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Causality Triangle Presentation

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Causality Triangle Presentation

  1. 1. Variations and Causal Assumptions Epistemological Remarks on Causal Modelling Federica Russo Université Catholique de Louvain Centre for Philosophy of Natural and Social Science (LSE)
  2. 2. Overview <ul><li>Different Causal Domains </li></ul><ul><ul><li>Metaphysics </li></ul></ul><ul><ul><li>Epistemology </li></ul></ul><ul><ul><li>Methodology </li></ul></ul><ul><li>The Epistemology of Causality </li></ul><ul><ul><li>The Rationale of Causality </li></ul></ul><ul><ul><ul><li>Structural Equation Models </li></ul></ul></ul><ul><ul><ul><li>Covariance Structure Models </li></ul></ul></ul><ul><ul><ul><li>Suppes’ Probabilistic Theory </li></ul></ul></ul><ul><ul><li>Causal Arrows in Causal Assumptions </li></ul></ul><ul><ul><ul><li>Features of Causal Models </li></ul></ul></ul><ul><ul><ul><li>Health & Wealth: an Example </li></ul></ul></ul>
  3. 3. Different Causal Domains <ul><li>A general and comprehensive account </li></ul><ul><li>of causation? Forget it! </li></ul><ul><li>Different causal questions lead to </li></ul><ul><li>different causal domains </li></ul>Metaphysics Epistemology Methodology
  4. 4. Different Causal Domains: Metaphysics <ul><li>Metaphysics studies </li></ul><ul><li>the nature of things </li></ul><ul><li>Questions: </li></ul><ul><ul><li>What is causation? </li></ul></ul><ul><ul><li>What are causal relations? </li></ul></ul><ul><ul><li>… </li></ul></ul><ul><li>Answers: </li></ul><ul><ul><li>From ontic causal processes to </li></ul></ul><ul><ul><li>epistemic mental representations </li></ul></ul><ul><ul><li>… </li></ul></ul>
  5. 5. Different Causal Domains: Epistemology <ul><li>Epistemology studies origin, nature, </li></ul><ul><li>and limits of human knowledge </li></ul><ul><li>Questions : </li></ul><ul><ul><li>What epistemic access to causal relations? </li></ul></ul><ul><ul><li>When are correlation causal? </li></ul></ul><ul><ul><li>Is invariance/structural stability/Markov condition </li></ul></ul><ul><ul><li>enough for causation? </li></ul></ul><ul><ul><li>… </li></ul></ul><ul><li>Answers : </li></ul><ul><ul><li>From invariance to variation, </li></ul></ul><ul><ul><li>Overlaps with methodology </li></ul></ul><ul><ul><li>… </li></ul></ul>
  6. 6. Different Causal Domains: Methodology <ul><li>Methodology is the study of </li></ul><ul><li>methods of scientific inquiry </li></ul><ul><li>Questions: </li></ul><ul><ul><li>Hypothetico-deductive or inductive methods? </li></ul></ul><ul><ul><li>How to characterise invariance? </li></ul></ul><ul><ul><li>New methods: Bayes Nets? Decision Analysis? </li></ul></ul><ul><ul><li>… </li></ul></ul><ul><li>Answers: </li></ul><ul><ul><li>Let the practising scientists speak … </li></ul></ul><ul><ul><li>with philosophers’ epistemological supervision </li></ul></ul>
  7. 7. The Epistemology of Causality <ul><li>Research Domain: </li></ul><ul><ul><li>Causal Modelling in the Social Sciences, e.g.: </li></ul></ul><ul><li>Epidemiology: Smoking & Lung Cancer </li></ul><ul><ul><ul><li>Demography: Mother’s education & </li></ul></ul></ul><ul><ul><ul><li>Child Survival </li></ul></ul></ul><ul><ul><ul><li>Econometrics: Health & Wealth </li></ul></ul></ul><ul><ul><ul><li>… </li></ul></ul></ul><ul><li>Questions: </li></ul><ul><li>What Rationale for Causality? </li></ul><ul><li>What Guarantees the Causal Interpretation? </li></ul>
