Check Assumptions

Overview

A Graphical Causal Model (GCM) is a compact way to write assumptions about the data-generating process. The arrows, missing arrows, latent nodes, and bidirected edges all carry substantive claims about which causal relations are present, absent, observed, or omitted from the analysis. For that reason, checking assumptions in a GCM is different from running a conventional statistical diagnostic.

The assumptions encoded by a DAG are not usually testable by a single statistical test. Instead, the goal is to make the assumptions explicit, inspect their role in the identification analysis, and compare alternative graphs when the substantive assumptions are uncertain. In causalinf, GCM assumptions can be retrieved with the method assumptions() after creating a gcm.DAG object.

For identification analysis, causalinf currently records three main assumptions:

Assumption	What it concerns	Why it matters
Correct DAG	Connection between the real data-generating process and the graph	Identification results are conditional on the graph being a defensible representation of the relevant causal relations.
Causal Markov Condition	Connection between the graph and the joint distribution of variables	It links graphical separation statements to conditional independence relations used by do-calculus and adjustment reasoning.
Positivity (Overlap)	Support of the observed variables	It ensures that causal contrasts are defined and estimable in the relevant regions of the covariate distribution.

Retrieve assumptions

Consider this example:

from causalinf import gcm

# use a DAG provided with the package as an example
G = gcm.examples("Front-door")
G.identification_analysis()

Searching for identification by adjustment variables for ACE...done!
Searching for identification by adjustment variables for ACDE...done!
Searching for identification by instrumental variables...done!
Searching for identification by do-calculus...done!

Exposure: D
Outcome: Y        


Average Causal Effect (ACE)
---------------------            
Method: Selection on Observables (SoO)
Identified: False
Not identifiable by adjustment.

Method: do-calculus (do)
Identified: True
Causal probability: p(Y | do(D)) = sum_{Z,Z2} p(Z|D)sum_{D} p(D,Z2)p(Y|Z,D,Z2)

Method: Instrumental Variable (IV)
Identified: False
No instrument available in the DAG.                

Average Controlled Direct Effect (ACDE)
--------------------------------            
Method: Selection on Observables (SoO)
Identified: False
Not identifiable by adjustment.                

Assumptions for identification:
------------------------------
1. Correct DAG
   - Definition: DAG structure matches the true causal relations: (a) A directed arrow from a variable A to a variable B means that there is a causal effect of A on B, which may or may not be zero; (b) Absence of an arrow from a variable C to a variable D implies certainty that C does not cause D; (c) A bidirected arrow between a variable E and a variable F means that they share a common unobserved or latent cause.
   - Scope: Connection between reality and the DAG model
   - Role: Ensures adjustment sets and do-calculus yield the correct identifiable causal effect.
   - Usage: identification
   - Violation: Biased or invalid causal effect estimates and incorrect adjustment sets.            
2. Causal Markov Condition (CMC)
   - Definition: Each variable is independent of its non-descendants given its parents
   - Scope: Connects the DAG and the conditional distribution of each variable
   - Role: Links d-separation to conditional independencies, grounding do-calculus.
   - Usage: identification, discovery
   - Violation: Graph–distribution link breaks and identification results may be incorrect.            
3. Positivity (Overlap)
   - Definition: Each treatment level has a positive probability of occurring, including at all relevant levels of the adjustment variables if they are used for identification.
   - Scope: Variables' distributions
   - Role: Required for the g-formula, IPW, and many identification and estimation strategies.
   - Usage: identification, estimation, inference
   - Violation: Effects are undefined or non-estimable in certain regions of the covariate space.

Use G.assumptions() to retrieve the assumptions associated with a graph. The argument category selects the type of analysis for which the assumptions are used.

G.assumptions()

Categories available:
- estimation
- inference
- identification
- discovery

For identification, use category="identification".

G.assumptions(category="identification")

['DAG structure matches the true causal relations: (a) A directed arrow from a '
 'variable A to a variable B means that there is a causal effect of A on B, '
 'which may or may not be zero; (b) Absence of an arrow from a variable C to a '
 'variable D implies certainty that C does not cause D; (c) A bidirected arrow '
 'between a variable E and a variable F means that they share a common '
 'unobserved or latent cause.',
 'Each variable is independent of its non-descendants given its parents',
 'Each treatment level has a positive probability of occurring, including at '
 'all relevant levels of the adjustment variables if they are used for '
 'identification.']

To include more detail about the scope, role, and possible consequence of violating each assumption, use verbose=True.

