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

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

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

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

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

Same Dependencies for Common Cause & Causal Chain

Same Dependencies for Common Cause & Causal Chain Sequence Can Help

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

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

Colliders Can Identify Causes in Sample Data

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