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Statistical Models for Social Networks: Inference and Degeneracy
Pages 229-240

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From page 229...
... A much studied sub-class of models are the Markov random graph models introduced by Frank and Strauss (19861. These models DYNAMIC SOCIAL NETWORK MODELING ED ^^YSIS 229
From page 230...
... In this paper we improve understanding of the nature and properties of graph models important to social networks by further considering methods for the stochastic simulation of, and inference for, random graphs. We address one aspect of modeling, that has been a persistent obstacle in the work in this area: inferential degeneracy.
From page 231...
... appear to be the first to propose log-linear models for social networks. Suppose that the dyads are independent with | my if x=l,y=i Pr(X`; =X,Xj, = y)
From page 232...
... covanates on the id"' dyed, text a q -vector of additional network statistics, ~ p -vector of regression parameters. ~ g -vector of degree parameters, and ~ a q -vector of DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS
From page 233...
... Third, if there are no decree distribution parameters and no additional network statistics Me mode] corresponds to the random graphs with independent dyads.
From page 234...
... The papers that use MCMC algorithms to simulate social network models report difficulties in convergence to realistic distributions (Crouch, Wasserman and Trachtenberg 1998 Conander et al 1998. and Snijders 2002)
From page 235...
... The idea is to use an alternative local version of the DYNAMIC SOCIAL NETWORK HODELI?
From page 236...
... In particular the standard errors of the estimates of ~ from the logistic regression will not be appropriate for the maximum pseudolikelihood estimator. The statistical properties of pseudolikelihood estimators for social networks are only partially understood and are discussed in Handcock (2000~.
From page 237...
... This result explains why attempts to calculate MC-MLE estimates for social network models fail. If the model used to simulate the graphs is not close enough to produce realizations that cover the observed values of the statistics, the MC-MLE will not exist even in cases where the MLE does.
From page 238...
... We are in the process of developing Bayesian methodology for random graphs paying particular attention to the specification of prior distributions for the parameters that are meaningful for social networks. Under a Bayesian formulation.
From page 239...
... 4. Iden~ability, Degeneracy and Stability for social networks models The research reviews in the previous sections has allowed progress to be made in both the estimation and simulation of random graphs models.
From page 240...
... One implication of these results is that the effective parameter space of exponentially parametenzed random graph models is bounded and a small subset of the theoretical parameter space. The Bayesian framework for inference promises to be very powerful in social network modeling.


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