IdentityLinkReducer

class pymc_marketing.mmm.incrementality.IdentityLinkReducer(scale)

Increment reducer for an additive response (link="identity").

With \(\text{inv} = \text{id}\) the base term cancels exactly:

\[\sum_t [\hat{Y}^{\text{cf}}_t - \hat{Y}_t] = s \sum_t \Delta_{t,m}\]

Per-channel increments are therefore independent of the baseline, of the control variables and of the other channels, and they sum to the total media increment – the setting in which the paper’s \(\text{ROAS}_m\) is derived.

Parameters:

scalexr.DataArray or float

Target scale \(s\) mapping the linear predictor back to the response scale. Scalar, or dimensioned for panel models (e.g. ("country",)).

Methods

IdentityLinkReducer.__init__(scale)
IdentityLinkReducer.counterfactual_minus_baseline(delta)	See IncrementalReducer.counterfactual_minus_baseline().