Estimation and prediction for stochastic blockstructures
(2001) In Journal of the American Statistical Association 96(455). p.10771087 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:
http://lup.lub.lu.se/record/1766816
 author
 Nowicki, Krzysztof ^{LU} and Snijders, Tom A.B.
 organization
 publishing date
 2001
 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
 01621459
 DOI
 10.1198/016214501753208735
 language
 English
 LU publication?
 yes
 id
 d4b4e5eb549940f4b26081c7e77cfa02 (old id 1766816)
 date added to LUP
 20110127 12:56:48
 date last changed
 20180218 04:26:57
@article{d4b4e5eb549940f4b26081c7e77cfa02, 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 = {01621459}, keyword = {Gibbs sampling,social network,latent class model,mixture model,cluster analysis,Colored graph}, language = {eng}, number = {455}, pages = {10771087}, publisher = {American Statistical Association}, series = {Journal of the American Statistical Association}, title = {Estimation and prediction for stochastic blockstructures}, url = {http://dx.doi.org/10.1198/016214501753208735}, volume = {96}, year = {2001}, }