Impact of Survey Design on Estimation of Exponential-Family Random Graph Models from Egocentrically-Sampled Data

Egocentric sampling of networks selects a subset of nodes ("egos") and collects information from them on themselves and their immediate network neighbours ("alters"), leaving the rest of the nodes in the network unobserved. This design is popular because it is relatively inexpensive to implement and can be integrated into standard sample surveys. Recent methodological developments now make it possible to statistically analyse this type of network data with Exponential-family Random Graph Models (ERGMs). This provides a framework for principled statistical inference, and the fitted models can in turn be used to simulate complete networks of arbitrary size that are consistent with the observed sample data, allowing one to infer the distribution of whole-network properties generated by the observed egocentric network statistics. In this paper, we discuss how design choices for egocentric network studies impact statistical estimation and inference for ERGMs. The design choices include both measurement strategies (for ego and alter attributes, and for ego-alter and alter-alter ties) and sampling strategies (for egos and alters). We discuss the importance of harmonising measurement specifications across egos and alters, and conduct simulation studies to demonstrate the impact of sampling design on statistical inference, specifically stratified sampling and degree censoring.