Network Analysis Statistical Analysis of Social Network Data

Network Analysis Statistical Analysis of Social Network Data MICHAEL T. HEANEY UNIVERSITY OF GLASGOW JUNE 24, 2021 LECTURE 07 UNIVERSITÄT ST. GALLEN 2021 GLOBAL SCHOOL ON EMPIRICAL RESEARCH METHODS (GSERM)

Models beyond ERGM

Models beyond ERGM �Temporal Exponential Random Graph Models (TERGM)

Models beyond ERGM �Temporal Exponential Random Graph Models (TERGM) �Stochastic Actor-Oriented Models (SAOM) – Sienna

Models beyond ERGM �Temporal Exponential Random Graph Models (TERGM) �Stochastic Actor-Oriented Models (SAOM) – Sienna �Generalized Exponential Random Graph Models (GERGM) – e. g. , count ERGMs

Models beyond ERGM �Temporal Exponential Random Graph Models (TERGM) �Stochastic Actor-Oriented Models (SAOM) – Sienna �Generalized Exponential Random Graph Models (GERGM) – e. g. , count ERGMs �Relational Event Models (REMs)

Models beyond ERGM �Temporal Exponential Random Graph Models (TERGM) �Stochastic Actor-Oriented Models (SAOM) – Sienna �Generalized Exponential Random Graph Models (GERGM) – e. g. , count ERGMs. �Relational Event Models (REMs) �Latent Space Models

Models beyond ERGM �Temporal Exponential Random Graph Models (TERGM) �Stochastic Actor-Oriented Models (SAOM) – Sienna �Generalized Exponential Random Graph Models (GERGM) – e. g. , count ERGMs. �Relational Event Models (REMs) �Latent Space Models �And more to come – the field is rapidly evolving. You have to keep learning to keep up.

Temporal Exponential Random Graph Models

Temporal Exponential Random Graph Models TERGM draws upon the same network generating process as does ERGM:

Re-write model using c()

Incorporate past time periods (NT) The current time period is a function of what happened in past time periods.

Now generalize to multiple time periods

h(N) can use same statistics as ERGM �Exogenous covariates �Single-period delayed reciprocity �Lagged Network / Positive Autoregression

Another h(N) statistic �Dyadic stability

Key Modeling Considerations �Is it reasonable to treat your network as changing in discrete time periods? �Does your data-generating process change over time? (Think of school friendship versus war. )

Key Data Considerations �Inter-temporal network statistics �Block-diagonal Adjacency Matrix

Block Diagonal Representation

Estimation �MCMC Pseudolikelihood for small networks �Bootstrap-corrected Maximum Pseudolikelidhood for large networks (BTERGM)

Comments/Questions?

Stochastic Actor-Oriented Model (SAOM) �Also known as “Siena” �Specification is only slightly different than TERGM �Models continuous time changes, rather than assuming discrete time �Big advantage: Models change in node attributes

Comments / Questions ?

Article Discussion Philip Leifeld and Skyler J. Cranmer, “A theoretical and empirical comparison of the temporal exponential random graph model and the stochastic actor-oriented model”, Network Science, 2019