Inference in curved exponential family models for networks
Joint Psychology/Applied Statistics Colloquium
by Professor Mark S. Handcock
Abstract: Network data arise in a wide variety of applications. Although descriptive statistics for networks abound in the literature, the science of fitting statistical models to complex network data is still in its infancy. The problem of maximum likelihood estimation for exponential random graph models (ERGMs) using Markov chain Monte Carlo is reviewed, and the methodology is extended to the situation where the model comes from a curved exponential family. The curved exponential family model is applied to new specifications of ERGMs proposed by Snijders, Pattison, Robins & Handcock (2004), having non-linear parameters to represent structural properties of networks such as transitivity and heterogeneity of degree. The difficult topic of implementing likelihood ratio tests for these models is also addressed, and these model-fitting and testing techniques are applied to the estimation of linear and non-linear parameters for a collaboration network among partners in a New England law firm.
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