Statistical Inference for Hierarchical Exponential Random Graph Models and Their Longitudinal Extension with Application on Infectious Disease Spreading
Social networks as a representation of relational data, often possess multiple types of dependency structures at the same time. Analyzing networks in real world requires comprehensive methods but most of the current statistical models only focus on one part while ignoring the other. Motivated by Schweinberger and Handcock (2015) which constructed a family of Exponential Random Graph Models (ERGM) with local dependence assumption, we argue that this kind of hierarchical models has potential to better fit real networks. To tackle the non-scalable estimation problem, we propose a two-stage working-model strategy. We use simulations to show how a good working-model approximation to the (assumed) true ERGM structures helps clustering performance and how the second stage serves as a further tuning to achieve goodness of fit. We apply our approach on a human contact network to demonstrate our aim of providing practitioners in the Social Network Analysis field a practically feasible and theoretically justifiable method. ^ Longitudinal networks provide opportunities to study link formation processes. To infer the (possibly) evolving clusters and other network structures within each community, simultaneously, we propose a class of statistical models named Temporal Hierarchical Exponential Random Graph Models (THERGM). While a direct sampling based Bayesian estimation is computational infeasible, we propose a two-stage strategy. Using simulations, we show the benefit of choosing a sensible working model to lower mis-clustering rate, the improvement of overall goodness-of-fit by fitting specific TERGM, and how mis-clustering rate impact TERGM parameter estimation and link prediction accuracy.^
Cao, Ming, "Statistical Inference for Hierarchical Exponential Random Graph Models and Their Longitudinal Extension with Application on Infectious Disease Spreading" (2017). Texas Medical Center Dissertations (via ProQuest). AAI10682907.