1. Center for Causal Discovery: Summer Short Course/Datathon - 2018
June 11-15, 2018
Carnegie Mellon University

2. Outline Models  Data Representing/Modeling Causal Systems
Estimation and Model fit
Hands on with Real Data
Models  Data
Markov Axiom and D-separation
Model Equivalence
Model Search

3. Estimation

4. Estimation

5. Tetrad Demo and Hands-on
Build the standardized SEM IM shown below
Generate simulated data N=1000
Estimate model.
Save session as “Estimate1”

6. Estimation

7. Coefficient inference vs. Model Fit
Coefficient Inference: Null: coefficient = 0, e.g., bX1 X3 = 0
p-value = p(Estimated value bX1 X3 ≥ | bX1 X3 = 0 & rest of model correct)
Reject null (coefficient is “significant”) when p-value < a, a usually = .05

8. Coefficient inference vs. Model Fit
Coefficient Inference: Null: coefficient = 0, e.g., bX1 X3 = 0
p-value = p(Estimated value bX1 X3 ≥ | bX1 X3 = 0 & rest of model correct)
Reject null (coefficient is “significant”) when p-value < < a, a usually = .05,
Model fit: Null: Model is correctly specified (constraints true in population)
p-value = p(f(Deviation(Sml,S)) ≥ | Model correctly specified)

9. Coefficient inference vs. Model Fit
bX1 X3
coefficient
Model fit c2 df
Null: bX1 X3 = 0
Null: Model is correctly specified
p-value
Can reject 0
Significant edge
Can reject correct specification,
Model not correctly specified
< .05
Can’t reject 0,
insignificant edge
Can’t reject correct specification,
model may be correctly specified
p-value
> .05

10. Model Fit Specified Model True Model Implied Covariance Matrix
Population Covariance Matrix X1 X2 X3 1 b1
b1*b2 b2 X1 X2 X3 1 .6 .3 .5
b1 = rX1,X2 = ~ .6
b2 = rX2,X3 = ~ .5
b1 b2 = ~ .3 = rX1,X3

11. Model Fit ≠ rX1,X3 = ~ .5 Specified Model True Model
Implied Covariance Matrix
Population Covariance Matrix X1 X2 X3 1 b1
b1*b2 b2 X1 X2 X3 1 .6 .5
b1 = rX1,X2 = ~ .6
b2 = rX2,X3 = ~ .5
b1 b2 = ~ .3 = rX1,X3
≠ rX1,X3 = ~ .5

12. Model Fit Specified Model True Model Implied Covariance Matrix
Population Covariance Matrix X1 X2 X3 1 b1
b1*b2 b2 X1 X2 X3 1 .6 .5
Unless rX1,X3 = rX1,X2 rX2,X3
Estimated Covariance Matrix ≠ Sample Covariance Matrix

13. Model Fit Specified Model True Model Implied Covariance Matrix
Population Covariance Matrix X1 X2 X3 1 b1
b1*b2 b2 X1 X2 X3 1 .6 .5
Model fit: Null: Model is correctly specified (constraints true in population)
rX1,X3 = rX1,X2 rX2,X3
p-value = p(f(Deviation(Sml,S)) ≥ c2 | Model correctly specified)

14. Tetrad Demo and Hands-on
Create two DAGs with the same variables – each with one edge flipped, and attach a SEM PM to each new graph (copy and paste by selecting nodes, Ctl-C to copy, and then Ctl-V to paste)
Estimate each new model on the data produced by original graph
Check p-values of:
Edge coefficients
Model fit
Save session as: “estimation2”

15. Charitable Giving What influences giving? Sympathy? Impact?
"The Donor is in the Details", Organizational Behavior and Human Decision Processes, Issue 1, 15-23, C. Cryder, with G. Loewenstein, R. Scheines.
N = 94
TangibilityCondition [1,0] Randomly assigned experimental condition
Imaginability [1..7] How concrete scenario I
Sympathy [1..7] How much sympathy for target
Impact [1..7] How much impact will my donation have
AmountDonated [0..5] How much actually donated 1

16. Theoretical Hypothesis

17. Tetrad Demo and Hands-on
Load charity.txt (tabular – not covariance data)
Build graph of theoretical hypothesis
Build SEM PM from graph
Estimate PM, check results

18. Foreign Investment
Does Foreign Investment in 3rd World Countries inhibit Democracy?
Timberlake, M. and Williams, K. (1984). Dependence, political exclusion, and government repression: Some cross-national evidence. American Sociological Review 49,
N = 72
PO degree of political exclusivity
CV lack of civil liberties
EN energy consumption per capita (economic development)
FI level of foreign investment 1

19. Tetrad Demo and Hands-on
Load tw.txt (this IS covariance data)
Do a regression
Manually build an alternative hypotheses, Graph - SEM PM, SEM IM
Estimate PM, check results

20. College Plans (Shaw,1979) 10,000 HS Seniors – Madison, WI Sex: 1,2
IQ: 1,2,3,4
SES: 1,2,3,4
PE: 1,2
CP: 1,2

21. College Plans (Hands-on)
Load in College_plans_data
Use file: College_plans_data
Set Variables = discrete
Attach Data  Graph
Build plausible graph
Add PM (input Graph and Data)
Add Estimator
Estimate Model