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Richard Scheines Carnegie Mellon University

Causal Graphical Models II: Applications with Search. Richard Scheines Carnegie Mellon University. Case Studies. Foreign Investment Welfare Reform Online Learning Charitable Giving Stress & Prayer Test Anxiety Causal Connectivity among Brain Regions. Case Studies. Exceedingly simple

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Richard Scheines Carnegie Mellon University

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  1. Causal Graphical Models II: Applications with Search Richard ScheinesCarnegie Mellon University

  2. Case Studies • Foreign Investment • Welfare Reform • Online Learning • Charitable Giving • Stress & Prayer • Test Anxiety • Causal Connectivity among Brain Regions

  3. Case Studies • Exceedingly simple • Background theory weak • Claim: • Not: search output is true • Is: search adds value

  4. Does Foreign Investment in 3rd World Countries cause Political Repression? Case Study 1: Foreign Investment 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

  5. Case Study 1: Foreign Investment Correlations po fi en fi -.175 en -.480 0.330 cv 0.868 -.391 -.430

  6. Case Study 1: Foreign Investment Regression Results po = .227*fi - .176*en + .880*cv SE (.058) (.059) (.060) t 3.941 -2.99 14.6 Interpretation: foreign investment increases political repression

  7. Case Study 1: Foreign Investment Alternatives There is no model with testable constraints (df > 0) in which FI has a positive effect on PO that is not rejected by the data.

  8. Case Study 2: Welfare Reform Single Mothers’ Self-Efficacy, Parenting in the Home Environment, and   Children’s Development in a Two-Wave Study (Social Work Research, 29, 1, 7-20) Aurora Jackson, Richard Scheines

  9. Case Study 2: Welfare Reform Two-Wave Longitudinal Study • Longitudinal Data • Time 1: 1996-97 (N = 188) • Time 2: 1998-99 (N = 178) • Single black mothers in NYC • Current and former welfare recipients • With a child who was 3 – 5 at time 1, and 6 to 8 at time 2

  10. Case Study 2: Welfare Reform Constructs/Scales/Measures • Employment Status • Perceived Self-efficacy • Depressive Symptoms • Quality of Mother/Father Relationship • Father/Child Contact • Quality of Home Environment • Behavior Problems • Cognitive Development

  11. Case Study 2: Welfare Reform Background Knowledge • Tier 1: • Employment Status • Tier 2: • Depression • Self-efficacy • Mother/Father Relationship • Father/Child Contact • Mother’s Parenting/HOME • Tier 3: • Negative Behaviors • Cognitive Development Over 22 million path models consistent with these constraints

  12. Case Study 2: Welfare Reform Conceptual Model c2 = 22.3, df = 20, p = .32 Tetrad Equivalence Class c2 = 18.87, df = 19, p = .46

  13. Case Study 2: Welfare Reform Points of Agreement: • Mother’s Self-Efficacy mediates the effect of Employment on all other variables. • Home environment mediates the effect of all other factors on outcomes: Cog. Develop and Prob. Behaviors Conceptual Model Points of Disagreement: • Depression key cause vs. only an effect Tetrad

  14. Case Study 3: Online Courseware Online Course in Causal & Statistical Reasoning

  15. Case Study 3: Online Courseware Variables • Pre-test (%) • Print-outs (% modules printed) • Quiz Scores (avg. %) • Voluntary Exercises (% completed) • Final Exam (%) • 9 other variables Tier 1 Tier 2 Tier 3

  16. 2002 2003 Case Study 3: Online Courseware Printing and Voluntary Comprehension Checks: 2002 --> 2003

  17. Case Study 4: Charitable Giving Variables Cryder & Loewenstein (in prep) • Tangibility/Concreteness (Exp manipulation) • Imaginability (likert 1-7) • Impact (avg. of 2 likerts) • Sympathy (likert) • Donation ($)

  18. Case Study 4: Charitable Giving Theoretical Model study 1 (N= 94) df = 5, c2 = 52.0, p= 0.0000

  19. Case Study 4: Charitable Giving GES Outputs study 1:df = 5, c2 = 5.88, p= 0.32 study 1:df = 5, c2 = 3.99, p= 0.55

  20. Case Study 4: Charitable Giving Theoretical Model study 2:df = 5, c2 = 8.23, p= 0.14 study 2 (N= 115) df = 5, c2 = 62.6, p= 0.0000 study 2:df = 5, c2 = 7.48, p= 0.18

  21. Build Pure Clusters Output - provably reliable (pointwise consistent): Equivalence class of measurement models over a pure subset of measures True Model Output

  22. Build Pure Clusters • Qualitative Assumptions • Two types of nodes: measured (M) and latent (L) • M L (measured don’t cause latents) • Each m  M measures (is a direct effect of) at least one l  L • No cycles involving M • Quantitative Assumptions: • Each m  M is a linear function of its parents plus noise • P(L) has second moments, positive variances, and no deterministic relations

