Recent Advanced in Causal Modelling Using Directed Graphs

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Causal Data Mining
Richard Scheines Dept. of Philosophy, Machine
Learning, Human-Computer Interaction
Carnegie Mellon
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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
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Causal Bayes Networks
The Joint Distribution Factors According to the
Causal Graph, i.e., for all X in V P(V)
?P(XImmediate 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)
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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

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Structural Equation Models

• Equations
• Education ?ed
• Income ????Education????income
• Longevity ????Education????Longevity
• Statistical Constraints
• (?ed, ?Income,?Income ) N(0,?2)
• ?????????2?diagonal
• - no variance is zero

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Tetrad 4 Demo www.phil.cmu.edu/projects/tetrad
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Causal Datamining in Ed. Research

1. Collect Raw Data
2. Build Meaningful Variables
3. Constrain Model Space with Background Knowledge
4. Search for Models
5. Estimate and Test
6. Interpret

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CSR Online
Are Online students learning as much?What
features of online behavior matter?
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CSR Online
Are Online students learning as much?
Raw Data Pitt 2001, 87 studentsFor everyone
Pre-test, Recitation attendance, final examFor
Online Students logged Voluntary question
attempts, online quizzes, requests to print
modules
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CSR Online

• Build Meaningful Variables
• Online 0,1
• Pre-test
• Recitation Attendance
• Final Exam

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CSR Online

• Data Correlation Matrix (corrs.dat, N83)

Pre Online Rec Final
Pre 1.0
Online .023 1.0
Rec -.004 -.255 1.0
Final .287 .182 .297 1.0
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CSR Online

• Background Knowledge
• Temporal Tiers
• Online, Pre
• Rec
• Final

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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

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• Tetrad Demo
• Online vs. Lecture
• Data file corrs.dat

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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)

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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.
  185-200.
• 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, 447-478
• Computation, Causation, Discovery (1999),
  edited by C. Glymour and G. Cooper, MIT Press