Identification¶

How causal effects are identified from observed data.

Strategies¶

Strategy	Assumptions	Use Case
Backdoor	No unobserved confounders	Most common
Frontdoor	Mediator blocks all paths, no confounder of M→Y	When backdoor blocked
Instrumental Variable	Z affects T, Z⊥Y given T,X	Endogeneity / RCT non-compliance
Mediation	No mediator-outcome confounders	Mechanism analysis
Regression Discontinuity	Cutoff assignment	Sharp/fuzzy RD

Backdoor Criterion¶

A set of variables Z satisfies the backdoor criterion relative to (T, Y) if: 1. No node in Z is a descendant of T 2. Z blocks all backdoor paths between T and Y

from causal_toolkit.visualization import CausalGraphVisualizer

viz = CausalGraphVisualizer().from_graph_spec(
    edges=[("X", "T"), ("X", "Y"), ("T", "Y"), ("U", "T"), ("U", "Y")],
    treatment="T",
    outcome="Y",
    common_causes=["X"]
)

# Find valid adjustment sets
adjustment_sets = viz.find_adjustment_sets()
print(adjustment_sets)
# [['X']]  # X blocks backdoor path T <- U -> Y? No - U unobserved!
# Actually: backdoor path is T <- X -> Y (blocked by X)
# AND T <- U -> Y (unblocked - needs U observed)

If unobserved confounders exist → backdoor fails → need IV, frontdoor, or sensitivity analysis.

Frontdoor Criterion¶

When direct T→Y path is confounded but there's mediator M: - T causes M - M causes Y - All T→Y paths go through M - No confounder of M→Y (or observed)

pipeline:
  identification:
    strategy: frontdoor
    mediators: ["compliance"]
    treatment: "assignment"
    outcome: "outcome"

Instrumental Variable¶

Z → T → Y, with Z ⊥ Y | T, X - Relevance: Z correlates with T - Exclusion: Z affects Y only through T - Exchangeability: Z independent of confounders

# Two-stage least squares
from causal_toolkit.core.base import EstimatorType
estimate = dowhy.estimate(EstimatorType.TWO_STAGE_LS)

Checking Identification¶

# From CausalModel
model = CausalModel(...)
dowhy = DoWhyWrapper(model)
estimand = dowhy.identify(IdentificationStrategy.BACKDOOR)

# Check assumptions
print(estimand.assumptions.validate())
# [] = no violations, or list of warnings

# Graphical check
from causal_toolkit.visualization.graphs import CausalGraphVisualizer
viz = CausalGraphVisualizer().from_graph_spec(...)
print(viz.compute_do_calculus_steps())
# Shows step-by-step do-calculus derivation