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

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

Estimation

Estimation

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

Estimation

Coefficient inference vs. Model Fit Coefficient Inference: Null: coefficient = 0, e.g., bX1 X3 = 0 p-value = p(Estimated value bX1 X3 ≥ .4788 | bX1 X3 = 0 & rest of model correct) Reject null (coefficient is “significant”) when p-value < a, a usually = .05

Coefficient inference vs. Model Fit Coefficient Inference: Null: coefficient = 0, e.g., bX1 X3 = 0 p-value = p(Estimated value bX1 X3 ≥ .4788 | 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)) ≥ 5.7137 | Model correctly specified)

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

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

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

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

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)

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”

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

Theoretical Hypothesis

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

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, 141-146. 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

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

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

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