Causal modeling aims to explain phenomena by modeling causal mechanisms and relationships between variables. It represents explanations as statistical models relating explanatory variables to outcomes. Explanations in causal modeling are flexible and allow testing causal hypotheses against data while incorporating background knowledge. Modeling mechanisms gives causal models explanatory power by representing how social, economic, and biological factors interact causally to influence outcomes.

1. Explaining causal modelling OR What a causal model ought to explain Federica Russo Universit é catholique de Louvain

2. Overview What is a causal model Explanatory vocabulary in causal modelling Modelling causal mechanisms Causal-model explanations Causal modelling vs. other models

3. What is a causal model

4.  54  4  13  34  12  2 X 1 Economic development X 2 Social development X 3 Sanitary infrastructures X 4 Use of sanitary infrastructures X 5 Age structure Y Mortality

5. Causal models Rest on a number of assumptions Model causal relations statistically Uncover stable variational relations

6. Explanatory vocabulary in causal modelling

7. Explanation in structural equations Y=  X+  X, Y : explanatory and response variables Xs explain Y Intuitively: Xs explain Y Xs account for Y Xs are relevant causal factors in the causal mechanism

8. CM explains variability in Y Y=  X+  Variations in X explain variations in Y How is explanation ‘quantified’?  r 2 represents the fraction of variability in Y explained by X  r 2 indicates how much variability in Y is accounted for by the regression function

9. But … r 2 measures the goodness of fit, not the validity of the model  r 2 doesn’t give any theoretical reason for the accounted variability r 2 depends on the correctness of assumptions

10. The philosophical answer Explanatory import is given by: Covariate sufficiency No-confounding Background knowledge

11. Modelling causal mechanisms

12. Causal models model mechanisms Most widespread conception: Mechanisms are made of physical processes, interactions, …, assembled to behave like a gear But: What if we have socio-economic-demographic variables? social and biological variables?

13. A mixed mechanism Treatment Prevention Socioeconomic determinants Maternal factors Environmental contamination Nutrient deficiency Injury Healthy Sick Personal illness control Growth faltering Mortality

14. The causal model incorporates social and biological variables Modelling the mechanism gives the causal model explanatory power

15. Causal-models explanations

16. Causal modelling is a model of explanation The formal structure of explanation is given by the methodology of causal modelling: Formulate the causal hypothesis Build the statistical model Draw consequences to conclude to empirical validity/invalidity of the hypothesis

17. CM explanations are flexible: they allow a va et viens between established theories and establishing theories they participate in establishing new theories negative results may trigger further research

18. CM explanations allow control: 1) statistical r 2 measures amount of variability explained 2) epistemic CM requires coherence of results with background knowledge 3) metaphysical CM requires ontological homogeneity between variables in the mechanism

19. Causal modelling vs other models of explanation

20. CM vs deductive-nomological model  well known problems with laws  not all explanations involve deduction CM vs statistical-relevance model  S-R is too narrow in scope CM vs causal-mechanical model  it cannot account for mixed mechanisms

21. CM vs manipulationist model Woodward (2003) A theory of causal explanation Causal generalisations are change-relating Change-relating relations are explanatory: they are invariant under a large class of interventions or environmental changes

22. Generalisations show: (i) that the explanandum was to be expected how the explanandum would change if initial conditions had changed What-if-things-had-been-different questions Relevant counterfactuals describe outcomes of interventions Explanatory power is tested by means of counterfactual questions

23. However … The manipulationist account: Overlooks the role of background knowledge Neglects the causal role of non-manipulable factors Takes for granted what the causes are

24. To sum up Causal modelling Aims at explaining social phenomena Makes essential use of explanatory vocabulary Has explanatory power insofar as it models mechanism

25. To conclude Causal modelling is a model of explanation Among its virtues, over and above alternative models: Flexibility Control