1. Correlational data,causal hypotheses, and validity Federica Russo Philosophy, Kent

2. Overview A shared problem across the sciences Making causal sense of correlational data The structural strategy Looking for, modelling and testing structures Establishing the validity of a causal model The interventionist strategy Invariance under intervention Interventions and experiments ‘Weak invariance’ and observational data 2

3. Making sense of correlational data A shared problem Correlational data coming from observations and/or from experiments Are those correlations causal or not? An old philosophical question, indeed What is the extra-content making correlations causal? An under-discussed issue How to make sense of correlations coming from observations? A reformulated question When is a statistical model built to make causal sense of correlational data valid? 3

4. Preliminary remarks Focus on methodology/epistemology rather than metaphysics of causality Narrow down the scope to quantitative social science A tradition of scientific inquiry back to Quetelet and Durkheim, Blalock and Duncan, … The hard task is with observational data Why reformulating the ‘old’ question? Is it a condition that grants causal results? 4

5. Structural strategy 5

6. The structural strategy A general methodological framework Embraces various statistical methods Provides the general principles of the test ‘set-up’ for causal hypotheses 6

7. Structural modelling vsstructural equation modelling Not co-extensive terms! Pearl: Ambiguous use of the two; not explicit meaning of structural Woodward Says it deals with SM, but does in fact with SEM Hoover Does not make explicit the meaning of structural Cartwright Restricted discussion to SEM in economics and role of ideal experiments 7

8. What makes a structural model structural? A question left by and large unanswered by current accounts The question I am going to tackle next In a nutshell: Structural modelling is the modelling of mechanisms 8

9. Structural models model mechanisms To model mechanisms means to formulate suitable causal hypotheses to put forward for empirical testing To decide about the results of tests is to decide whether the model is valid 9

10. Looking for structures Beyond descriptive knowledge Unveil the mechanism that supposedly explains correlations Not just assuming a ‘data generating process’ 10

11. What mechanism? ‘Modelling mechanisms’ does not depend on a metaphysical account of mechanism No ontological commitment to the (degree of) physical existence of (social) mechanisms Mechanisms are epistemic: they carry explanatory power ‘Mechanism schemata’ give the description of the behaviour Do track something real: making sense of what actually happens In line with MDC or Bechtel & Abrahmsen At variance with Woodwardian account 11

12. Building structures Formulate causal hypotheses Build the statistical model Test the model Conclude to the validity/invalidity of the model The role of background knowledge Yes … that’s hypothetico-deductivism… But … 12

13. Causal hypotheses and mechanisms: how they are linked Causal hypotheses are not of the form X causes Y There is a whole set of hypotheses and assumptions that altogether can be interpreted as hypothesising the mechanism This whole set is formally translated into the so-called recursive decomposition 13

14. What are the causes of self-rated health in the Baltic countries in the ‘90s? XY Take the joint probability distribution + Make assumptions P(Education, Locus of Control, Physical Health, …, Self-Rated Health) P(X1, X1, X3, …Y) perform a recursive decomposition of the type P(Y)= P(X1) P(X3) P(X2|X3) … P(Y|X2, X3) Read as: Self-Rated Health depends on Education; on Locus of Control through Psychological distress; on Alcohol Consumption which also depends on Physical Health; … 14

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16. Testing structures Goodness of fit, significance of parameters … Invariance under intervention … better, under changes of the environment That is: whether the relation actually remains stable across different portions of the data set, different data sets with observations from different populations different time periods 16

17. Validity Decide whether the story about the mechanism meant to make sense of correlational data provides a plausible explanation about what is really going on in the world Cook and Campbell on internal validity Representativeness of the sample and Replicability of the study To be complemented with Background knowledge Explanatory power 17

18. Take home message To decide whether correlations are causal or not we have to decide about the validity of the whole model. That is, whether the mechanism provides a good enough explanation of the correlations. 18

19. The interventionist strategy 19

20. Invariance under intervention “A generalization G is invariant if G would continue to hold under some intervention that changes the value of X in such a way that, according to G, the value of Y would change — ’continue to hold’ in the sense that G correctly describes how the value of Y would change under this intervention.” (Woodward and Hitchcock 2003) Invoked because it provides a definition of causality, or it bestows empirical generalisations explanatory power, or some combination of the two It is counterfactually defined Under intervention, the generalisationwould continue to hold Relevant for explanation Invariant generalisations allow answering withbd-questions 20 What if things had been different

21. How does the interventionist modeller make causal sense of correlational data? Invariance under intervention!

22. The role of experiments Does interventionism presuppose experimentalism, or does it not? If it does: we have no methodological story for observational contexts If it does not: we have to modify the requirement of invariance 22

23. […] The kind of counterfactuals that are relevant to understanding causation are connected to experiments — either actual or hypothetical. […] Counterfactuals are understood as claims about what would happen if a certain sort of experiment were to be performed […] (Woodward 2002, emphasis in the original) 23

26. Some remarks There are many tests to perform, not just invariance And we need to assess the validity of the whole model Ideal manipulations won’t do Indeed it depends on the meaning of ideal … 26

27. How much ideal is ‘ideal’? You don’t have to actually intervene: idealmanipulationswill do Not quite: 1. Some ideal interventions don’t make physical sense 2. Some ideal interventions cannot be tested Were we to intervene: a conceptualanalysis 27

28. Observational data andweak invariance ‘Possible-cause generalisations’: Those established by structural models in the special sciences [my case!] They are weakly invariant, i.e. stable across subpopulations or partitions of the data set 28

29. For example, the authors note that some association appears between smoking and lung cancer in every well-designed study on sufficiently large and representative populations with which they are familiar. There is evidence of a higher frequency of lung cancer among smokers than among nonsmokers, when potentially confounding variables are controlled for, among both men and women, among people of different genetic backgrounds, across different diets, different environments, and different socioeconomic conditions […]. The precise level and quantitative details of the association do vary, for example, the incidence of lung cancer among smokers is higher in lower socioeconomic groups, but the fact that there is some association or other is stable or robust across a wide variety or different groups and background circumstances. […] Thus, although Cornfield et al. do not exhibit a precise deterministic or probabilistic generalization that is invariant across different circumstances [meaning: across interventions] the cumulative impact of their evidence is to show that the relationship between smoking and lung cancer is relatively invariant in the weak sense described above. (Woodward 2003, p.312, emphasis and brackets added) 29

32. To conclude Consider an overarching view of causal modelling Switch focus from establishing a causal claim by testing acondition to evaluatingthevalidity of the model Do justice to those scientific domains where causal relations are established in absence of interventions strictusensu Discuss how metaphysical and methodological accounts can possibly live together 32