Did Causal Analysis

Difference-in-Differences Framework

DiD framework for causal inference with automatic method selection (Multivariate vs Univariate) based on sample size.

Methodology

Intensive Margin

• Definition: How much behavior changed among participants (continuous outcome)
• Data Structure: Sparse data - only entities that participated (made purchases, had events, etc.)
• Outcome: Continuous (e.g., spending amount per purchaser)
• Key Point: Do NOT include non-participants or create complete grids - only analyze actual participants

Extensive Margin

• Definition: How many people changed behavior (binary 0/1 outcome)
• Data Structure: Complete panel - all entities × all periods (includes non-participants)
• Outcome: Binary (0/1 indicating participation)
• Key Point: MUST include non-participants to measure adoption ratess

Regression Methods

Both methods use: Y = α + βX + γPost + δ(X × Post) + ε where δ is the DiD estimate.

Multivariate Heterogeneous DiD

• Estimates ALL features simultaneously in one regression
• Controls for confounding between features
• Used when: n ≥ k × min_sample_ratio (default: 10k samples minimum)

Univariate DiD

• Separate regression for EACH feature
• More robust with small samples
• Used when: Insufficient sample size, or as fallback

CRITICAL: Both use statsmodels regression to provide p-values for statistical inference.

⚠️ CRITICAL: Data Preparation Requirements

Intensive Margin - Sparse Data (Purchasers/Participants Only)

CORRECT approach - Only aggregate actual transactions:

# Group actual transactions by entity-period
intensive_df = transactions.groupby(['entity_id', 'period'])['value'].sum().reset_index()
# Result: Only rows where events occurred (e.g., 3,404 rows for active participants)

Why this matters: Intensive margin measures "how much MORE did participants engage", not "did non-participants start engaging". Including zeros for non-participants dilutes the effect and changes the research question.

Extensive Margin - Complete Panel (All Users)

CORRECT approach - Create complete entity × group × period grid:

# Create all possible combinations
from itertools import product
all_entities = entities_df['entity_id'].unique()
all_groups = target_groups  # e.g., categories, regions, products
all_periods = ['baseline', 'treatment']

complete_grid = pd.DataFrame(
    list(product(all_entities, all_groups, all_periods)),
    columns=['entity_id', 'period']
)

# Mark who participated (1) vs who didn't (0)
events_lookup = transactions[['entity_id',  'period']].drop_duplicates()
events_lookup['participated'] = 1

extensive_df = complete_grid.merge(events_lookup, how='left')
extensive_df['participated'] = extensive_df['participated'].fillna(0).astype(int)
# Result: All entities × groups × periods with binary outcome

Why this matters: Extensive margin measures "did the participation rate increase", which requires knowing both who participated AND who didn't participate.

API

Constructor Parameters DIDAnalyzer(min_sample_ratio=10, significance_level=0.05, min_group_size=1)

• min_sample_ratio=10: Samples-to-features ratio for multivariate DiD
• significance_level=0.05: P-value threshold 0.05-0.1 based on the context and requirement
• min_group_size=1: Min observations per group for univariate DiD

intensive_margin(df, features, value_col, top_n=None, sort_by='estimate', asc=False)

Analyzes intensive margin: how much behavior changed among participants.

Input Data: Sparse entity-period data (only participants)

• df: Sparse DataFrame - only entities with participation
• features: List of demographic column names
• value_col: Continuous outcome column (e.g., 'amount', 'spending')
• top_n: Top N features (None = all)
• sort_by: 'estimate' or 'p_value'
• asc: True for ascending, False for descending

Returns: List of {"feature": str, "did_estimate": float, "p_value": float, "method": str}

extensive_margin(df, features, value_col='purchased', top_n=None, sort_by='estimate', asc=False)

Analyzes extensive margin: how many people changed behavior.

Input Data: Complete entity-period panel (all entities including non-participants)

• df: Complete DataFrame - ALL entities × ALL periods (includes non-participants)
• features: List of demographic column names
• value_col: Binary outcome column (0/1), default 'purchased'
• top_n: Top N features (None = all)
• sort_by: 'estimate' or 'p_value'
• asc: True for ascending, False for descending

Returns: List of {"feature": str, "did_estimate": float, "p_value": float, "method": str}

Internal Method Selection Logic

• Tries Multivariate Heterogeneous DiD first (if sample size sufficient)
• Falls back to Univariate DiD if needed
• Both methods provide p-values via regression

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