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Russo invariance-cits-paris


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What is invariance and how to test it.

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Russo invariance-cits-paris

  1. 1. What is invariance and how to test it Federica Russo Center Leo Apostel, VrijeUniversiteitBrussel
  2. 2. Overview Invariance The concept inherited from early econometrics Invariance across changes Of the effect-variable due to interventions in the cause-variable Of the environment, i.e. across appropriate partitions of the dataset Invariance of what? Of joint-variations of variables Of regular associations Is it worthextendingthe concept? 2
  3. 3. Invariance in early econometrics The beginning of contemporary causal modelling: Modelling and testing economic structures Marschak, Frisch, Haavelmo: Learning invariance properties of the model or economic system from data Test whether hypothetical variations (theoretical level) in economic structure are actually invariant (empirical level) Invariance of the parametrisation of the system 3
  4. 4. Invariance across changes Experimental contexts Changes in the effect-variable due to interventions in the cause-variable Observational contexts Changes across environments, i.e. across appropriate partitions of the data set 4
  5. 5. Changes in the effect-variable P V = n R T Pressure Volume Number of moles Gas constant Temperature 5
  6. 6. Woodward’s conditions Interventions I on cause-variable X: Change in X (cause) is totally due to I Change in Y (effect) totally due to change in X I is not correlated with other possible causes of Y If all this holds – and that’s a big if – empirical generalisations are causal 6
  7. 7. Changes in the environment Environments are appropriate partitions of the population of reference Age groups Socio-economic conditions Exposures … Invariance is a test for stability across environments Of the causal structure (arrangements) Of the parametrisation (numerical values) 7
  8. 8. What are the causes of self-rated health in the Baltic countries in the ‘90s? 8
  9. 9. What environments? 1994 and 1999 data sets Estonian Males; Estonian Females Latvian Males; Latvia Females Lithuanian Males; Lithuanian Females Age groups (18–29, 30–44, 45–59, 60+) Autochthons and other (mainly Russians) Background knowledge looms large … 9
  10. 10. Stability of the parametrisation Baltic study: parametrisation stable for most environments: Time-frames, Gender, Age, Ethnical groups Impact of alcohol consumption on self-rated health Sign of parameter and numerical value are stable Female Male Estonia −0.094 −0.039 Latvia −0.181 −0.054 Lithuania −0.157 −0.068 10
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  12. 12. Parametrisation of the causal model is stable for each environment The structure (= arrangement of variables) is the same for 3 Baltic countries studied Men and women Ethnic groups … Stability of the causal structure 12
  13. 13. Parametrisation and causal structure Clearly not independent If stability of parametrisationfails, we are led to rethink causal structure for at least some sub-populations Homogeneity and heterogeneity of population of reference 13
  14. 14. What has to be invariant? Detect joint-variations within and between variables Woodward: change-relating relations How regular are joint variations? Dependencies Strength of association How stable are dependencies? Invariance across changes Variation Regularity Invariance 14
  15. 15. Variation • Visibility No variation, no statistical analysis Regularity • How strong Frequency of occurrence Invariance • How stable Invariance across changes 15
  16. 16. Why extending the concept of invariance? Do not conflate experimental and policy interventions Interventions to get causal knowledge vs interventions based on available causal knowledge Avoid gold standards Compare comparable methods Preserving diversity of causal methods Observational and experimental methods need different tests 16
  17. 17. 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) 17