gwdegree: Improving interpretation of geometrically-weighted degree estimates in exponential random graph models

Abstract

Exponential random graph models (ERGMs) are maximum entropy statistical models that provide estimates on network tie formation of variables both exogenous (covariate) and endogenous (structural) to a network. Network centralization-the tendency for edges to accrue among a small number of popular nodes-is a key network variable in many fields, and in ERGMs it is primarily modeled via the geometrically-weighted degree (GWD) statistic (Snijders et al. 2006; Hunter 2007). However, the published literature is ambiguous about how to interpret GWD estimates, and there is little guidance on how to interpret or fix values of the GWD shape-parameter, θ S. This Shiny application seeks to improve the use of GWD in ERGMs by demonstrating: 1. how the GWD statistic responds to adding edges to nodes of various degrees, contingent on the value of the shape parameter, θ S ; 2. how the degree distribution of networks of various size and density are shaped by GWD parameter and θ S values; 3. how GWD and GWESP-an ERGM term used to model triadic closure-interact to affect network centralization and clustering.