Levels of causation andthe interpretation of

probabilitySeminar 2

Federica RussoPhilosophy, Louvain & Kent

RecapLevels 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 scienceDoes this distinction have anycounterpart in the scientific talk?

Hierarchical structuresPupils / classes / schools / school systems

Individuals / family / local population / national population

Firms / regional market / national market / global market

…

Traditional approachesHolism

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

Individualismsocial phenomena and behaviours can be explained by appealing to individual decisions and actions, without invoking any factor transcending them

Dangers

Atomistic fallacywrongly infer a relation between units at a higher level of analysis from units at a lower level of analysis.

Ecological fallacydraw inferences about relations between individual level variables based on the group level data.

Types of variablesIndividual: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

Farmers’ migration in NorwayData from the Norwegian population registry (since

1964)and from two national censuses (1970 and 1980)

Aggregate model and individual modelshow opposite results:

Aggregate—regions with more farmers are thosewith higher rates of migrations;Individual—in a same region migration rates are higherfor non-farmers than for farmers

Reconciliation: multilevel modelaggregate characteristics (e.g. the percentage of farmers)explain individual behaviour (e.g. migrants’ behaviour)

Types of modelsIndividual: explain individual-level outcomes by individual-

level explanatory variablese.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

Multilevel models0 1 2ij j j ij j ijY x z

response variable

explanatory variable at the individual level

explanatory variable at the group level

i: index for the individualsj: index for the group

those vary depending on the group

Errors are independent at each level and between levels

CompareClassical multiple regression

model

Multilevel model

0 1 2ij ij j ijY x z

0 1 2ij j j ij j ijY x z

The individual in causal modelling

Statistical vs. real individual – Courgeau 2003

In the search for individual random processes, two individuals observedindividuals 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 individualsstatistical 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.

Level terminology revisited

Genericaggregate variablesindividual variablesyet generic

Single-casereal individuals

Levels of analysis

By aggregationIndividual / aggregate level

By disciplineInclude in the model variablesof different sortse.g. biological and social

Variation in multilevel modelsMultilevel models do not assume

group homogeneity

Variation in multilevel modelsat 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 varyin different contexts

Probability and multilevelRecall:

Statistical understanding of the levels:At the type-level, causal relations are represented by

joint probability distributionsjoint probability distributionsAt the token-level, causal relations are realisationsrealisations of an

observation of the joint probability distributions

Therefore:Generic-level relata are not reifiedinto supervenient properties of populationsFrequentism at the generic levelprevents from dubious social ontologies