Scaling bias in pooled exponential random graph models

Researchers often use pooled exponential random graph models (ERGM) to analyze samples of networks. However, pooled ERGM—here, understood to include both meta-regression and combined estimation on a stacked adjacency matrix—may be biased if there is heterogeneity in the latent error variance (‘scaling’) of each lower-level model. This study explores the implications of scaling for pooled ERGM analysis. We illustrate that scaling can produce bias in pooled ERGM coefficients that is more severe than in single-network ERGM and we introduce two methods for reducing this bias. Simulations suggest that scaling bias can be large enough to alter conclusions about pooled ERGM coefficient size, significance, and direction, but can be substantially reduced by estimating the marginal effect within a block diagonal or random effects meta-regression framework. We illustrate each method in an empirical example using Add Health data on 15 in-school friendship networks. Results from the application illustrate that many substantive conclusions vary depending on choice of pooling method and interpretational quantity.