# 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.