ROAS and Metrics

Use this page for channel-efficiency outputs and aggregate predictive metrics.

Abacus separates these into two surfaces:

• mmm.summary and mmm.data for ROAS and cost-per-target outputs
• mmm.diagnostics for RMSE, MAE, NRMSE, NMAE, and CRPS

For contribution tables that feed these ratios, see Contributions and Decomposition.

Element-wise ROAS and cost per target

The lowest-level efficiency accessors live on mmm.data:

roas_samples = mmm.data.get_elementwise_roas(original_scale=True)
cost_per_target_samples = mmm.data.get_elementwise_cost_per_target(
    original_scale=True,
)

These are direct ratios built from fitted media contributions and the model’s channel inputs, stored as constant_data.channel_data. Abacus does not look up a separate monetary spend series or convert exposures to spend.

With original_scale=True, the financial interpretations require:

Use consistent currency, time periods and panel aggregation for both sides of the ratio. For example, £200 of contribution divided by £100 of spend gives ROAS 2; £200 divided by 1,000 impressions gives £0.20 per impression, not ROAS. If contributions are left on the scaled target space, the result is not in original business units.

These are model-conditional contribution ratios. Their posterior intervals do not establish incremental causal returns; see Causal Identification.

The arrays are element-wise over time, channel, and any panel dims, with posterior sample dimensions on top.

Abacus returns NaN when it would otherwise divide by zero.

Summarise ROAS

Use mmm.summary.roas(...) for a tidy summary table:

roas_df = mmm.summary.roas(
    hdi_probs=[0.80, 0.94],
    frequency="monthly",
    start_date="2024-01-01",
    end_date="2024-06-30",
)

Abacus applies start_date and end_date before any optional aggregation.

The returned table includes:

• identifying columns such as date, channel, and any panel dims
• mean
• median
• HDI bound columns such as abs_error_94_lower and abs_error_94_upper

Summarise cost per target

For conversion-style targets, use cost_per_target(...):

cpa_df = mmm.summary.cost_per_target(frequency="monthly")

This is the same retained summary surface that mmm.summary.efficiency() uses for target_type="conversion".

Use the default efficiency metric

Abacus chooses the default efficiency metric and label from the target type. This selects an accessor; it does not validate currency or convert channel inputs to spend. The financial labels below require the units stated above:

You can inspect the selected metric with:

metric_key = mmm.summary.efficiency_metric
metric_label = mmm.summary.efficiency_metric_label

Export channel spend

Use channel_spend() when you want the raw channel-input table with no posterior aggregation:

spend_df = mmm.summary.channel_spend()

This returns the observed channel inputs with columns such as date, channel, panel dims, and channel_data. They represent spend only when the model’s channel inputs are monetary amounts.

Predictive error metrics

Predictive metrics live under mmm.diagnostics.predictive_summary():

mmm.sample_posterior_predictive(
    X=X,
    random_seed=42,
    progressbar=False,
)

predictive_metrics = mmm.diagnostics.predictive_summary()

The returned one-row DataFrame includes:

• rmse
• mae
• nrmse
• nmae
• crps
• residual_mean
• residual_std

These metrics are calculated from the stored posterior predictive samples and the observed target. See the canonical predictive metric definitions, including the observed-range denominator for NRMSE/NMAE and its constant-target NaN case.

Practical guidance

• Use roas() for revenue targets with monetary channel inputs in a common currency.
• Use cost_per_target() for conversion-count targets with monetary channel inputs.
• Use efficiency() when you want target-type-aware reporting.
• Sample posterior predictive values before using predictive metrics.

Common pitfalls

• Reporting revenue per exposure as ROAS because a channel input was labelled spend without checking its units
• Forgetting that zero spend or zero contribution produces NaN
• Using predictive diagnostics before calling sample_posterior_predictive(...)