The Relative Fit measure for evaluating a blockmodel

A blockmodel is a network in which the nodes are clusters of equivalent (in terms of the structure of the links connecting) nodes in the network being studied. The term block refers to the links between two clusters. When structural equivalence is relied on, two types of blocks are possible: complet...

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Bibliographic Details
Published in:Statistical methods & applications 2021-12, Vol.30 (5), p.1315-1335
Main Authors: Cugmas, Marjan, Žiberna, Aleš, Ferligoj, Anuška
Format: Article
Language:English
Subjects:
Algorithms
Chemistry and Earth Sciences
Clusters
Computer Science
Criteria
Economics
Equivalence
Finance
Health Sciences
Humanities
Insurance
Law
Links
Management
Mathematics and Statistics
Medicine
Networks
Nodes
Original Paper
Physics
Relocation
Statistical Theory and Methods
Statistics
Statistics for Business
Statistics for Engineering
Statistics for Life Sciences
Statistics for Social Sciences
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Summary:A blockmodel is a network in which the nodes are clusters of equivalent (in terms of the structure of the links connecting) nodes in the network being studied. The term block refers to the links between two clusters. When structural equivalence is relied on, two types of blocks are possible: complete blocks and null blocks. Ideally, all possible links are found in complete blocks while there are no links in null blocks. Yet, in the case of empirical networks, some links frequently appear in null blocks and some non-links appear in complete blocks. These links and non-links are called inconsistencies. When a relocation algorithm is applied to obtain a blockmodel, the criterion function is minimised. The number of inconsistencies is reflected in a criterion function’s value, leading to it being regularly used to fit an empirical network to an ideal blockmodel. Since the value of a criterion function depends on various factors (e.g. the block types allowed, the network size and its density), the values obtained for different networks are incomparable. To address this deficiency, the Relative Fit measure is proposed in this paper. Relative Fit values may be used to select the appropriate blockmodel type and/or number of clusters. Values of the Relative Fit measure can also be of value when fitting different empirical networks to a given blockmodel.
ISSN:1618-2510
1613-981X
DOI:10.1007/s10260-021-00595-1