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The Relative Fit measure for evaluating a blockmodel

Author

Listed:
  • Marjan Cugmas

    (University of Ljubljana)

  • Aleš Žiberna

    (University of Ljubljana)

  • Anuška Ferligoj

    (University of Ljubljana
    National Research University Higher School of Economics)

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.

Suggested Citation

  • Marjan Cugmas & Aleš Žiberna & Anuška Ferligoj, 2021. "The Relative Fit measure for evaluating a blockmodel," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1315-1335, December.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:5:d:10.1007_s10260-021-00595-1
    DOI: 10.1007/s10260-021-00595-1
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    References listed on IDEAS

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    1. Giovanni Strona & Domenico Nappo & Francesco Boccacci & Simone Fattorini & Jesus San-Miguel-Ayanz, 2014. "A fast and unbiased procedure to randomize ecological binary matrices with fixed row and column totals," Nature Communications, Nature, vol. 5(1), pages 1-9, September.
    2. Marjan Cugmas & Anuška Ferligoj & Miha Škerlavaj & Aleš Žiberna, 2021. "Global structures and local network mechanisms of knowledge-flow networks," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-23, February.
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