Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models

Details Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models

2010-04-29

arxiv.org/abs/1004.5328v2

Statistical Methodology 8 (2011) 319-339

Statistics

Methodology

37 pages, 2 figures, 5 tables; notation revised and clarified, some sections (particularly 4.3 and 5) made more rigorous, some

Scientific paper

10.1016/j.stamet.2011.01.005

Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without adjustment, ERGMs preserve density as network size increases. Density invariance is often not appropriate for social networks. We suggest a simple modification based on an offset which instead preserves the mean degree and accommodates changes in network composition asymptotically. We demonstrate that this approach allows ERGMs to be applied to the important situation of egocentrically sampled data. We analyze data from the National Health and Social Life Survey (NHSLS).

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