Marginal Structural Effects for Exponential Random Graph Models

Exponential random graph models (ERGMs) are now a staple for social network analysis due to their ability to parameterize effects from endogenous network structures, such as two stars and triangles. However, interpreting coefficients for structural ERGM terms poses two problems. First, it is not possible to change the value of a structural term “holding all else constant” in models with nontrivial dyadic dependencies. Second, parameters for structural ERGM terms may be affected by scaling (noncollapsibility), which can alter the direction, size, and significance of structural coefficients. While the first issue is known in the literature, the second has not been previously reported. This study introduces a methodological framework based on marginal structural effects (MSEs) to address both problems. MSEs capture the discrete marginal effect of an endogenous network structure by calculating the difference in probability when comparing two potential ties that differ only by the value of a structural term. MSEs provide an intuitive interpretation for structural network effects and are robust to the effects of scaling. Extensions to comparisons between models, interactions with exogenous covariates, and analysis of samples of networks are discussed. An example is provided using the largest AddHealth school network to demonstrate how the framework can be applied.