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Scott Duxbury Associate Professor of Sociology University of North Carolina email: duxbury@unc.edu

Micro-Macro Analysis in Social Networks using netmediate

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Overview

  • Key features :
    • A focal network structure is the dependent variable
    • Statistical
    • Post-estimation
    • Case-specific inference
    • Agnostic about modeling choices and data structure

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Macro-level: Any summary measure of a network calculated above the dyadic level—could be node, subgraph, or network-level

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Micro-level: Any dyadic process that guides tie formation

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  • Example research questions:
    • Does dating through friendship networks concentrate STIs in local network clusters?
    • Does racial homophily create structural holes in organizational networks?
    • Does neighbor-helping create pathogen hot- �spots in village household networks?

MEMS

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Roadmap

    • Definition, interpretation, estimation

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    • Sensitivity tests

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    • Moderation and mediation

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A is the network we observe

Micro Effect on Macro �Structure (MEMS)

But Y is the feature we want to

explain*

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*e.g., segregation, betweenness

centrality, mean distances,

modularity

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A can be expressed as a function of micro selection mechanisms

 

Micro Effect on Macro �Structure (MEMS)

f() denotes an assumed functional form or model for the observed data

We have many modeling options to

characterize the network—but how

do we get to Y?

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Y can be expressed as a function of A and by extension, micro selection mechanisms

 

Micro Effect on Macro �Structure (MEMS)

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Micro Effect on Macro �Structure (MEMS)

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The MEMS is the difference between the two potential outcomes

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We can interpret the MEMS as the total contribution of a selection process to a focal network structure

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Micro Effect on Macro �Structure (MEMS)

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Notes on Interpretation:

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  • Rooted in but-for logic
  • Case-specific
  • Effect of observed “treatment” on observed outcome in observed data
  • Counterfactuals are not interpretable

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Micro Effect on Macro �Structure (MEMS)

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Estimation:

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The MEMS is estimated algorithmically by using the parameter and variance estimates from an observed model to simulate a distribution of potential MEMS values, subject to uncertainty in the coefficients of the observed model.

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We typically rely on confidence intervals and Monte Carlo p-values because the MEMS distribution may be non-normal.

 

 

Micro Effect on Macro �Structure (MEMS)

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Switch to R

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Micro Effect on Macro �Structure (MEMS)

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Key assumptions:

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No omitted covariates

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Functional form is correct

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Sensitivity tests

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Key assumptions:

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No omitted covariates

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Functional form is correct

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Sensitivity tests

The MEMS for an unobserved confounding micro process would need to be 50% larger than the observed MEMS to eliminate its effect

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Key assumptions:

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No omitted covariates

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Functional form is correct

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Sensitivity tests

Consider two possible models:

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Sensitivity test:

 

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Key assumptions:

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No omitted covariates

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Functional form is correct

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Sensitivity tests

MEMS estimate decreases by .15 between models, but change is nonsignificant

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  • Right-hand interactions

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  • Left hand interactions

Moderation: Two-types

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  • Right-hand interactions are the interactions we are familiar with from standard statistical modeling. They capture whether a selection preference is stronger or weaker in the presence of a conditioning covariate.

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  • Left hand interactions

Moderation: Two-types

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  • Right-hand interactions

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  • Left hand interactions are unique to micro-macro analysis.
      • Left hand interactions refer to circumstances where a micro process only matters in the presence of another micro process, but not because of a change in actors’ preferences

Moderation: Two-types

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Right hand interactions require single-parameter tests on the multiplicative effect of an interaction term between two variables

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Left hand interactions require joints tests on the combined effects of multiple covariates

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Moderation: Two-types

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  • Left hand interactions in three steps:
    • 1) Single parameter test for term of interest

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Moderation: Two-types

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  • Left hand interactions in three steps:
    • 1) Single parameter test for term of interest
    • 2) Joint parameter test for interacting term

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Moderation: Two-types

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  • Left hand interactions in three steps:
    • 1) Single parameter test for term of interest
    • 2) Joint parameter test for interacting term
    • 3) Calculate difference

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Joint test

Single test

Difference

Moderation: Two-types

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  • Mediation
    • In some instances, we are interested in confounding and indirect pathways.
    • Smoking homophily may contribute to smoking segregation by acting on triadic closure

Mediation

Target quantity

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Mediation

 

 

 

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Mediation

 

 

 

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Mediation