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Estimation and prediction for stochastic blockstructures

Nowicki, Krzysztof LU and Snijders, Tom A.B. (2001) In Journal of the American Statistical Association 96(455). p.1077-1087
Abstract
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... (More)
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). (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Gibbs sampling, social network, latent class model, mixture model, cluster analysis, Colored graph
in
Journal of the American Statistical Association
volume
96
issue
455
pages
1077 - 1087
publisher
American Statistical Association
external identifiers
  • scopus:0442296603
ISSN
0162-1459
DOI
language
English
LU publication?
yes
id
d4b4e5eb-5499-40f4-b260-81c7e77cfa02 (old id 1766816)
date added to LUP
2011-01-27 12:56:48
date last changed
2018-06-24 04:38:58
@article{d4b4e5eb-5499-40f4-b260-81c7e77cfa02,
  abstract     = {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).},
  author       = {Nowicki, Krzysztof and Snijders, Tom A.B.},
  issn         = {0162-1459},
  keyword      = {Gibbs sampling,social
network,latent class model,mixture model,cluster analysis,Colored graph},
  language     = {eng},
  number       = {455},
  pages        = {1077--1087},
  publisher    = {American Statistical Association},
  series       = {Journal of the American Statistical Association},
  title        = {Estimation and prediction for stochastic blockstructures},
  url          = {http://dx.doi.org/},
  volume       = {96},
  year         = {2001},
}