The Relative Fit measure for evaluating a blockmodel

Marjan Cugmas (), Aleš Žiberna () and Anuška Ferligoj ()
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Marjan Cugmas: University of Ljubljana
Aleš Žiberna: University of Ljubljana
Anuška Ferligoj: University of Ljubljana

Statistical Methods & Applications, 2021, vol. 30, issue 5, No 3, 1315-1335

Abstract: Abstract 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.

Keywords: Social network; Blockmodeling; Criterion function; Relative fit; Randomising networks (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10260-021-00595-1

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