Estimating exponential random graph models using sampled network data via graphon

Analysis of large networks is of interest to many disciplines. Full network data are often hard to collect, storage and analyze. In particular, in many social science surveys, ego nomination techniques have been used to collect the egocentric networks of the randomly sampled survey respondents. In this paper, we propose a sample-GLMLE method that fits exponential random graph models (ERGM) to such sampled egocentric networks. It is an extension of a previous graph-limit based maximum likelihood estimation (GLMLE) method for full network that uses graphon to bridge the estimation of ERGM using observed network data. In this paper, we provide solutions to computational issues that are unique to sampled network data and evaluate the proposed method using simulations. We also apply sample-GLMLE to the public-use set of the National Longitudinal Study of Adolescent Health (AddHealth) study.