## Causal Diagram: Three-Level Model of Fairness in Educational Outcomes
### Overview
The diagram illustrates a three-level causal model examining how protected attributes (race, sex) influence educational outcomes (FYA) through observable/unobservable factors. It uses color-coded nodes and directional arrows to represent causal relationships, mediators, and error terms.
### Components/Axes
- **Nodes**:
- **Blue**: Protected Attributes (RACE, SEX)
- **Purple**: Unfair Observables (GPA, LSAT)
- **Orange**: Outcome (FYA)
- **Yellow**: Fair Observable (X_fair)
- **Green**: Fair Unobservable (K)
- **Dashed Green**: Error Terms (ε_GPA, ε_LSAT)
- **Arrows**:
- Solid arrows: Direct causation
- Dotted arrows: Additive noise
- Dashed arrows: Causal paths seen by Conditional Fairness Preservation (CFP)
- **Legend**: Located at the bottom, mapping colors to node types.
### Detailed Analysis
#### Level-One
- **Protected Attributes** (RACE, SEX) directly influence **Unfair Observables** (GPA, LSAT).
- **Unfair Observables** collectively affect the **Outcome** (FYA) through a **Fair Observable** (X_fair).
- **Additive Noise** (dotted lines) connects RACE/SEX to X_fair, indicating unmeasured confounding.
#### Level-Two
- Introduces **Fair Unobservable** (K) as a mediator between Unfair Observables (GPA, LSAT) and Outcome (FYA).
- K is influenced by both GPA and LSAT, suggesting it captures latent fairness-related factors.
- X_fair remains a direct predictor of FYA, now alongside K.
#### Level-Three
- Adds **Error Terms** (ε_GPA, ε_LSAT) as dashed green nodes, representing unobserved variability in GPA/LSAT.
- These errors directly influence FYA, acknowledging measurement limitations or omitted variables.
### Key Observations
1. **Protected Attributes** (RACE, SEX) exert influence through both observable (GPA, LSAT) and unobservable pathways.
2. **Mediation by K**: The fair unobservable K partially mediates the effect of GPA/LSAT on FYA, suggesting latent fairness mechanisms.
3. **Error Terms**: Unobserved variability in GPA/LSAT (ε_GPA, ε_LSAT) directly impacts FYA, highlighting model uncertainty.
4. **Causal Flow**: Protected attributes → Unfair Observables → Outcome, with K and X_fair as fairness-correcting mediators.
### Interpretation
This model demonstrates how protected attributes may indirectly affect educational outcomes through observable metrics (GPA, LSAT) and unobservable factors (K). The inclusion of K as a fairness unobservable suggests that traditional metrics alone may not capture equity dynamics. The error terms emphasize the limitations of relying solely on observed data. The diagram implies that fairness interventions should address both observable metrics (via X_fair) and latent factors (K) to mitigate bias in outcomes like FYA. The additive noise in Level-One indicates that racial/sexual disparities may persist even after accounting for observed variables, pointing to systemic biases beyond individual-level factors.
