Network Analysis Statistical Analysis of Social Network Data

Network Analysis Statistical Analysis of Social Network Data MICHAEL T. HEANEY UNIVERSITY OF GLASGOW JUNE 25, 2021 LECTURE 08 UNIVERSITÄT ST. GALLEN 2021 GLOBAL SCHOOL ON EMPIRICAL RESEARCH METHODS (GSERM)

Continuous Valued Data for ERGM • A key limitation of ERGM is that it is requires binary dependent variables. • However, there are many instances where network flows may be best understood in nonbinary terms. • Examples: Ø Migration flows from region to region. Ø Trade of goods and services from place to place – such as balance of trade or supply-chain management. Ø Giving financial contributions to political candidates. Ø Movement of employees from firm to firm. Ø Progression of students from course to course.

Generalized ERGM (GERGM) �A new class of ERGMs. �Allows the introduction of weights for the edges of a network �More flexible than the Count ERGM, which is a straightforward adaptation of the binary ERGM �If all network edges have zero values, then GERGM simplifies to OLS (Ordinary Least Squares). �Estimated using a two-equation structure: 1. 2. Effects of covariates on, and marginal distribution of, the edges Relationships among the edges

Adapting the ERGM Equation

Transform the Equation

Specifying h() �Reciprocity �Two stars �Transitive Triads

Specifying h() Continued �Cyclic triads �In Two-Stars versus Out Two-Stars

Estimation Issues �Estimation is often slow, but degeneracy is usually not an issue. �a-outside approach may speed estimation.

The Promise of GERGM �GERGM is a relatively new application that has not yet been widely applied. �Hence, there are many opportunities for contributions to the literature in this area.

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