Causal Modeling with TETRAD

1. July, 23-24, 1999 Richard Scheines Dept. of Philosophy Carnegie Mellon University Session 5: Search Algorithms 2 Causal Modeling with TETRAD

2. Search for Patterns • Adjacency: • X and Y are adjacent if they are dependent conditional on all subsets that don’t include them • X and Y are not adjacent if they are independent conditional on any subset that doesn’t include them

3. Search

4. Search

5. Search: Adjacency

6. Search: Adjacency

8. Search: Orientation Patterns

9. Search: Orientation PAGs

10. Search: Orientation Away from Collider

11. Search: Orientation After Orientation Phase X1 || X2 X1 || X4 | X3 X2 || X4 | X3

12. Search Algorithms in TETRAD 3 • PC Algorithm • Input: Independence facts, {time order, required causes, prohibited causes} • Assumes no unmeasured common causes (Causal Sufficiency) • Output: Pattern • FCI Algorithm • Input: Independence facts, {time order, required causes, prohibited causes} • Does not assume Causal Sufficiency • Output: PAG

13. Search Algorithms in TETRAD 3: The Build Module

14. DEMO Build

15. Build • Create a graph among {X1,X2,X3,X4} • Create a SEM model • Generate data N=2000 • Give data to neighbor • Run build twice on data from neighbor • PC • FCI • Compare output with neighbor

16. Applications: Regression to select Causes • Y = 0 + 1X1 + 2X2 + .....nXn +  • Causal Interpretation of regression model: Edge from Xi Y just in case i 0. • Y = 1X1 + 2X2 + 3X3 + 2= 0 corresponds to:

17. Applications: Causal Regression Let the other regressors O = {X1, X2,....,Xi-1, Xi+1,...,Xn} i = 0 if and only if Xi,Y.O = 0 In a multivariate normal distribuion, Xi,Y.O = 0if and only if Xi || Y | O

18. Applications: Causal Regression

19. Applications: Causal Regression

20. Detecting a Causal Relation 1. From Assuming Z prior to X and Y 2. From Assuming nothing about time order

21. Detecting a Causal Relation 1. From Assuming Z prior to X and Y

22. Detecting a Causal Relation

23. The Instruments

24. The Causal Relation

25. Detecting a Causal Relation 1. Find a triple Z1, Z2, X s.t. - Z1_||_ Z2 - Z1 strongly associated with X - Z2 strongly associated with X 2. Find a Y s.t. - Y strongly associated with X - Y _||_ {Z1Z2} | X

26. Parallel to Randomized Trials X treatment - Y response We need a Z that is: 1) Into X Z o X 2) No direct connection to Y except through X

27. Parallel to Randomized Trials X treatment - Y response We need a Z that is: 1) Into X : Z o X 2) No direct connection to Y except through X: 3) Z _||_ Y | X - no common cause of X - Y.

28. Sewell and Shaw College Plans 10,318 Wisconsin high school seniors. Variables sex [male = 0, female = 1] iq = Intelligence Quotient [least = 0, ... highest = 3] cp = college plans [yes = 0, no = 1] pe = parental encouragement [0 = low, 1 = high] ses = socioeconomic status [0 = lowest, ... 3 = highest]

29. The Causes of College Plans Questions: 1) Do sex, IQ, socio-economic status, and parental encouragement have any influence on college plans? 2) Does SES influence iq?