## Assessing Degeneracy in Statistical Models of Social Networks (2003)

Venue: | Journal of the American Statistical Association |

Citations: | 55 - 14 self |

### BibTeX

@ARTICLE{Handcock03assessingdegeneracy,

author = {Mark S. Handcock and Garry Robins and Tom Snijders and Jim Moody and Julian Besag},

title = {Assessing Degeneracy in Statistical Models of Social Networks},

journal = {Journal of the American Statistical Association},

year = {2003},

volume = {76},

pages = {33--50}

}

### Years of Citing Articles

### OpenURL

### Abstract

discussions. This paper presents recent advances in the statistical modeling of random graphs that have an impact on the empirical study of social networks. Statistical exponential family models (Wasserman and Pattison 1996) are a generalization of the Markov random graph models introduced by Frank and Strauss (1986), which in turn are derived from developments in spatial statistics (Besag 1974). These models recognize the complex dependencies within relational data structures. A major barrier to the application of random graph models to social networks has been the lack of a sound statistical theory to evaluate model fit. This problem has at least three aspects: the specification of realistic models, the algorithmic difficulties of the inferential methods, and the assessment of the degree to which the graph structure produced by the models matches that of the data. We discuss these and related issues of the model degeneracy and inferential degeneracy for commonly used estimators.

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Citation Context ... models (Wasserman and Pattison 1996) are a generalization of the Markov random graph models introduced by Frank and Strauss (1986), which in turn are derived from developments in spatial statistics (=-=Besag 1974-=-). These models recognize the complex dependencies within relational data structures. A major barrier to the application of random graph models to social networks has been the lack of a sound statisti... |

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Citation Context ...ssions.sAbstract This paper presents recent advances in the statistical modeling of random graphs that have an impact on the empirical study of social networks. Statistical exponential family models (=-=Wasserman and Pattison 1996-=-) are a generalization of the Markov random graph models introduced by Frank and Strauss (1986), which in turn are derived from developments in spatial statistics (Besag 1974). These models recognize ... |

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Citation Context ...ar, the standard errors of the estimates of θ from the logistic regression will not be appropriate for the maximum pseudolikelihood estimator (MPLE). While in common use (Wasserman and Pattison 1996; =-=Anderson et al. 1999-=-), the statistical properties of pseudolikelihood estimators for social networks are only partially understood. 3.1 Existence and uniqueness of MPLE One concern with the maximum psuedolikelihood algor... |

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Citation Context ...gest, in the context of logistic regression, a penalized likelihood approach. For social networks, we can consider a penalized psuedolikelihood using Jeffreys invariant prior as the penalty function (=-=Heinze and Schemper 2002-=-; Firth 1993). Under this modification the estimates will be finite and may reduce the bias of order O(N −1 ). 3.2 Existence and uniqueness of MLE Many properties of the MLE can be derived from statis... |

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Citation Context ...e extent that they are useful for modeling realistic graphs. Recent advances in model specification, cognizant of these issues, hold much promise (Nowicki and Snijders 2001; Pattison and Robins 2002; =-=Hoff et al. 2002-=-; Schweinberger and Snijders 2003; Snijders et al. 2004). APPENDIX: TECHNICAL DETAILS In this appendix we provide support for the results given in the paper. The model (1) is a finite statistical expo... |

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Citation Context ...models has limited the insight that can be obtained using analytical methods. Second, statistical methods for stochastic simulation from general random graph models have only recently been developed (=-=Crouch et al. 1998-=-; Corander and Dahmstrom 1998; Snijders 2002). Because of this, the properties of general models have not been explored in depth though simulation studies. Third, the properties of statistical methods... |

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