GuidesFind adjustment sets, front-door sets and instruments

Find adjustment sets, front-door sets and instruments

Find the variables to adjust for, check a set you already have in mind, and look for front-door sets and instruments when adjustment fails. You'll also list the answers across an equivalence class.

Run the program#

The first graph is a known trap. Z3 confounds X and Y, but it is also a collider: both Z1 and Z2 cause it. W mediates the effect and I affects only X.

from ergodic.graph import cpdag, dag
from ergodic.identification import (
    adjustment_set,
    frontdoor_set,
    ida,
    instruments,
    is_instrument,
    is_valid_adjustment_set,
    minimal_adjustment_set,
)

# 1. Confounders Z1, Z2, Z3, a mediator W and an instrument I.
graph = dag([
    "Z1 -> X", "Z1 -> Z3", "Z2 -> Z3", "Z2 -> Y", "Z3 -> X", "Z3 -> Y",
    "X -> W", "W -> Y", "I -> X",
])

# 2. The canonical adjustment set, and a minimal one.
print("canonical:", sorted(adjustment_set(graph, "X", "Y")))
print("minimal:", sorted(minimal_adjustment_set(graph, "X", "Y")))

# 3. Check sets of your own.
for candidate in [[], ["Z3"], ["Z1", "Z3"], ["Z3", "W"]]:
    print(candidate, is_valid_adjustment_set(graph, "X", "Y", candidate))

# 4. Instruments, then a check with a larger conditioning set.
print("instruments:", instruments(graph, "X", "Y"))
print("Z1 given Z2, Z3:", is_instrument(graph, "Z1", "X", "Y", given=["Z2", "Z3"]))

# 5. With the confounder hidden, adjustment fails but the front door is open.
hidden = dag(["U -> X", "U -> Y", "X -> M", "M -> Y"], latent=["U"])
print("adjustment:", adjustment_set(hidden, "X", "Y"))
print("front-door:", sorted(frontdoor_set(hidden, "X", "Y")))

# 6. On a CPDAG, identify the effect in each member graph.
result = ida(cpdag(["Z --- X", "X --- Y", "Z --- Y"]), "X", "Y")
print(result)
print(sorted(member.strategy for member in result.members))

canonical: ['I', 'Z1', 'Z2', 'Z3']
minimal: ['Z2', 'Z3']
[] False
['Z3'] False
['Z1', 'Z3'] True
['Z3', 'W'] False
instruments: [('I', frozenset())]
Z1 given Z2, Z3: True
adjustment: None
front-door: ['M']
IDA(['X'] -> ['Y'], cpdag: 6/6 identify, strategies=['adjustment', 'null'], agree=False)
['adjustment', 'adjustment', 'adjustment', 'null', 'null', 'null']

• Step 2. The canonical set holds every ancestor of X or Y that X doesn't affect. If any valid set exists, this one is valid. It includes I. That adds no bias when the graph is right, but it usually widens the interval, and if a confounder is missing from the graph it makes that bias larger. {Z2, Z3} is a smaller valid set.
• Step 3. The empty set leaves X <- Z3 -> Y open. {Z3} closes it but opens X <- Z1 -> Z3 <- Z2 -> Y, because conditioning on a collider connects its causes. Adding Z1 closes that path again. W sits on the causal path, so any set holding it is invalid.
• Step 4. I is an instrument with no conditioning. Z1 is one only given both Z2 and Z3; the search tries just the empty set and single variables, so it doesn't list it.
• Step 5. adjustment_set returns None when no valid set exists. The mediator M satisfies the front-door criterion instead.
• Step 6. The class holds 6 DAGs. In 3 the effect is zero, because Y causes X; in 3 it is identified by adjustment. They don't agree, so the class has no single answer.

The functions#

Every set excludes latent nodes, since you can't condition on what you didn't measure.

Adjustment and its checks work on DAGs, ADMGs, CPDAGs, MAGs and PAGs. On a class, a set is valid only when it is valid in every member (the generalized adjustment criterion of Perković et al., 2018). The front-door and instrument functions need a single graph.

Read an IDA result#

ida enumerates the DAGs in a CPDAG and identifies the effect in each. IDA reports n_members, n_identifiable, the strategies and estimands seen, and agree: True when every member identifies and all share one formula. members holds each member's Identification.

Next steps#