Causal Diagram Construction

Causal Diagram Construction

Construct a directed acyclic graph (DAG) representing the causal structure of a problem before any data analysis. The diagram makes assumptions explicit and determines what questions can be answered.

When to Use

• User presents a data analysis problem and wants to understand relationships
• Before running any statistical analysis on observational data
• User asks "What causes what?" or "How are these variables related?"
• A/B test interpretation requires understanding of causal structure
• User wants to identify confounders, mediators, or colliders
• Someone confuses correlation with causation and needs clarity
• Research design requires explicit causal assumptions

Inputs

The Causal Diagram Framework

Step 1: Identify All Relevant Variables

List all variables that might be involved in the causal system:

Questions to ask:

• What is the treatment/exposure of interest (X)?
• What is the outcome of interest (Y)?
• What might affect both X and Y (potential confounders)?
• What might be caused by X and cause Y (mediators)?
• What might be affected by both X and other variables (colliders)?
• What background factors set the context (exogenous variables)?

Important: Include variables even if unmeasured. The diagram represents the true causal structure, not just measured variables.

Step 2: Determine Causal Directions

For each pair of related variables, ask:

• Does A cause B, or B cause A, or neither?
• Is there a common cause creating spurious association?
• Is this a definitional relationship or a causal one?

Key principle: Causation is asymmetric. If A causes B, then intervening on A changes B, but intervening on B does not change A.

When uncertain about direction:

• Consider temporal order (causes precede effects)
• Consider manipulation (can you intervene on A to change B?)
• Consider mechanisms (is there a plausible causal pathway?)

Step 3: Draw the Graph

Create the directed acyclic graph (DAG):

• Each variable is a node
• Draw an arrow from cause to effect
• No cycles allowed (A cannot cause B which causes A)
• Missing arrows are assertions of non-causation

Notation:

A -> B       A causes B
A -> M -> B  M mediates A's effect on B
A <- C -> B  C confounds A and B
A -> D <- B  D is a collider
U (dashed)   Unmeasured variable

Step 4: Verify the Structure

Check the diagram for:

• Completeness: Are all relevant variables included?
• Direction correctness: Does each arrow point from cause to effect?
• Missing paths: Are there potential relationships not represented?
• Impossible structures: Are there cycles? (If so, reconsider)
• Testable implications: What conditional independencies does this imply?

Step 5: Identify Key Structural Features

Classify paths between treatment (X) and outcome (Y):

Causal paths (what we want to estimate):

• Paths where all arrows point from X toward Y
• These transmit the causal effect

Backdoor paths (confounding):

• Paths with an arrow into X
• These create spurious association
• Must be blocked for causal identification

Frontdoor paths (mediation):

• Causal paths through intermediate variables
• May allow identification via frontdoor criterion

Collider paths:

• Paths blocked by colliders
• Conditioning on colliders opens them (bias!)

Workflow

Step 1: Gather and Review Inputs

Collect all relevant information:

• Review the provided data and context
• Identify key parameters and constraints
• Clarify any ambiguities or missing information
• Establish success criteria

Step 2: Analyze the Situation

Perform systematic analysis:

• Identify patterns and relationships
• Evaluate against established frameworks
• Consider multiple perspectives
• Document key findings

Step 3: Generate Recommendations

Create actionable outputs:

• Synthesize insights from analysis
• Prioritize recommendations by impact
• Ensure recommendations are specific and measurable
• Consider implementation feasibility

Output Format

## Causal Diagram: [Problem Description]

### Variables Identified

| Variable | Role | Measured? | Description |
|----------|------|-----------|-------------|
| X | Treatment/Exposure | Yes/No | [What it represents] |
| Y | Outcome | Yes/No | [What it represents] |
| [Var 1] | Confounder/Mediator/Collider | Yes/No | [Description] |
| [Var 2] | Confounder/Mediator/Collider | Yes/No | [Description] |

### Causal Diagram

[ASCII or description of the DAG]

### Path Analysis

**Causal paths (X to Y):**
1. [Path 1]: X -> ... -> Y
2. [Path 2]: X -> ... -> Y

**Backdoor paths (confounding):**
1. [Path 1]: X <- ... -> Y (blocked by: [variable] / open)
2. [Path 2]: X <- ... -> Y (blocked by: [variable] / open)

**Colliders identified:**
- [Collider variable]: Do not condition on this (would open path)

### Structural Implications

**What we can estimate:**
[Given this structure, what causal effects are identifiable?]

**What we cannot estimate:**
[What would require additional assumptions or data?]

**Critical assumptions:**
[What must be true for this diagram to be correct?]

### Recommendations

[What analysis is appropriate given this structure?]
[What variables should be controlled for?]
[What data would strengthen the analysis?]

