structure. More rows of the same campaign schedule may add little information about separate channels.
National spend that is identical across geographies can still vary over time within each geography. Unit fixed effects do not remove that variation, but extra geographies do not create independent national spend changes. Common shocks may remain confounders. Fully flexible time effects would absorb a regressor varying only by date; AMMM4’s specialised FE estimator does not include such time effects.
An always-on channel can be estimable if it has informative variation. A constant or nearly collinear transformed series may instead be inseparable from the baseline or another channel. Rank, VIF and condition-number screens identify some design problems; they do not certify nonlinear or causal identification. Report a grouped estimand or collect better variation when channel-specific evidence is insufficient.
Saturation and changing media effectiveness can produce similar observed patterns but different allocations. This is a documented identification concern in Dew, Padilla and Shchetkina.
Priors and reporting
A justified informative prior adds external information; tightening a prior merely to obtain a desired answer does not. Report its provenance and sensitivity. A proper, narrow posterior alone does not show that the data identified the effect. Positive-support priors constrain signs by construction.
State the interval probability and method. If an interval contains zero, the estimate is inconclusive as to sign at that threshold; if it also rules out practically important effects, state that narrower conclusion. A predictive interval describes future observations, whereas a parameter or contribution interval describes uncertainty in the corresponding model quantity.
Passing holdout checks supports prediction for that evaluation design. A matched experiment supports its own causal contrast under its design assumptions. Neither automatically validates every channel or a new allocation. Review calibration, interpretation and optimisation against the intended intervention.
Specify common commercial inputs causally
Choose controls from the timing and intervention question before fitting. The
ordinary model can add linear controls to its predictor, but inclusion does not
establish that they are valid adjustment variables
(src/ammm/mmm/_mmm_graph.py:298).
| Situation | Decision before specification | Evidence and sensitivity to retain |
|---|---|---|
| Price changes respond to expected demand | Decide whether price is a confounder, part of the intervention, or jointly determined with demand | Pricing process, timing, demand proxies and sensitivity to alternative adjustment sets; a conditional coefficient alone is insufficient |
| Promotion changes alongside media | Define whether the target is a media-only change holding promotion fixed or a joint policy | Promotion calendar, operational coupling, overlap/support and contrasts matching the policy |
| An always-on channel has little independent variation | Assess what remains after baseline, trend and other channels | Transformed exposure variation and prior/baseline sensitivity; narrow the claim or group channels if separate effects remain inconclusive |
| One revenue channel affects another | Define outcome aggregation, spillovers and possible double counting | Intervention population, outcome measurement, common causes and whether an exclusion/no-spillover assumption is defensible |
For example, controlling for a promotion caused by the media intervention can remove part of the total policy effect you intended to estimate. Conversely, omitting a promotion that independently drove both media spending and outcomes can confound the media association. State which causal relation you assume and what evidence supports its timing; source code cannot settle that design choice.
A national regressor that varies over time can survive unit fixed effects; unit
FE does not absorb common time shocks or all time-varying confounding
(src/ammm/mmm/fixed_effects.py:261, src/ammm/mmm/fixed_effects.py:377). If a
reported interval includes zero, describe the estimate as inconclusive as to
sign unless it supports a separately defined equivalence or non-inferiority
claim. Report practically important effect thresholds as well as uncertainty.
See methodological sources for identification and workflow context.