Exponential-Family Random Graph Models for Networks with Endogenous Vertex Sets

Music City Center 

Standard statistical models for network structure (prominently including exponential-family random graph models, or ERGMs) begin with an exogenously specified vertex set, and posit probability distributions for the edge set conditional on the vertex set. In emergent networks in demographic exchange with their environments, however, the joint distribution of network size, composition, and structure are of potential interest. Here, we introduce a family of ERGMs with support on the set of graphs of arbitrary order, allowing for endogenous modeling of the vertex set. We also provide extensions to vertices with discrete-valued covariates, as well as a Markov-chain Monte Carlo scheme for simulating draws from both the homogeneous and inhomogeneous network distributions. Approximate likelihood-based inference using contrastive divergence and simulation-based adequacy checking are also discussed.

Exponential Family Random Graph Models (ERGMs)

Networks

Random Graphs

Markov Chain Monte Carlo

Discrete Exponential Families

Relational Data 

Social Statistics Section