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

Abstract

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.

Formal Hierarchies and Informal Networks: How Organizational Structure Shapes Information Search in Local Government

“…node(i/o)factor) overspecifies the model. Recently developed, multilevel ERGMS could be used to control for departmental clustering in intraorganizational networks (see Stewart et a. 2019).…”

Exponential-Family Random Graph Models for Multi-Layer Networks

“…Then θ 1 controls the overall strength and direction of the triad closure or anti-closure effect, and θ 2 controls the effect of each additional shared partner. The latter parameter can either be fixed as a tuning parameter, or (with some difficulty (Hunter and Handcock 2006;Stewart et al 2019)) estimated from the data. EP a (•) can be further decomposed into a sum of indicators that test whether there are exactly a 2-paths between i and j:…”

Finite Mixtures of ERGMs for Modeling Ensembles of Networks

“…Data involving ensembles of networks -that is, multiple independent networks -arise in various scientific fields, including sociology (Slaughter and Koehly, 2016;Stewart et al, 2019), neuroscience (Simpson et al, 2011;Obando and De Vico Fallani, 2017), molecular biology (Unhelkar et al, 2017;Grazioli et al, 2019), and political science (Moody and Mucha, 2013) among others. Typically, ensembles of networks represent the action of multiple generative processes, with different processes being prominent in different settings.…”

“…Faust and Skvoretz (2002) introduced both multivariate meta-analysis of ERGM parameters from a common model family (fit to an ensemble of graphs) and predicted conditional edge probabilities from the generative base models as tools for leveraging ERGMs to compare networks. More elaborate meta-analytic procedures and hierarchical models for population of networks were subsequently developed by, among others, Zijlstra et al (2006); Slaughter and Koehly (2016); McFarland et al (2014); Butts (2017), and Stewart et al (2019). In general, those methods have either not posited a generative model for the parameters of the base distribution, as in descriptive meta-analytic approaches (which can be problematic when model interpretation and simulation from the resulting model are of interest), or not suitable for identifying subpopulations from heterogeneous data (as in hierarchical models without mixture structure).…”