  8. 8. Variation: the Rationale of Causality <ul><li>Structural Equation Models: </li></ul><ul><li>Y= β X +  </li></ul><ul><li>Variations in X accompany Variations in Y </li></ul><ul><li> s quantify those variations </li></ul>
  9. 9. Variation: the Rationale of Causality <ul><li>Covariance Structure Models: </li></ul><ul><li>Measurement Model </li></ul><ul><li>+ </li></ul><ul><li>Structural Model </li></ul><ul><li>Causal relations in the Structural Model explain covariances (= co- variations ) </li></ul><ul><li>in the Measurement Model </li></ul>
  10. 10. Variation: the Rationale of Causality <ul><li>Suppes’ Probabilistic Theory: </li></ul><ul><li>Pr (Effect | Cause) > Pr (Effect) </li></ul><ul><li>The cause produces a variation </li></ul><ul><li>in the probability of the effect </li></ul>
  11. 11. <ul><li>Variation is the bottom-line concept </li></ul><ul><li>of causality, </li></ul><ul><li>is not a further condition on models </li></ul><ul><li>Why not invariance ? </li></ul><ul><li>Invariance of what? Of a variation … </li></ul><ul><li>Why not regularity ? </li></ul><ul><li>Regularity of what? Of a variation … </li></ul>
  12. 12. Nonetheless … <ul><li>See Level in Venice & Bread Prices in England </li></ul><ul><li>Storks & Birth Rate in Alsace </li></ul><ul><li>Those variations don’t seem to be causal… </li></ul><ul><li>Hence, </li></ul><ul><li>What guarantees the causal interpretation? </li></ul>
  13. 13. Causal Arrows in Causal Assumptions <ul><li>Features of Causal Models: </li></ul><ul><ul><li>Knowledge of the causal context </li></ul></ul><ul><ul><li>Conceptual hypothesis </li></ul></ul><ul><ul><li>Statistical assumptions </li></ul></ul><ul><ul><li>Extra-statistical assumptions </li></ul></ul><ul><ul><li>Causal assumptions </li></ul></ul>
  14. 14. Causal Arrows in Causal Assumptions <ul><li>Knowledge of the causal context: </li></ul><ul><ul><li>Previous studies, scientific theories, </li></ul></ul><ul><ul><li>background knowledge </li></ul></ul><ul><li>Conceptual hypothesis: </li></ul><ul><ul><li>The causal claim stating </li></ul></ul><ul><ul><li>the causal link to test </li></ul></ul>
  15. 15. Causal Arrows in Causal Assumptions <ul><li>Statistical assumptions: </li></ul><ul><ul><li>Linearity </li></ul></ul><ul><ul><li>Normality </li></ul></ul><ul><ul><li>Non measurement error </li></ul></ul><ul><ul><li>Non correlation of error terms </li></ul></ul><ul><ul><li>… </li></ul></ul>
  16. 16. Causal Arrows in Causal Assumptions <ul><li>Extra-statistical assumptions: </li></ul><ul><ul><li>Direction of time </li></ul></ul><ul><ul><li>Causal asymmetry </li></ul></ul><ul><ul><li>Causal priority </li></ul></ul><ul><ul><li>Causal ordering </li></ul></ul><ul><ul><li>Causal mechanism </li></ul></ul><ul><ul><li>Determinism </li></ul></ul><ul><ul><li>… </li></ul></ul>
  17. 17. Causal Arrows in Causal Assumptions <ul><li>Causal assumptions: </li></ul><ul><ul><li>Structure of the causal relation </li></ul></ul><ul><ul><ul><li>Linearity </li></ul></ul></ul><ul><ul><ul><li>Separability </li></ul></ul></ul><ul><ul><li>Covariate sufficiency </li></ul></ul><ul><ul><li>No confounding </li></ul></ul><ul><ul><li>Non causality of error terms </li></ul></ul><ul><ul><li>Stability </li></ul></ul><ul><ul><li>Invariance condition </li></ul></ul><ul><ul><li>… </li></ul></ul>