  23. Specified Model Case Study 5: Stress, Depression, and Religion • MSW Students (N = 127) 61 - item survey (Likert Scale) • Stress: St1 - St21 • Depression: D1 - D20 • Religious Coping: C1 - C20 p = 0.00

  24. Case Study 5: Stress, Depression, and Religion Build Pure Clusters

  25. Case Study 5: Stress, Depression, and Religion • Assume Stress temporally prior: • MIMbuild to find Latent Structure: p = 0.28

  26. Case Study 6: Test Anxiety Bartholomew and Knott (1999), Latent variable models and factor analysis 12th Grade Males in British Columbia (N = 335) 20 - item survey (Likert Scale items): X1 - X20: Exploratory Factor Analysis:

  27. Case Study 6: Test Anxiety Build Pure Clusters:

  28. Case Study 6: Test Anxiety Build Pure Clusters: Exploratory Factor Analysis: p-value = 0.00 p-value = 0.47

  29. MIMbuild Scales: No Independencies or Conditional Independencies p = .43 Uninformative Case Study 6: Test Anxiety

  30. Case Study 7: fMRI Brain Connectivity • Goals: • Identify relatively BIG brain regions (ROIs). • Figure out how they influence one another, with what timing sequences, in producing behaviors of interest. • Figure out individual differences.

  31. Case Study 7: fMRI • Experiment: (Xue and Poldrack, unpublished) • 13 right handed subjects • On each trial, subject judged whether visual stimuli rhymed or not • 8 pairs of words/nonwords presented for 2.5 seconds each in eight 20 second blocks, separated by 20 seconds of visual fixation • TR = 2000 milliseconds • 160 time points.

  32. Case Study 7: fMRI Brain Connectivity • Problems: • Criteria for identifying ROIs • Individuals differ • Brain ROIs • Parameter values • Brain processing is cyclic • Time: • Varying time delays of neuron  ROI BOLD response • Time series sampling rate vs. processing rate • Search Space • 11 ROIs – 323 DAGs

  33. Case Study 7: fMRI ROI Construction • Mean of signal intensity among voxels in a cluster at a time • 1st or ....4th principal component • Average of top X% variance • Maximum variance voxel. • Eyeballs • Etc., etc

  34. Case Study 7: fMRI Example ROIs

  35. Case Study 7: fMRI Brain Connectivity • Individuals differ • Brain ROIs • Parameter values • Assume • same qualitiative causal structure • different quantitative causal structure (mixed effects) • iMAGES search • Apply GES to each subject, 1 step • Take step = max(avg. BIC score) to each search • Repeat

  36. Case Study 7: fMRI Time Problem 1 • fMRI recordings at time intervals can be analyzed as a collection of independent cases. • Or, they can be analyzed as an auto-regressive time series. • Which is better? • No general answer. • But if you think the neural activities measured at time t influence the measurements at time t+1 then the data should be treated as a lag 1 auto-regressive time series. • But then Granger causality isn’t a consistent estimator of causal relations.

  37. Case Study 7: fMRI Granger Causality Corrected Causal processes faster than the sampling rate: Xt Xt+1 X Yt Yt+1 Y Zt Zt+1 Z Regress on t variables Apply GES to the RESIDUALS of the regression (Demiralp, Hoover) NO False path

  38. Case Study 7: fMRI Time Problem 2 • Varying time delays : neurons  BOLD responses • Try all time shifts of one or two units over all subsets of 3 vars, choose shift that leads to best likelihoods

  39. Lag 0 result Lag 1 result.

  40. Case Study 7: fMRI Simulation Studies: • 11 ROIs, each consisting of 50 simulated neurons: • Neuron output spikes simulated by thresholding a tanh function of the sum of neuron inputs. • Excitatory feedback • Random subset of neurons in one ROI input to random subset of neurons in an “effectively connected ROI” • Measured variables = BOLD function of sum of ROI neurons + Gaussian error with variance = error variances of empirical measured variables in the X/P experiment.

  41. Case Study 7: fMRI Simulate the Xue/Poldrack Experiment Time Series: • Repeat 10 times: • Randomly generate a graphical structure with 11 nodes and 11 (feedforward) directed edges • Randomly select a subset of simulated ROIs. • Generate data • Randomly shift 0 to 3 variables one or 2 time steps forward. • Apply the iMAGES method with 0 lag and 1 lag, with backshifting. • Tabulate the errors.

