IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v87y2022i1d10.1007_s11336-021-09760-7.html
   My bibliography  Save this article

Disentangling relationships in symptom networks using matrix permutation methods

Author

Listed:
  • Michael J. Brusco

    (Florida State University)

  • Douglas Steinley

    (University of Missouri)

  • Ashley L. Watts

    (University of Missouri)

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.

Suggested Citation

  • Michael J. Brusco & Douglas Steinley & Ashley L. Watts, 2022. "Disentangling relationships in symptom networks using matrix permutation methods," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 133-155, March.
  • Handle: RePEc:spr:psycho:v:87:y:2022:i:1:d:10.1007_s11336-021-09760-7
    DOI: 10.1007/s11336-021-09760-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-021-09760-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11336-021-09760-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Epskamp, Sacha & Cramer, Angélique O.J. & Waldorp, Lourens J. & Schmittmann, Verena D. & Borsboom, Denny, 2012. "qgraph: Network Visualizations of Relationships in Psychometric Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i04).
    2. Michael Brusco & Stephanie Stahl, 2005. "Optimal Least-Squares Unidimensional Scaling: Improved Branch-and-Bound Procedures and Comparison to Dynamic Programming," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 253-270, June.
    3. L. Hubert & R. Golledge, 1981. "Matrix reorganization and dynamic programming: Applications to paired comparisons and unidimensional seriation," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 429-441, December.
    4. Korte, Bernhard & Oberhofer, Walter, 1971. "Triangularizing input-output matrices and the structure of production," European Economic Review, Elsevier, vol. 11(4), pages 493-522.
    5. J. M. Blin & A. B. Whinston, 1974. "Note--A Note on Majority Rule under Transitivity Constraints," Management Science, INFORMS, vol. 20(11), pages 1439-1440, July.
    6. Michael Brusco, 2002. "A branch-and-bound algorithm for fitting anti-robinson structures to symmetric dissimilarity matrices," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 459-471, September.
    7. Michael Brusco & Stephanie Stahl, 2001. "An interactive multiobjective programming approach to combinatorial data analysis," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 5-24, March.
    8. V. J. Bowman & C. S. Colantoni, 1973. "Majority Rule Under Transitivity Constraints," Management Science, INFORMS, vol. 19(9), pages 1029-1041, May.
    9. Korte, Bernhard & Oberhofer, Walter, 1971. "Triangularizing input-output matrices and the structure of production," European Economic Review, Elsevier, vol. 2(4), pages 493-522.
    10. Eugene L. Lawler, 1963. "The Quadratic Assignment Problem," Management Science, INFORMS, vol. 9(4), pages 586-599, July.
    11. Douglas Steinley & Lawrence Hubert, 2008. "Order-Constrained Solutions in K-Means Clustering: Even Better Than Being Globally Optimal," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 647-664, December.
    12. Michael Brusco & Hans-Friedrich Köhn & Stephanie Stahl, 2008. "Heuristic Implementation of Dynamic Programming for Matrix Permutation Problems in Combinatorial Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 503-522, September.
    13. Scutari, Marco, 2010. "Learning Bayesian Networks with the bnlearn R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i03).
    14. Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1984. "A Cutting Plane Algorithm for the Linear Ordering Problem," Operations Research, INFORMS, vol. 32(6), pages 1195-1220, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Maarten Marsman & Mijke Rhemtulla, 2022. "Guest Editors’ Introduction to The Special Issue “Network Psychometrics in Action”: Methodological Innovations Inspired by Empirical Problems," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 1-11, March.
    2. Denny Borsboom, 2022. "Possible Futures for Network Psychometrics," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 253-265, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael Brusco & Hans-Friedrich Köhn & Stephanie Stahl, 2008. "Heuristic Implementation of Dynamic Programming for Matrix Permutation Problems in Combinatorial Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 503-522, September.