G.assumptions(category="identification", verbose=True)

Correct DAG
   - Definition: DAG structure matches the true causal relations: (a) A directed arrow from a variable A to a variable B means that there is a causal effect of A on B, which may or may not be zero; (b) Absence of an arrow from a variable C to a variable D implies certainty that C does not cause D; (c) A bidirected arrow between a variable E and a variable F means that they share a common unobserved or latent cause.
   - Scope: Connection between reality and the DAG model
   - Role: Ensures adjustment sets and do-calculus yield the correct identifiable causal effect.
   - Usage: identification
   - Violation: Biased or invalid causal effect estimates and incorrect adjustment sets.            
Causal Markov Condition (CMC)
   - Definition: Each variable is independent of its non-descendants given its parents
   - Scope: Connects the DAG and the conditional distribution of each variable
   - Role: Links d-separation to conditional independencies, grounding do-calculus.
   - Usage: identification, discovery
   - Violation: Graph–distribution link breaks and identification results may be incorrect.            
Positivity (Overlap)
   - Definition: Each treatment level has a positive probability of occurring, including at all relevant levels of the adjustment variables if they are used for identification.
   - Scope: Variables' distributions
   - Role: Required for the g-formula, IPW, and many identification and estimation strategies.
   - Usage: identification, estimation, inference
   - Violation: Effects are undefined or non-estimable in certain regions of the covariate space.

The verbose output is useful when preparing a report because it separates the definition of each assumption from its role in the analysis.

Interpret the assumptions

Correct DAG

The Correct DAG assumption says that the graph is a defensible representation of the causal relations relevant to the estimand. A directed arrow means that a causal effect may exist; the absence of an arrow means that the analyst is ruling out that direct causal effect; and a bidirected arrow means that the two variables share an unobserved or latent common cause.

This is the central modeling assumption. If it fails, the identification result may still be unaffected in some cases, but in other cases the selected adjustment set, instrumental-variable strategy, or do-calculus result can be wrong.

Causal Markov Condition

The Causal Markov Condition says that each variable is independent of its non-descendants after conditioning on its parents. This assumption is what makes graphical reasoning operational: it connects d-separation in the DAG to conditional independence restrictions in the joint distribution.

For identification, this assumption supports the use of graphical criteria such as adjustment and do-calculus. If the distribution does not behave as the DAG implies, then graphical identification claims may not correspond to the target causal effect.

Positivity

Positivity or overlap says that each treatment level has positive probability in the relevant parts of the covariate distribution. When adjustment variables are used for identification, each treatment level must be possible at the relevant values of those adjustment variables.

This assumption is not only conceptual; it also affects estimation. If overlap is absent, the causal effect may be undefined for part of the target population or may require extrapolation beyond the observed data.

Print assumptions with identification output

Assumptions can also be printed together with identification results. This is useful when the assumptions need to travel with the identified estimand in a report.

from causalinf import gcm

G = gcm.examples("Front-door")
G.identification_analysis(verbose=False)
G.print('identification', identification={"print_assumptions":True})

Exposure: D
Outcome: Y        


Average Causal Effect (ACE)
---------------------            
Method: Selection on Observables (SoO)
Identified: False
Not identifiable by adjustment.

Method: do-calculus (do)
Identified: True
Causal probability: p(Y | do(D)) = sum_{Z,Z2} p(Z|D)sum_{D} p(D,Z2)p(Y|Z,D,Z2)

Method: Instrumental Variable (IV)
Identified: False
No instrument available in the DAG.                

Average Controlled Direct Effect (ACDE)
--------------------------------            
Method: Selection on Observables (SoO)
Identified: False
Not identifiable by adjustment.                

Assumptions for identification:
------------------------------
1. Correct DAG
   - Definition: DAG structure matches the true causal relations: (a) A directed arrow from a variable A to a variable B means that there is a causal effect of A on B, which may or may not be zero; (b) Absence of an arrow from a variable C to a variable D implies certainty that C does not cause D; (c) A bidirected arrow between a variable E and a variable F means that they share a common unobserved or latent cause.
   - Scope: Connection between reality and the DAG model
   - Role: Ensures adjustment sets and do-calculus yield the correct identifiable causal effect.
   - Usage: identification
   - Violation: Biased or invalid causal effect estimates and incorrect adjustment sets.            
2. Causal Markov Condition (CMC)
   - Definition: Each variable is independent of its non-descendants given its parents
   - Scope: Connects the DAG and the conditional distribution of each variable
   - Role: Links d-separation to conditional independencies, grounding do-calculus.
   - Usage: identification, discovery
   - Violation: Graph–distribution link breaks and identification results may be incorrect.            
3. Positivity (Overlap)
   - Definition: Each treatment level has a positive probability of occurring, including at all relevant levels of the adjustment variables if they are used for identification.
   - Scope: Variables' distributions
   - Role: Required for the g-formula, IPW, and many identification and estimation strategies.
   - Usage: identification, estimation, inference
   - Violation: Effects are undefined or non-estimable in certain regions of the covariate space.