  42. Case Study 6: fMRI Simulation Results 0 Lag: Average number of false positive edges: 0.7 Average number of mis-directed edges: 1.6 1 Lag Residuals: Average number of false positive edges: 1.2 Average number of mis-directed edges: 1.8

  43. Other Cases Climate Research • Glymour, Chu, , Teleconnections Epidemiology • Scheines, Lead & IQ Economics • Bessler, Pork Prices • Hoover, multiple • Cryder & Loewenstein, Charitable Giving Biology • Shipley, • SGS, Spartina Grass Educational Research • Easterday, Bias & Recall • Laski, Numerical coding Neuroscience • Glymour & Ramsey, fMRI

  44. Straw Men! • Model Search ignores theory • Model Search hides assumptions • Model Search needs more assumptions than standard statistical models

  45. References General • Spirtes, P., Glymour, C., Scheines, R. (2000). Causation, Prediction, and Search, 2nd Edition, MIT Press. • Pearl, J. (2000). Causation: Models of Reasoning and Inference, Cambridge University Press. Biology • Chu, Tianjaio, Glymour C., Scheines, R., & Spirtes, P, (2002). A Statistical Problem for Inference to Regulatory Structure from Associations of Gene Expression Measurement with Microarrays. Bioinformatics, 19: 1147-1152. • Shipley, B. Exploring hypothesis space: examples from organismal biology. Computation, Causation and Discovery. C. Glymour and G. Cooper. Cambridge, MA, MIT Press. • Shipley, B. (1995). Structured interspecific determinants of specific leaf area in 34 species of herbaceous angeosperms. Functional Ecology 9.

  46. References Scheines, R. (2000). Estimating Latent Causal Influences: TETRAD III Variable Selection and Bayesian Parameter Estimation: the effect of Lead on IQ, Handbook of Data Mining, Pat Hayes, editor, Oxford University Press. Jackson, A., and Scheines, R., (2005). Single Mothers' Self-Efficacy, Parenting in the Home Environment, and Children's Development in a Two-Wave Study, Social Work Research , 29, 1, pp. 7-20. Timberlake, M. and Williams, K. (1984). Dependence, political exclusion, and government repression: Some cross-national evidence. American Sociological Review 49, 141-146.

  47. References Economics Akleman, Derya G., David A. Bessler, and Diana M. Burton. (1999). ‘Modeling corn exports and exchange rates with directed graphs and statistical loss functions’, in Clark Glymour and Gregory F. Cooper (eds) Computation, Causation, and Discovery, American Association for Artificial Intelligence, Menlo Park, CA and MIT Press, Cambridge, MA, pp. 497-520. Awokuse, T. O. (2005) “Export-led Growth and the Japanese Economy: Evidence from VAR and Directed Acyclical Graphs,” Applied Economics Letters 12(14), 849-858. Bessler, David A. and N. Loper. (2001) “Economic Development: Evidence from Directed Acyclical Graphs” Manchester School 69(4), 457-476. Bessler, David A. and Seongpyo Lee. (2002). ‘Money and prices: U.S. data 1869-1914 (a study with directed graphs)’, Empirical Economics, Vol. 27, pp. 427-46. Demiralp, Selva and Kevin D. Hoover. (2003) !Searching for the Causal Structure of a Vector Autoregression," Oxford Bulletin of Economics and Statistics 65(supplement), pp. 745-767. Haigh, M.S., N.K. Nomikos, and D.A. Bessler (2004) “Integration and Causality in International Freight Markets: Modeling with Error Correction and Directed Acyclical Graphs,” Southern Economic Journal 71(1), 145-162. Sheffrin, Steven M. and Robert K. Triest. (1998). ‘A new approach to causality and economic growth’, unpublished typescript, University of California, Davis.

  48. References Economics Swanson, Norman R. and Clive W.J. Granger. (1997). ‘Impulse response functions based on a causal approach to residual orthogonalization in vector autoregressions’, Journal of the American Statistical Association, Vol. 92, pp. 357-67. Demiralp, S., Hoover, K., & Perez, S. A Bootstrap Method for Identifying and Evaluating a Structural Vector Autoregression Oxford Bulletin of Economics and Statistics, 2008, 70, (4), 509-533 - Searching for the Causal Structure of a Vector Autoregression Oxford Bulletin of Economics and Statistics, 2003, 65, (s1), 745-767 • Kevin D. Hoover, SelvaDemiralp, Stephen J. Perez, Empirical Identification of the Vector Autoregression: The Causes and Effects of U.S. M2*, This paper was written to present at the Conference in Honour of David F. Hendry at Oxford University, 2325 August 2007. • SelvaDemiralp and Kevin D. Hoover , Searching for the Causal Structure of a Vector Autoregression, OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 65, SUPPLEMENT (2003) 0305-9049 A. Moneta, and P. Spirtes “Graphical Models for the Identification of Causal Structures in Multivariate Time Series Model”, Proceedings of the 2006 Joint Conference on Information Sciences, JCIS 2006, Kaohsiung, Taiwan, ROC, October 8-11,2006, Atlantis Press, 2006.

  49. Extra

  50. Lead and IQ: Variable Selection Final Variables (Needleman) -lead baby teeth -fab father’s age -mab mother’s age -nlb number of live births -med mother’s education -piq parent’s IQ -ciq child’s IQ

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