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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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)

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 1