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Csf Russo Seminar2

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Csf Russo Seminar2

  1. 1. Levels of causation and the interpretation of probability Seminar 2 Federica Russo Philosophy, Louvain & Kent
  2. 2. <ul><li>Recap </li></ul><ul><ul><li>Levels of causation </li></ul></ul><ul><ul><ul><li>Type-level: frequency of occurrence in the population </li></ul></ul></ul><ul><ul><ul><li>Token-level: belief in what did or will happen in a particular individual </li></ul></ul></ul><ul><li>Levels of causation in social science </li></ul><ul><ul><li>Does this distinction have any </li></ul></ul><ul><ul><li>counterpart in the scientific talk? </li></ul></ul>
  3. 3. Hierarchical structures <ul><li>Pupils / classes / schools / school systems </li></ul><ul><li>Individuals / family / local population / national population </li></ul><ul><li>Firms / regional market / national market / global market </li></ul><ul><li>… </li></ul>
  4. 4. Traditional approaches <ul><li>Holism </li></ul><ul><ul><li>properties of a given system cannot be reduced to the mere sum of its components; the system as a whole determines in a fundamental way how the parts behave </li></ul></ul><ul><li>Individualism </li></ul><ul><ul><li>social phenomena and behaviours can be explained by appealing to individual decisions and actions, without invoking any factor transcending them </li></ul></ul>
  5. 5. Dangers <ul><li>Atomistic fallacy </li></ul><ul><ul><li>wrongly infer a relation between units at a higher level of analysis from units at a lower level of analysis. </li></ul></ul><ul><li>Ecological fallacy </li></ul><ul><ul><li>draw inferences about relations between individual level variables based on the group level data. </li></ul></ul>
  6. 6. Types of variables <ul><li>Individual: </li></ul><ul><li>measure individual characteristics, take values of each of the lower units in the sample. </li></ul><ul><ul><ul><li>e.g. income of each individual in the sample </li></ul></ul></ul><ul><li>Aggregate: </li></ul><ul><li>summary of the characteristics of individuals composing the group </li></ul><ul><ul><ul><li>e.g.: mean income of state residents </li></ul></ul></ul>
  7. 7. Farmers’ migration in Norway <ul><li>Data from the Norwegian population registry (since 1964) </li></ul><ul><li>and from two national censuses (1970 and 1980) </li></ul><ul><li>Aggregate model and individual model </li></ul><ul><li>show opposite results: </li></ul><ul><ul><li>Aggregate—regions with more farmers are those </li></ul></ul><ul><ul><li>with higher rates of migrations; </li></ul></ul><ul><ul><li>Individual—in a same region migration rates are higher </li></ul></ul><ul><ul><li>for non-farmers than for farmers </li></ul></ul><ul><li>Reconciliation: multilevel model </li></ul><ul><ul><li>aggregate characteristics (e.g. the percentage of farmers) </li></ul></ul><ul><ul><li>explain individual behaviour (e.g. migrants’ behaviour) </li></ul></ul>
  8. 8. Types of models <ul><li>Individual: explain individual-level outcomes by individual-level explanatory variables </li></ul><ul><ul><ul><li>e.g.: explain the individual probability of migrating through the individual characteristics of being/not being farmer </li></ul></ul></ul><ul><li>Aggregate: explain aggregate-level outcomes through explanatory aggregate-level variables </li></ul><ul><ul><ul><li>e.g.: explain the percentage of migrants in a region through the percentage of people in the population having a certain occupational status (e.g. being a farmer) </li></ul></ul></ul><ul><li>Multilevel: make claims across the levels, from the aggregate-level to the individual-level and vice-versa </li></ul><ul><ul><ul><li>e.g.: explain the individual probability to migrate for non-farmers through the percentage of farmers in the same region </li></ul></ul></ul>
  9. 9. Multilevel models response variable explanatory variable at the individual level explanatory variable at the group level i : index for the individuals j : index for the group those  vary depending on the group Errors are independent at each level and between levels
  10. 10. Compare Classical multiple regression model Multilevel model
  11. 11. The individual in causal modelling <ul><li>Statistical vs. real individual – Courgeau 2003 </li></ul><ul><ul><li>In the search for individual random processes, two individuals observed by the survey , possessing identical characteristics, have no reason to follow the same process. By contrast, in the search for a process underlying the population, two statistical individuals —seen as units of a repeated random draw, subject to the same selection conditions and exhibiting the same characteristics—automatically obey the same process. </li></ul></ul>
  12. 12. Level terminology revisited <ul><li>Generic </li></ul><ul><ul><li>aggregate variables </li></ul></ul><ul><ul><li>individual variables </li></ul></ul><ul><ul><li>yet generic </li></ul></ul><ul><li>Single-case </li></ul><ul><ul><li>real individuals </li></ul></ul>
  13. 13. Levels of analysis <ul><li>By aggregation </li></ul><ul><ul><li>Individual / aggregate level </li></ul></ul><ul><li>By discipline </li></ul><ul><ul><li>Include in the model variables </li></ul></ul><ul><ul><li>of different sorts </li></ul></ul><ul><ul><li>e.g. biological and social </li></ul></ul>
  14. 14. Variation in multilevel models <ul><li>Multilevel models do not assume </li></ul><ul><li>group homogeneity </li></ul><ul><li>Variation in multilevel models </li></ul><ul><ul><li>at the individual level: how the individual characteristics vary depending on another individual characteristic </li></ul></ul><ul><ul><li>at the contextual level: how an individual characteristic varies depending on an aggregate characteristic </li></ul></ul><ul><li>How individual variations vary </li></ul><ul><li>in different contexts </li></ul>
  15. 15. Probability and multilevel <ul><li>Recall: </li></ul><ul><ul><li>Statistical understanding of the levels: </li></ul></ul><ul><ul><ul><li>At the type-level , causal relations are represented by joint probability distributions </li></ul></ul></ul><ul><ul><ul><li>At the token-level, causal relations are realisations of an observation of the joint probability distributions </li></ul></ul></ul><ul><li>Therefore: </li></ul><ul><ul><li>Generic-level relata are not reified </li></ul></ul><ul><ul><li>into supervenient properties of populations </li></ul></ul><ul><ul><li>Frequentism at the generic level </li></ul></ul><ul><ul><li>prevents from dubious social ontologies </li></ul></ul>

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