Goodness of Fit of Social Network Models

We present a systematic examination of a real network data set using maximum likelihood estimation for exponential random graph models as well as new procedures to evaluate how well the models fit the observed networks. These procedures compare structural statistics of the observed network with the corresponding statistics on networks simulated from the fitted model. We apply this approach to the study of friendship relations among high school students from the National Longitudinal Study of Adolescent Health (AddHealth). We focus primarily on one particular network of 205 nodes, although we also demonstrate that this method may be applied to the largest network in the AddHealth study, with 2,209 nodes. We…