Interpreting Results

After exploring your data, choosing methods, systematically searching, and evaluating candidate models
(see Data Exploration, Algorithm Selection and Assumptions, Running Searches, and Model Evaluation and Markov Checking),
the final step in the causal analysis workflow is interpreting results responsibly.

Causal discovery outputs — whether DAGs, CPDAGs, or PAGs — are not definitive truths.
They are models that fit patterns in the data under specific assumptions.
This page explains what you can reasonably conclude, how to assess robustness, and how to communicate uncertainty clearly.

1. What a Discovered Graph Represents

A graph estimated from data is best understood as:

  • a hypothesis about causal structure,

  • consistent with observed conditional independences,

  • dependent on modeling assumptions (e.g., causal sufficiency, functional form),

  • influenced by algorithm and parameter choices.

It is not a guarantee of causal truth.

Interpretation is about plausibility under assumptions, not certainty.

Your conclusions should always be read as conditional statements:

“If these assumptions hold, then this structure is plausible.”

2. Types of Output and Their Meaning

2.1 Fully Directed Acyclic Graphs (DAGs)

A fully oriented DAG proposes causal directions for all adjacencies.

When they deserve attention:

  • Strong assumptions are made (e.g., no latent confounding)

  • Models pass evaluation diagnostics (e.g., Markov checking)

  • Results align with domain knowledge

How to interpret:

  • Directions are hypotheses, not proofs

  • Emphasize which assumptions support each orientation

2.2 Completed Partially Directed Acyclic Graphs (CPDAGs)

CPDAGs represent a Markov equivalence class of DAGs.

What you can conclude:

  • Adjacencies are supported by the data

  • Some orientations are identifiable

  • Unoriented edges indicate directions that cannot be determined from the data and assumptions alone

Unoriented edges are informative: they mark genuine limits of identifiability.

2.3 Partial Ancestral Graphs (PAGs)

PAGs allow for latent confounders and selection effects.

They use richer edge markings to represent uncertainty about:

  • causal direction

  • the presence of latent common causes

Interpretation focus:

  • Which variables are adjacent

  • Which directions are identifiable

  • Which relationships remain ambiguous due to latent structure

PAGs are often the most appropriate representation when causal sufficiency is doubtful.

3. Interpreting Common Edge Marks

Mark

Meaning

A → B

Oriented edge under stated assumptions

A – B

Adjacent; direction not identifiable

A o→ B

Possible direction with latent uncertainty

A ↔ B

Evidence consistent with latent confounding

A o–o B

Both direction and confounding unresolved

When presenting results, explain edge marks in plain language — most readers will not know their formal meaning.

4. Robustness and Stability

Strong conclusions depend on robustness, not a single run.

Look for features that persist across:

  • algorithms (e.g., PC vs FCI vs score-based),

  • parameter settings (α, penalties),

  • tests or scores,

  • reasonable variations in assumptions.

Edges or orientations that appear only under narrow settings should be treated as tentative.

Grid Search is particularly valuable here, as it highlights which features are stable versus fragile.

5. What You Can Say (With Care)

When supported by diagnostics and robustness:

  • “X and Y are adjacent”

  • “X → Y is plausible under these assumptions”

  • “This structure is stable across methods”

  • “Under causal sufficiency, this orientation holds”

These statements communicate support, not certainty.

6. What You Should Avoid Saying Unqualified

Avoid absolute claims such as:

  • “This is the true causal graph”

  • “This direction is definitely causal”

  • “No edge means no causal relationship”

Absence of an edge may reflect:

  • limited statistical power,

  • violated assumptions,

  • inappropriate tests or scores.

7. Using Background Knowledge

If background knowledge was incorporated (e.g., time tiers, forbidden edges):

  • State what constraints were imposed

  • Explain how they influenced the results

  • Note whether conclusions depend on those constraints

Discrepancies between data-driven results and prior knowledge are important signals and worth investigating.

8. Communicating Uncertainty Clearly

Responsible interpretation includes:

  • identifying stable versus unstable features,

  • explaining unresolved edges or orientations,

  • tying conclusions explicitly to assumptions.

Example phrasing:

“Across algorithms and parameter settings, X–Y is consistently adjacent; however, its orientation varies, so we refrain from asserting a causal direction.”

This approach strengthens credibility rather than weakening conclusions.

9. Documenting Your Analysis

For transparency and reproducibility, record:

  • data exploration findings,

  • assumptions made,

  • algorithms and parameters explored,

  • evaluation results,

  • which conclusions are robust,

  • which remain tentative.

This documentation is part of doing causal analysis well.

10. Summary

Interpreting causal discovery results requires more than reading a graph:

  • Results are conditional on assumptions

  • Robustness matters more than single outputs

  • Simplicity and consistency are guiding principles

  • Uncertainty should be communicated explicitly

Interpretation is where causal discovery becomes scientific reasoning, not just graphical output.

🧭 What’s Next

With careful interpretation in place, you are positioned to:

  • report findings responsibly,

  • refine models with new assumptions or data,

  • integrate results into downstream causal analysis or decision-making.