Estimation for Dyadic-Dependent Exponential Random Graph Models
Yang, Xiaolin
Creator
Graduate Student
sonoale@gmail.com
Rinaldo, Alessandro
Creator
Fienberg, Stephen E.
Creator
MATH / Applied Mathematics
Illinois Institute of Technology
Affiliated department
Dyadic dependence
ERGMs
Markov random graph models
Maximum likelihood estimation
Pseudo-likelihood estimation
Social networks
2014
2014-04-30
Graphs are the primary mathematical representation for networks, with nodes or vertices corresponding to units (e.g., individuals) and edges corresponding to relationships. Exponential Random Graph Models (ERGMs) are widely used for describing network data because of their simple structure as an exponential function of a sum of parameters multiplied by their corresponding sufficient statistics. As with other exponential family settings the key computational difficulty is determining the normalizing constant for the likelihood function, a quantity that depends only on the data. In ERGMs for network data, the normalizing constant in the model often makes the parameter estimation intractable for large graphs, when the model involves dependence among dyads in the graph. One way to deal with this problem is to approximate the likelihood function by something tractable, e.g., by using the method of pseudo-likelihood estimation suggested in the early literature. In this paper, we describe the family of ERGMs and explain the increasing complexity that arises from imposing different edge dependence and homogeneous parameter assumptions. We then compare maximum likelihood (ML) and maximum pseudo-likelihood (MPL) estimation schemes with respect to existence and related degeneracy properties for ERGMs involving dependencies among dyads.
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