    2. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    3. Jose Apesteguia & Miguel A. Ballester, 2015. "A Measure of Rationality and Welfare," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1278-1310.
    4. Kelin Luo & Yinfeng Xu & Bowen Zhang & Huili Zhang, 2018. "Creating an acceptable consensus ranking for group decision making," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 307-328, July.
    5. Jean-Marie Blin & Frederic H. Murphy, 1973. "Intersectoral Interdependence and Dominance in Input-Output Systems," Discussion Papers 34, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Michael Brusco & Renu Singh & Douglas Steinley, 2009. "Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 705-726, December.
    7. L. Hubert & R. Golledge, 1981. "Matrix reorganization and dynamic programming: Applications to paired comparisons and unidimensional seriation," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 429-441, December.
    8. Nordlund, Carl, 2023. "Transformations, trajectories and similarities of national production structures: a comparative fingerprinting approach," SocArXiv 6byxh, Center for Open Science.
    9. Tavana, M. & Kennedy, D. T. & Joglekar, P., 1996. "A group decision support framework for consensus ranking of technical manager candidates," Omega, Elsevier, vol. 24(5), pages 523-538, October.
    10. Michael Brusco & Stephanie Stahl, 2005. "Optimal Least-Squares Unidimensional Scaling: Improved Branch-and-Bound Procedures and Comparison to Dynamic Programming," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 253-270, June.
    11. Henrique Morrone, 2018. "Which Sectors To Stimulate First In Brazil? Estimating The Sectoral Power To Pull The Economy Out Of The Recession," Anais do XLIV Encontro Nacional de Economia [Proceedings of the 44th Brazilian Economics Meeting] 95, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    12. Köhn, Hans-Friedrich, 2010. "Representation of individual differences in rectangular proximity data through anti-Q matrix decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2343-2357, October.
    13. Kim, Jiyoung & Nakano, Satoshi & Nishimura, Kazuhiko, 2016. "Productivity growth and the structure of production," IDE Discussion Papers 624, Institute of Developing Economies, Japan External Trade Organization(JETRO).
    14. Akram Dehnokhalaji & Pekka J. Korhonen & Murat Köksalan & Nasim Nasrabadi & Diclehan Tezcaner Öztürk & Jyrki Wallenius, 2014. "Constructing a strict total order for alternatives characterized by multiple criteria: An extension," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(2), pages 155-163, March.
    15. Ostblom, Goran, 1997. "Use of the convergence condition for triangularizing input-output matrices and the similarity of production structures among Nordic countries 1970, 1980 and 1985," Structural Change and Economic Dynamics, Elsevier, vol. 8(1), pages 115-128, March.
    16. Prabal Das & D. A. Sachindra & Kironmala Chanda, 2022. "Machine Learning-Based Rainfall Forecasting with Multiple Non-Linear Feature Selection Algorithms," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(15), pages 6043-6071, December.
    17. Georgia Mangion & Melanie Simmonds-Buckley & Stephen Kellett & Peter Taylor & Amy Degnan & Charlotte Humphrey & Kate Freshwater & Marisa Poggioli & Cristina Fiorani, 2022. "Modelling Identity Disturbance: A Network Analysis of the Personality Structure Questionnaire (PSQ)," IJERPH, MDPI, vol. 19(21), pages 1-17, October.
    18. Roland R. Ramsahai, 2020. "Connecting actuarial judgment to probabilistic learning techniques with graph theory," Papers 2007.15475, arXiv.org.
    19. Tang, Kayu & Parsons, David J. & Jude, Simon, 2019. "Comparison of automatic and guided learning for Bayesian networks to analyse pipe failures in the water distribution system," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 24-36.
    20. Myriam Patricia Cifuentes & Clara Mercedes Suarez & Ricardo Cifuentes & Noel Malod-Dognin & Sam Windels & Jose Fernando Valderrama & Paul D. Juarez & R. Burciaga Valdez & Cynthia Colen & Charles Phill, 2022. "Big Data to Knowledge Analytics Reveals the Zika Virus Epidemic as Only One of Multiple Factors Contributing to a Year-Over-Year 28-Fold Increase in Microcephaly Incidence," IJERPH, MDPI, vol. 19(15), pages 1-21, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:87:y:2022:i:1:d:10.1007_s11336-021-09760-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.