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Disentangling Relationships in Symptom Networks Using Matrix Permutation Methods

Published online by Cambridge University Press:  01 January 2025

Michael J. Brusco ,
Douglas Steinley Open the ORCID record for Douglas Steinley [Opens in a new window]  and
Ashley L. Watts
Michael J. Brusco
Affiliation:
Florida State University
Douglas Steinley*
Affiliation:
University of Missouri
Ashley L. Watts
Affiliation:
University of Missouri
*
Correspondence should be made to Douglas Steinley, University of Missouri, Columbia, USA. Email:steinleyd@missouri.edu
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Abstract

Common outputs of software programs for network estimation include association matrices containing the edge weights between pairs of symptoms and a plot of the symptom network. Although such outputs are useful, it is sometimes difficult to ascertain structural relationships among symptoms from these types of output alone. We propose that matrix permutation provides a simple, yet effective, approach for clarifying the order relationships among the symptoms based on the edge weights of the network. For directed symptom networks, we use a permutation criterion that has classic applications in electrical circuit theory and economics. This criterion can be used to place symptoms that strongly predict other symptoms at the beginning of the ordering, and symptoms that are strongly predicted by other symptoms at the end. For undirected symptom networks, we recommend a permutation criterion that is based on location theory in the field of operations research. When using this criterion, symptoms with many strong ties tend to be placed centrally in the ordering, whereas weakly-tied symptoms are placed at the ends. The permutation optimization problems are solved using dynamic programming. We also make use of branch-search algorithms for extracting maximum cardinality subsets of symptoms that have perfect structure with respect to a selected criterion. Software for implementing the dynamic programming algorithms is available in MATLAB and R. Two networks from the literature are used to demonstrate the matrix permutation algorithms.

Keywords

symptom networksnetwork matricesmatrix permutationdynamic programmingdominance indexRobinson index
Type
Applications and case Studies
Information
Psychometrika , Volume 87 , Issue 1: Special Issue on Network Psychometrics in Action , March 2022 , pp. 133 - 155
Copyright
Copyright © 2021 The Psychometric Society

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