The printed assumptions correspond to the identification category. To make the output more detailed, set the global options or pass the corresponding print options in the identification print configuration.

from causalinf import options as opt

opt.set_options(print_assumptions=True, print_assumptions_verbose=True)
G.print(what="identification")

Exposure: D
Outcome: Y        


Average Causal Effect (ACE)
---------------------            
Method: Selection on Observables (SoO)
Identified: False
Not identifiable by adjustment.

Method: do-calculus (do)
Identified: True
Causal probability: p(Y | do(D)) = sum_{Z,Z2} p(Z|D)sum_{D} p(D,Z2)p(Y|Z,D,Z2)

Method: Instrumental Variable (IV)
Identified: False
No instrument available in the DAG.                

Average Controlled Direct Effect (ACDE)
--------------------------------            
Method: Selection on Observables (SoO)
Identified: False
Not identifiable by adjustment.                

Assumptions for identification:
------------------------------
1. Correct DAG
   - Definition: DAG structure matches the true causal relations: (a) A directed arrow from a variable A to a variable B means that there is a causal effect of A on B, which may or may not be zero; (b) Absence of an arrow from a variable C to a variable D implies certainty that C does not cause D; (c) A bidirected arrow between a variable E and a variable F means that they share a common unobserved or latent cause.
   - Scope: Connection between reality and the DAG model
   - Role: Ensures adjustment sets and do-calculus yield the correct identifiable causal effect.
   - Usage: identification
   - Violation: Biased or invalid causal effect estimates and incorrect adjustment sets.            
2. Causal Markov Condition (CMC)
   - Definition: Each variable is independent of its non-descendants given its parents
   - Scope: Connects the DAG and the conditional distribution of each variable
   - Role: Links d-separation to conditional independencies, grounding do-calculus.
   - Usage: identification, discovery
   - Violation: Graph–distribution link breaks and identification results may be incorrect.            
3. Positivity (Overlap)
   - Definition: Each treatment level has a positive probability of occurring, including at all relevant levels of the adjustment variables if they are used for identification.
   - Scope: Variables' distributions
   - Role: Required for the g-formula, IPW, and many identification and estimation strategies.
   - Usage: identification, estimation, inference
   - Violation: Effects are undefined or non-estimable in certain regions of the covariate space.

Compare alternative graphs

When an assumption is uncertain, a useful workflow is to create a second graph that represents the alternative causal claim and then repeat the identification analysis. This does not test which graph is true, but it clarifies whether the causal conclusion depends on the disputed assumption.

For example, the first graph below assumes no unobserved common cause between D and Y. The second graph adds a bidirected edge, representing an omitted common cause.

from causalinf import gcm

dag_without_latent = """
Z -> D
D -> Y
Z -> Y
"""

dag_with_latent = """
Z -> D
D -> Y
Z -> Y
D <-> Y
"""

roles = {"Exposure": "D", "Outcome": "Y"}

G1 = gcm.DAG(dag_without_latent, nodes_role=roles)
G2 = gcm.DAG(dag_with_latent, nodes_role=roles)

G1.identification_analysis(verbose=False)
G2.identification_analysis(verbose=False)

The comparison answers a practical question: does the intended identification strategy survive the alternative graph, or does the causal effect become unidentified under that revised assumption?

Practical checklist

Before moving from a GCM to estimation, it is useful to record the following:

Which arrows are included because a direct causal effect is plausible?
Which arrows are omitted because a direct causal effect is being ruled out?
Which variables are observed, and which relevant common causes are represented as latent or bidirected edges?
Which adjustment, instrumental-variable, or do-calculus strategy is implied by the graph?
Which parts of the graph are uncertain enough to justify a sensitivity analysis or an alternative identification analysis?
Whether positivity is plausible for the treatment and adjustment variables used by the identification strategy.

This checklist should be read together with the more general discussion in Model Assumptions and the identification workflow in Identification Analysis.

References

Ferrari, D. (forthcoming). The Identification of Causal Effects. Cambridge University Press.
Pearl, J. (2009). Causality: Models, Reasoning and Inference. Cambridge University Press.