  18. 18. Health & Wealth: an Example <ul><li>Adams et al. (2003), “Healthy, Wealthy, and Wise” </li></ul><ul><li>Journal of Econometrics, 112, pp.3-56. </li></ul><ul><li>Objective : analysing possible paths between health and socioeconomic status </li></ul><ul><li>Methods : Granger-causality augmented with invariance condition </li></ul><ul><li>Results : no causal link health  wealth accepted </li></ul><ul><li>no causal link wealth  health rejected </li></ul>
  19. 19. Health & Wealth <ul><li>Knowledge of the causal context: </li></ul><ul><ul><li>Links health-wealth studied by far and large </li></ul></ul><ul><ul><li>The association widely holds </li></ul></ul><ul><li>Conceptual hypothesis: </li></ul><ul><ul><li>Health doesn’t cause Wealth </li></ul></ul><ul><ul><li>Wealth causes Health </li></ul></ul>
  20. 20. Health & Wealth <ul><li>Statistical assumptions: </li></ul><ul><ul><li>Granger-causality is based on </li></ul></ul><ul><ul><li>regression methods, </li></ul></ul><ul><ul><li>hence it satisfies standard </li></ul></ul><ul><ul><li>statistical assumptions </li></ul></ul>
  21. 21. Health & Wealth <ul><li>Extra-statistical assumptions: </li></ul><ul><ul><li>Causal priority and causal ordering </li></ul></ul><ul><ul><li>the past history of Y t-1 determines </li></ul></ul><ul><ul><li>the current value of Y </li></ul></ul><ul><ul><li>Asymmetry of causation </li></ul></ul><ul><ul><li>Granger-causality assumes that </li></ul></ul><ul><ul><li>the future cannot cause the past </li></ul></ul>
  22. 22. Health & Wealth <ul><li>Causal assumptions: </li></ul><ul><ul><li>Structure of the causal relation & </li></ul></ul><ul><ul><li>Covariate sufficiency </li></ul></ul><ul><ul><li>Granger-causality rules out instantaneous causation; </li></ul></ul><ul><ul><li>the components of Y form a causal chain </li></ul></ul><ul><ul><li>where in Y t-1 are causes of Y </li></ul></ul><ul><ul><li>Invariance condition </li></ul></ul><ul><ul><li>test for causality: are model parameters </li></ul></ul><ul><ul><li>invariant among panels? </li></ul></ul>
  23. 23. To sum up … <ul><li>Metaphysics: “objects” of causality </li></ul><ul><li> </li></ul><ul><li>Epistemology: epistemic access to causality </li></ul><ul><li> </li></ul><ul><li>Methodology: methods to discover/confirm </li></ul><ul><li>causal relations </li></ul><ul><li>The Epistemology of Causality </li></ul><ul><ul><li>Variation is the bottom-line concept </li></ul></ul><ul><ul><li>Causal assumptions guarantee </li></ul></ul><ul><ul><li>the causal interpretation </li></ul></ul>
  24. 24. <ul><li>Selected Readings: </li></ul><ul><ul><li>Hausman D. (1998), Causal Asymmetries . </li></ul></ul><ul><ul><li>Holland P.W. (1986), “Statistics and Causal Inference”, JASA 81. </li></ul></ul><ul><ul><li>Pearl J. (2000), Causality. </li></ul></ul><ul><ul><li>Stone R. (1993), “The Assumptions on which Causal Inferences Rest”, JASA 55. </li></ul></ul><ul><ul><li>Suppes P. (1970), A Probabilistic Theory of Causality. </li></ul></ul><ul><ul><li>Williamson J. (2004), Bayesian Nets and Causality. </li></ul></ul>Many thanks to Jon Williamson for useful discussions Comments? Mail to: [email_address] [email_address]
  • BenjavanUpatising

    Jan. 22, 2014

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