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.

Multilevel network data facilitate statistical inference for curved ERGMs with geometrically weighted terms.

Multilevel network data provide two important benefits for ERG modeling. First, they facilitate estimation of the decay parameters in geometrically weighted terms for degree and triad distributions. Estimating decay parameters from a single network is challenging, so in practice they are typically fixed rather than estimated. Multilevel network data overcome that challenge by leveraging replication. Second, such data make it possible to assess out-of-sample performance using traditional cross-validation techniques. We demonstrate these benefits by using a multilevel network sample of classroom networks from Poland. We show that estimating the decay parameters improves in-sample performance of the model and that the out-of-sample performance of our best model is strong, suggesting that our findings can be generalized to the population of interest.