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Estimation and prediction for stochastic blockstructures

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Author

Summary, in English

A statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed. The probability model assumes that the vertices of the digraph are partitioned into several unobserved (latent) classes and that the probability distribution of the relation between two vertices depends only on the classes to which they belong. A Bayesian estimator based on Gibbs sampling is proposed. The basic model is not identified, because class labels are arbitrary. The resulting identifiability problems are solved by restricting inference to the posterior distributions of invariant functions of the parameters and the vertex class membership. In addition, models are considered where class labels are identified by prior distributions for the class membership of some of the vertices. The model is illustrated by an example from the social networks literature (Kapferer's tailor shop).

Publishing year

2001

Language

English

Pages

1077-1087

Publication/Series

Journal of the American Statistical Association

Volume

96

Issue

455

Document type

Journal article

Publisher

American Statistical Association

Topic

  • Probability Theory and Statistics

Keywords

  • Gibbs sampling
  • social network
  • latent class model
  • mixture model
  • cluster analysis
  • Colored graph

Status

Published

ISBN/ISSN/Other

  • ISSN: 0162-1459