A tutorial on Bayesian model averaging for exponential random graph models

The use of exponential random graph models (ERGMs) is becoming prevalent in psychology due to their ability to explain and predict the formation of edges between vertices in a network. Valid inference with ERGMs requires correctly specifying endogenous and exogenous effects as network statistics, guided by theory, to represent the network-generating process while ensuring key effects shaping network topology are not omitted. However, specifying a comprehensive model is challenging, particularly when relying on a single model. Despite this, most applied research continues to use a single ERGM, raising two concerns: Selecting misspecified models compromises valid statistical inference, and single-model inference ignores uncertainty in model selection. One approach to addressing these issues is Bayesian model averaging (BMA), which evaluates multiple candidate models, accounts for uncertainty in parameter estimation and model selection, and is more robust to model misspecification than single-model inference. This tutorial provides a guide to implementing BMA for ERGMs. We illustrate its application using data from a college friendship network, with a supplementary example based on the Florentine marriage network; both focus on averaging exogenous covariate effects. We demonstrate how BMA incorporates theoretical considerations and addresses modelling challenges in ERGMs, with annotated R code provided for replication and extension.