Snowball sampling for estimating exponential random graph models for large networks

The exponential random graph model (ERGM) is a well-established statistical approach to modelling social network data. However, Monte Carlo estimation of ERGM parameters is a computationally intensive procedure that imposes severe limits on the size of full networks that can be fitted. We demonstrate the use of snowball sampling and conditional estimation to estimate ERGM parameters for large networks, with the specific goal of studying the validity of inference about the presence of such effects as network closure and attribute homophily. We estimate parameters for snowball samples from the network in parallel, and combine the estimates with a meta-analysis procedure. We assess the accuracy of this method by applying it to simulated networks with known parameters, and also demonstrate its application to networks that are too large (over 40 000 nodes) to estimate social circuit and other more advanced ERGM specifications directly. We conclude that this approach offers reliable inference for closure and homophily.