Minimum distance estimators of population size from snowball samples using conditional estimation and scaling of exponential random graph models

New distance-based estimators of population size for snowball sample network data using exponential random graph models (ERGMs) are presented. After ERGM parameters are obtained using conditional estimation it is possible to simulate networks from the ERGM across a range of hypothesized sizes and then estimate the population's size. This is done by creating simulated snowball samples from the simulated networks and then minimizing their distances from an observed network statistic across network sizes. The number of nodes in the snowball sample (snowball size) combined with a moment-based distance is shown to be an effective estimator. For ERGM conditional estimate parameters, the moment-based snowball size estimator can outperform a multivariate Mahalanobis estimator, where the latter would be a maximum likelihood estimator under the assumption the network statistics are multivariate Gaussian. “Extreme” ERGM scaling across network sizes, which prevents finding a minimum-distance estimate, is also discussed.