Power and multicollinearity in small networks: A discussion of "Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks" by Krivitsky, Coletti & Hens.

The recent work by Krivitsky, Coletti & Hens [KCH] provides an important new contribution to the Exponential-Family Random Graph Models [ERGMs], a start-to-finish approach to dealing with multi-network ERGMs. Although multi-network ERGMs have been around for a while (mostly in the form of block-diagonal models and multi-level ERGMs, see Duxbury and Wertsching (2023), Wang et al. (2013), Slaughter and Koehly (2016)), not much care has been given to the estimation and post-estimation steps. In their paper, Krivitsky, Coletti & Hens give a detailed layout of how to build, estimate, and analyze multi-ERGMs with heterogeneous data sources. In this comment, I will focus on two issues the authors did not discuss, namely, sample size requirements and multicollinearity.