1. Levels of causation and the interpretation of probability Seminar 2 Federica Russo Philosophy, Louvain & Kent

2. Recap Levels of causation Type-level: frequency of occurrence in the population Token-level: belief in what did or will happen in a particular individual Levels of causation in social science Does this distinction have any counterpart in the scientific talk?

3. Hierarchical structures Pupils / classes / schools / school systems Individuals / family / local population / national population Firms / regional market / national market / global market …

4. Traditional approaches Holism 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 Individualism social phenomena and behaviours can be explained by appealing to individual decisions and actions, without invoking any factor transcending them

5. Dangers Atomistic fallacy wrongly infer a relation between units at a higher level of analysis from units at a lower level of analysis. Ecological fallacy draw inferences about relations between individual level variables based on the group level data.

6. Types of variables Individual: measure individual characteristics, take values of each of the lower units in the sample. e.g. income of each individual in the sample Aggregate: summary of the characteristics of individuals composing the group e.g.: mean income of state residents

7. Farmers’ migration in Norway Data from the Norwegian population registry (since 1964) and from two national censuses (1970 and 1980) Aggregate model and individual model show opposite results: Aggregate—regions with more farmers are those with higher rates of migrations; Individual—in a same region migration rates are higher for non-farmers than for farmers Reconciliation: multilevel model aggregate characteristics (e.g. the percentage of farmers) explain individual behaviour (e.g. migrants’ behaviour)

8. Types of models Individual: explain individual-level outcomes by individual-level explanatory variables e.g.: explain the individual probability of migrating through the individual characteristics of being/not being farmer Aggregate: explain aggregate-level outcomes through explanatory aggregate-level variables 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) Multilevel: make claims across the levels, from the aggregate- level to the individual-level and vice-versa e.g.: explain the individual probability to migrate for non-farmers through the percentage of farmers in the same region

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. Compare Classical multiple regression model Multilevel model

11. The individual in causal modelling Statistical vs. real individual – Courgeau 2003 individuals observed statistical individuals 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.

12. Level terminology revisited Generic aggregate variables individual variables yet generic Single-case real individuals

13. Levels of analysis By aggregation Individual / aggregate level By discipline Include in the model variables of different sorts e.g. biological and social

14. Variation in multilevel models Multilevel models do not assume group homogeneity Variation in multilevel models at the individual level: how the individual characteristics vary depending on another individual characteristic at the contextual level: how an individual characteristic varies depending on an aggregate characteristic How individual variations vary in different contexts

15. Probability and multilevel Recall: Statistical understanding of the levels: joint probability distributions At the type-level, causal relations are represented by joint probability distributions realisations At the token-level, causal relations are realisations of an observation of the joint probability distributions Therefore: Generic-level relata are not reified into supervenient properties of populations Frequentism at the generic level prevents from dubious social ontologies