Fixed-effects Estimator

The released fe preset fits a one-unit fixed-effects marketing-mix model. It absorbs a separate intercept for each unit and identifies shared media and control effects from temporal changes within each unit.

For units i and dates t, the level formulation is:

y_it = alpha_i + f(media_it; theta) + controls_it * gamma + error_it.

AMMM3 fits the equivalent exact within-unit orthonormal-contrast likelihood. The unit intercepts alpha_i are not regularised parameters in the graph. Consequently, persistent differences between units do not identify the shared media coefficients.

Released contract

estimator:
  type: fe
  unit: geo

The released surface has these deliberate limits:

Use the bundled starting point at data/demo/geo_fe/config.yml. It contains only settings supported by this contract.

Run it from the repository root:

python3 runme.py --demo geo_fe

Data requirements

The dataset must be balanced on the declared unit and date columns: every unit must have the same dates, and each unit-date pair must occur once. It must have at least two units and two dates.

Each channel and control must vary within at least one fitted unit. A predictor that is constant within every unit cannot be estimated by FE and causes a pre-fit error. The target must also have non-zero within-unit variation.

This is not the same as adding geo controls to a pooled model. FE discards between-geo level variation from the likelihood for the shared slope coefficients.

Estimability screen

Before the main graph is created, AMMM3 evaluates media after the configured adstock and saturation transforms at a fixed-seed PyMC initial point. It saves:

• 10_pre_diagnostics/fixed_effects_estimability.csv
• 10_pre_diagnostics/fixed_effects_estimability.json

The report records the reference basis, within-variation share, VIF, condition number, rank, and the thresholds used. Its default policy is:

You may version a stricter or looser warning policy in the estimator block:

estimator:
  type: fe
  unit: geo
  estimability:
    within_variation_share_warning: 0.10
    max_vif_warning: 10
    condition_number_warning: 20

The zero-variation and rank checks remain errors. Do not suppress a warning by changing a threshold without recording why the underlying design remains fit for purpose.

The screen is a reference-design diagnostic. It cannot prove identification for every posterior draw because adstock and saturation parameters are estimated. A pass is necessary for the released graph, not sufficient evidence for a causal or decision claim.

Interpretation

For a media channel to be identified, it needs meaningful within-unit temporal variation after the configured transforms. National media that is identical in every geography can still vary over time, but it can be difficult to separate from common shocks. The initial FE contract does not add time fixed effects, so it does not claim to solve that problem.

FE removes time-invariant unit characteristics. It does not solve time-varying endogeneity, anticipation, simultaneous promotions, or measurement error. Use the preflight report, posterior diagnostics, predictive checks, prior sensitivity, and an explicit causal design before making attribution or budget decisions.

What comes next

RE and CRE are separate estimator contracts. CRE is released under its own transformed-summary and prediction boundary; RE remains unavailable.

For a direct comparison, see Choose an Estimator.