⚠️ CRITICAL DATA INCONSISTENCY: Lift Metric Calculation Error

[apierr]

Issue Summary

The reported Lift values in the PRIM Subgroup Analysis table contain a fundamental calculation error that makes the metric uninterpretable and potentially misleading. Specifically, the EI scenario shows Lift = 0.931 despite having the highest adoption density (81.07%) of all scenarios.

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The Problem

Contradictory Values

Scenario	Density (Adoption %)	Lift	Interpretation Problem
NI	32.46%	1.176	Reasonable
SI	67.89%	1.781	Seems reasonable
EI	81.07%	0.931	❌ IMPOSSIBLE

Key Issue: A Lift value < 1.0 means the segment has below-average adoption. Yet EI has the highest adoption rate (81.07%) across all scenarios.

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Root Cause Analysis

Expected Definition of Lift

Lift should measure: "How much better does this segment perform compared to a reference?"

$$\text{Lift} = \frac{\text{Density}_{\text{segment}}}{\text{Reference Mean}}$$

Two Standard Approaches

Option A: Within-Scenario Comparison

Compare segment to the mean of its own scenario:

Lift_EI = Density_EI / Mean_Adoption_EI
Lift_EI = 0.8107 / 0.4637 = 1.748

Option B: Cross-Scenario Comparison

Compare all segments to the baseline (NI) mean:

Lift_EI = Density_EI / Mean_Adoption_NI
Lift_EI = 0.8107 / 0.28 = 2.895

Both approaches yield Lift > 1.0, which is correct for a high-adoption segment.

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Verification Against Reported Data

Using Aggregate Adoption Metrics

From the second table:

• Mean Adoption NI = 28.00%
• Mean Adoption SI = 47.03%
• Mean Adoption EI = 46.37%

Reconstructing Lift (Option A: Within-Scenario)

Scenario	Density	Mean (Same Scenario)	Calculated Lift	Reported Lift	✓/✗
NI	32.46%	28.00%	1.160	1.176	✓ Close
SI	67.89%	47.03%	1.444	1.781	✗ Off by 23%
EI	81.07%	46.37%	1.748	0.931	✗ Wrong by 88%

Reconstructing Lift (Option B: Baseline Reference)

Scenario	Density	Mean NI (Baseline)	Calculated Lift	Reported Lift	✓/✗
NI	32.46%	28.00%	1.160	1.176	✓ Close
SI	67.89%	28.00%	2.425	1.781	✗ Off by 36%
EI	81.07%	28.00%	2.895	0.931	✗ Wrong by 211%

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Impact on Interpretation

Current (Incorrect) Interpretation

"The EI segment has Lift = 0.931, meaning it performs 7% worse than the population average despite targeting high-trust, high-income individuals."

Correct Interpretation (Option A)

"The EI segment has Lift = 1.748, meaning it performs 75% better than the EI scenario average, successfully concentrating adoption in the targeted demographic."

Correct Interpretation (Option B)

"The EI segment has Lift = 2.895, achieving nearly 3× the baseline adoption rate, demonstrating substantial policy effectiveness."

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Hypotheses for the Error

1. Inconsistent denominators: Different reference means used across scenarios (e.g., NI uses scenario mean, but SI/EI accidentally use segment-specific or inverted values)

2. Inverted calculation: The EI Lift may have been calculated as Mean / Density instead of Density / Mean:

   0.4637 / 0.8107 = 0.572 (still doesn't match 0.931)

3. Wrong variable substitution: Code may be pulling from incorrect columns in data structure

4. Copying error: Manual transcription error when populating the table

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Required Actions

Immediate

• Audit the source code that calculates Lift for each scenario
• Verify which denominator is used: scenario mean, baseline mean, or other
• Check if calculation method differs between NI, SI, and EI scenarios
• Re-run analysis with corrected formula

Documentation

• Add explicit formula for Lift to methods section:

  Lift_scenario = Density_segment / Mean_Adoption_scenario

• Clarify interpretation: "Lift > 1 indicates segment outperforms scenario average"
• Report corrected values in results table

Quality Control

• Implement assertion tests: assert all(Lift > 1) if segment is "high-adoption"
• Add sanity checks: assert Density_segment > Mean_population if Lift > 1
• Cross-validate with alternative calculation methods

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Recommended Table Correction

Corrected PRIM Subgroup Analysis (assuming Option A: within-scenario Lift):

Scenario	Coverage	Density	SD (Density)	Lift (Corrected)	Effect Size (d)	95% CI Lower	95% CI Upper	p-value	Stability	n_segment
NI	0.1734	0.3246	0.1309	1.160	0	0	0	1.00	0	867
SI	0.1050	0.6789	0.1581	1.444 ⚠️	0.814	0.537	1.091	< 0.001	0.067	525
EI	0.4126	0.8107	0.1579	1.748 ⚠️	1.037	0.760	1.315	< 0.001	0.067	2063

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Statistical Implications

This error affects:

1. Interpretability: Readers cannot understand which segments truly outperform
2. Reproducibility: Others cannot validate calculations without source code
3. Policy recommendations: Incorrect Lift values may lead to wrong targeting decisions
4. Credibility: Undermines trust in other reported metrics

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Additional Concerns

While investigating Lift, review these related issues:

1. Why is NI Lift ≠ 1.0? If NI is "baseline population (no segmentation)", its Lift should be exactly 1.0 by definition
2. Stability = 6.67%: Why do optimal segments appear in only 1/15 iterations?
3. n_segment for NI = 867: With 5,000 agents, why does "baseline population" only include 867 (17.34%)?

These suggest the NI "segment" may not actually represent the full population baseline as described.

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Status: 🔴 BLOCKING ISSUE - Must be resolved before publication or policy recommendations.

Priority: CRITICAL - Affects core interpretation of primary results.

Assigned to: [Data Analysis Team / Lead Author]

Deadline: Before manuscript submission / next revision cycle

[apierr]

SÌ

L'errore è già nei dati CSV.

Prova:

Dal tuo CSV demographic_profiles.csv:

EI scenario:

• Density = 0.4141 (41.41%)
• Lift riportato = 0.9309

Se applichiamo la formula standard del Lift:

Lift = Density / Population_Mean
0.9309 = 0.4141 / Population_Mean
Population_Mean = 0.4141 / 0.9309 = 0.4448 (44.48%)

Ma dalla tua Aggregate Table:

• EI Mean Adoption = 46.37% (non 44.48%)

Quindi:

❌ Il valore di Lift = 0.9309 nel CSV è matematicamente incompatibile con:

• Density = 41.41%
• Population Mean = 46.37%

✅ Il Lift corretto dovrebbe essere:

Lift = 0.4141 / 0.4637 = 0.893

Conclusione: Il CSV contiene valori di Lift calcolati in modo errato o con una formula diversa da quella standard.

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Vuoi che lo script ricalcoli tutti i Lift corretti basandosi sui dati raw (heatmap_grid.csv)?