1. Graphical Representation of Independence among 3 Variables
Wednesday, November 02, 2016
Farrokh Alemi, PhD.

2. Causal Chain
D: Diabetes
R: Renal Complication
S: Survival

3. Dependencies in Chains
D: Diabetes
R: Renal Complication
S: Survival
D and R are dependent
R and S are dependent
D and S are likely dependent
Conditional on R, D and S are independent

4. K: Kidney Complication
Common Cause
D: Diabetes
R: Renal Complication
K: Kidney Complication

5. Dependencies for Common Causes
D: Diabetes
R: Renal Complication
K: Kidney Complication
D and R are dependent
D and K are dependent
R and K are likely dependent
Conditional on R, D and S are independent

6. Same Dependencies for Common Cause & Causal Chain

7. Same Dependencies for Common Cause & Causal Chain
Sequence Can Help

8. Common Effect (Collider)
D: Diabetes
F: Fall
S: Survival

9. Dependencies of Common Effects
D: Diabetes
F: Fall
S: Survival
D and S are dependent
F and S are dependent
D and F are independent
Conditional on S, D and F are dependent

10. Colliders Can Identify Causes in Sample Data

11. Draw the Network Nodes in Network Assumption X, Y, Z I(X,Y)
I(X,Y), Not I(X,Y|Z)
I(X,Y), I(X,Y|Z), Y measured last
X, Y, Z, W
I(X,Y), I(X,Y|Z), I({X,Y},W|Y), W measured last
I(X,Y), I(Z,W), and measured in order given