1. Causal Data Mining Richard Scheines
Dept. of Philosophy, Machine Learning, &
Human-Computer Interaction
Carnegie Mellon

2. Causal Graphs Causal Graph G = {V,E}
Each edge X  Y represents a direct causal claim:
X is a direct cause of Y relative to V
Chicken Pox
1. don’t define causality - but will introduce axioms to connect probability to causality
2. many fields proceed without agreement on definition - probability, “force” in mechanics, interpretation of quantum mechanics, etc.
3. a number of different kinds of graphs represent probability distributions and independence - advantage of directed graphs is also represents causal relations
4. will introduce several extensions

3. Causal Bayes Networks The Joint Distribution Factors
According to the Causal Graph,
i.e., for all X in V
P(V) = P(X|Immediate Causes of(X))
P(S = 0) = .7
P(S = 1) = .3
P(YF = 0 | S = 0) = .99 P(LC = 0 | S = 0) = .95
P(YF = 1 | S = 0) = .01 P(LC = 1 | S = 0) = .05
P(YF = 0 | S = 1) = .20 P(LC = 0 | S = 1) = .80
P(YF = 1 | S = 1) = .80 P(LC = 1 | S = 1) = .20
P(S,YF, LC) = P(S) P(YF | S) P(LC | S)

4. Structural Equation Models
Causal Graph
Structural Equations:
One Equation for each variable V in the graph:
V = f(parents(V), errorV)
for SEM (linear regression) f is a linear function
Statistical Constraints:
Joint Distribution over the Error terms
1. example of recursive structural equation model without correlated errors
2. can show that assumption of independence of errors guarantees correctness of probabilitic interpretation
3. this represents both probability and causality

5. Structural Equation Models
Causal Graph
Equations:
Education = ed
Income =Educationincome
Longevity =EducationLongevity
Statistical Constraints:
(ed, Income,Income ) ~N(0,2)
2diagonal
- no variance is zero
SEM Graph
(path diagram)
1. example of recursive structural equation model without correlated errors
2. can show that assumption of independence of errors guarantees correctness of probabilitic interpretation
3. this represents both probability and causality

6. Tetrad 4: Demo www.phil.cmu.edu/projects/tetrad
1. don’t define causality - but will introduce axioms to connect probability to causality
2. many fields proceed without agreement on definition - probability, “force” in mechanics, interpretation of quantum mechanics, etc.
3. a number of different kinds of graphs represent probability distributions and independence - advantage of directed graphs is also represents causal relations
4. will introduce several extensions

7. Causal Datamining in Ed. Research
Collect Raw Data
Build Meaningful Variables
Constrain Model Space with Background Knowledge
Search for Models
Estimate and Test
Interpret

8. CSR Online
Are Online students learning as much? What features of online behavior matter?

9. Are Online students learning as much?
CSR Online
Are Online students learning as much?
Raw Data : Pitt 2001, 87 students For everyone: Pre-test, Recitation attendance, final exam For Online Students: logged: Voluntary question attempts, online quizzes, requests to print modules

10. CSR Online Build Meaningful Variables: Online [0,1] Pre-test [%]
Recitation Attendance [%]
Final Exam [%]

11. CSR Online Data: Correlation Matrix (corrs.dat, N=83) Pre Online Rec
Final
1.0
.023
-.004
-.255
.287
.182
.297

12. CSR Online
Background Knowledge:
Temporal Tiers:
Online, Pre
Rec
Final

13. CSR Online Model Search: No latents (patterns – with PC or GES)
- no time order : 729 models
- temporal tiers: 96 models)
With Latents (PAGs – with FCI search)
- no time order : 4,096
- temporal tiers: 2,916

14. Tetrad Demo
Online vs. Lecture
Data file: corrs.dat

15. Estimate and Test: Results
Model fit excellent
Online students attended 10% fewer recitations
Each recitation gives an increase of 2% on the final exam
Online students did 1/2 a Stdev better than lecture students (p = .059)

16. References
An Introduction to Causal Inference, (1997), R. Scheines, in Causality in Crisis?, V. McKim and S. Turner (eds.), Univ. of Notre Dame Press, pp
Causation, Prediction, and Search, 2nd Edition, (2000), by P. Spirtes, C. Glymour, and R. Scheines ( MIT Press)
Causality: Models, Reasoning, and Inference, (2000), Judea Pearl, Cambridge Univ. Press
“Causal Inference,” (2004), Spirtes, P., Scheines, R.,Glymour, C., Richardson, T., and Meek, C. (2004), in Handbook of Quantitative Methodology in the Social Sciences, ed. David Kaplan, Sage Publications,
Computation, Causation, & Discovery (1999), edited by C. Glymour and G. Cooper, MIT Press 1