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With the growth of interest in network data across fields, the ExponentialRandom Graph Model (ERGM) has emerged as the leading approach to thestatistical analysis of network data. ERGM parameter estimation requires theapproximation of an intractable normalizing constant. Simulation methodsrepresent the state-of-the-art approach to approximating the normalizingconstant, leading to estimation by Monte Carlo maximum likelihood (MCMLE).MCMLE is accurate when a large sample of networks is used to approximate thenormalizing constant. However, MCMLE is computationally expensive, and may beprohibitively so if the size of the network is on the order of 1,000 nodes(i.e., one million potential ties) or greater. When the network is large, oneoption is maximum pseudolikelihood estimation (MPLE). The standard MPLE issimple and fast, but generally underestimates standard errors. We show that aresampling method---the parametric bootstrap---results in accurate coverageprobabilities for confidence intervals. We find that bootstrapped MPLE can berun in 1/5th the time of MCMLE. We study the relative performance of MCMLE andMPLE with simulation studies, and illustrate the two different approaches byapplying them to a network of bills introduced in the United State Senate.

Exponential Random Graph Models with Big Networks: Maximum Pseudolikelihood Estimation and the Parametric Bootstrap