Key Concepts for Diagram Construction

Confounders

• Common causes of treatment and outcome
• Create backdoor paths that must be blocked
• Example: Socioeconomic status affects both education and health

Mediators

• Variables on the causal path between treatment and outcome
• Controlling for mediators removes (part of) the causal effect
• Example: Tar deposits mediate smoking -> lung cancer

Colliders

• Variables caused by two other variables
• Conditioning on a collider opens a spurious path
• Example: Being in hospital (caused by both disease and accident)

Selection Bias

• Occurs when analyzing a selected sample
• Often involves conditioning on a collider
• Example: Analyzing only hospitalized patients

Common Diagram Patterns

Simple Confounding

    C
   / \
  v   v
  X   Y

C confounds X-Y relationship. Control for C.

Mediation

X -> M -> Y

M mediates X's effect on Y. Don't control for M to get total effect.

Collider Bias

X -> D <- Y

D is a collider. Never condition on D.

Unmeasured Confounding

    U (unmeasured)
   / \
  v   v
  X   Y

Backdoor path through U cannot be blocked by conditioning.

Frontdoor Pattern

    U (unmeasured)
   / \
  v   v
  X   Y
  |   ^
  v   |
  M --+

Can identify X->Y effect via M even with unmeasured U.

Constraints

• The diagram represents your assumptions, not discovered truth
• All causal conclusions depend on the diagram being correct
• Unmeasured confounders are common and often undetectable
• No diagram can be proven correct from data alone
• Direction of causation requires domain knowledge, not statistics
• Cycles indicate you need a more sophisticated model (e.g., feedback systems)

Error Handling

Outputs

Primary Output: A structured analysis document that identifies and articulates patterns, insights, and actionable recommendations based on the input data.

Format:

## Analysis: [Topic]

### Key Findings
- [Finding 1]
- [Finding 2]
- [Finding 3]

### Recommendations
1. [Action 1]
2. [Action 2]
3. [Action 3]

Anti-Patterns to Avoid

Example

Input: "We found that people who drink coffee have lower rates of depression. Is coffee protective?"

Output:

Causal Diagram: Coffee and Depression

Variables Identified

Causal Diagram

     Genetics         SES        Social Activity
        |              |               |
        v              v               v
    +---+---+      +---+---+      +----+----+
    |       |      |       |      |         |
    v       v      v       v      v         v
  Coffee   Depression <---------+         Sleep
    |         ^                             |
    |         |                             |
    v         |                             v
  Energy -----+----------------------------Depression

Simplified version focusing on key paths:

        SES
       /   \
      v     v
   Coffee  Depression
      |       ^
      v       |
   Energy ---+

Path Analysis

Causal paths (Coffee to Depression):

1. Coffee -> Energy -> Depression (potential protective mechanism)
2. Coffee -> Depression (direct effect, if any)

Backdoor paths (confounding):

1. Coffee <- SES -> Depression (OPEN - must control for SES)
2. Coffee <- Genetics -> Depression (OPEN - usually unmeasured)
3. Coffee <- Social Activity -> Depression (OPEN - may be measurable)

Colliders identified:

• None in simplified structure

Structural Implications

What we can estimate:

• If SES, social activity, and other confounders are measured and controlled, we can estimate the causal effect of coffee on depression
• However, genetic confounding is likely unmeasured

What we cannot estimate:

• The causal effect if genetic confounding exists and is unmeasured
• We would need a natural experiment or instrumental variable

Critical assumptions:

• SES captures most socioeconomic confounding
• No reverse causation (depression doesn't cause coffee drinking)
• Energy is a mediator, not a confounder

Recommendations

Your observed association (coffee drinkers have less depression) likely reflects multiple phenomena:

1. Possible causal effect: Coffee may genuinely improve mood via energy/alertness
2. Likely confounding: Higher SES enables coffee habit and protects against depression
3. Possible reverse causation: Depressed people may drink less coffee (fatigue, anhedonia)

To analyze this properly:

• Control for SES, social activity, and other measured confounders
• Acknowledge genetic confounding cannot be controlled
• Consider longitudinal data to address reverse causation
• A randomized trial would be definitive but impractical

Bottom line: The association is real, but calling it "protective" requires believing the diagram has no unmeasured confounders. Given the likelihood of genetic confounding, caution is warranted.

"You cannot analyze this data until you draw the diagram. Once you draw the arrows, the mathematics tells you what you can and cannot conclude."

Integration

This skill is part of the Judea Pearl expert persona. Use it as the first step in any causal analysis. It pairs with:

• ladder-classification to determine what type of question is being asked
• confounding-diagnosis to analyze the backdoor paths identified
• counterfactual-reasoning for "what if" questions after structure is established