Diagnosing Multicollinearity in Exponential Random Graph Models

Exponential random graph models (ERGM) have been widely applied in the social sciences in the past 10 years. However, diagnostics for ERGM have lagged behind their use. Collinearity-type problems can emerge without detection when fitting ERGM, yielding inconsistent model estimates and problematizing inference from parameters. This article provides a method to detect multicollinearity in ERGM. It outlines the problem and provides a method to calculate the variance inflation factor (VIF) from ERGM parameters. It then evaluates the method with a Monte Carlo simulation, fitting 216,000 ERGMs and calculating the VIFs for each model. The distribution of VIFs is analyzed using multilevel regression to determine what network characteristics lend themselves to collinearity-type problems. The relationship between VIFs and unstable standard errors (a standard sign of collinearity) is also examined. The method is shown to effectively detect multicollinearity, and guidelines for interpretation are discussed.