LinearRegression.calculate_impact

LinearRegression.calculate_impact(y_true, y_pred)

Calculate the causal impact as the difference between observed and predicted values.

The impact is calculated using the posterior expectation (mu) rather than the posterior predictive (y_hat). This means the causal impact represents the difference from the expected value of the model, excluding observation noise. This approach provides a cleaner measure of the causal effect by focusing on the systematic difference rather than including sampling variability from the observation noise term.

Parameters:

• y_true (xr.DataArray) – The observed outcome values with dimensions [“obs_ind”, “treated_units”].

• y_pred (az.InferenceData) – The posterior predictive samples containing the “mu” variable, which represents the expected value (mean) of the outcome.

Returns:

The causal impact with dimensions ending in “obs_ind”. The impact includes posterior uncertainty from the model parameters but excludes observation noise.

Return type:

xr.DataArray

Notes

By using mu (the posterior expectation) rather than y_hat (the posterior predictive with observation noise), the uncertainty in the impact reflects: - Parameter uncertainty in the fitted model - Uncertainty in the counterfactual prediction

But excludes: - Observation-level noise (sigma)

This makes the impact plots focus on the systematic causal effect rather than individual observation variability.