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Matrix comparison, Part 2: Measuring the resemblance between proximity measures or ordination results by use of the mantel and procrustes statistics

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  • Jesper W. Schneider
  • Pia Borlund

Abstract

The present two‐part article introduces matrix comparison as a formal means for evaluation purposes in informetric studies such as cocitation analysis. In the first part, the motivation behind introducing matrix comparison to informetric studies, as well as two important issues influencing such comparisons, matrix generation, and the composition of proximity measures, are introduced and discussed. In this second part, the authors introduce and thoroughly demonstrate two related matrix comparison techniques the Mantel test and Procrustes analysis, respectively. These techniques can compare and evaluate the degree of monotonicity between different proximity measures or their ordination results. In common with these techniques is the application of permutation procedures to test hypotheses about matrix resemblances. The choice of technique is related to the validation at hand. In the case of the Mantel test, the degree of resemblance between two measures forecast their potentially different affect upon ordination and clustering results. In principle, two proximity measures with a very strong resemblance most likely produce identical results, thus, choice of measure between the two becomes less important. Alternatively, or as a supplement, Procrustes analysis compares the actual ordination results without investigating the underlying proximity measures, by matching two configurations of the same objects in a multidimensional space. An advantage of the Procrustes analysis though, is the graphical solution provided by the superimposition plot and the resulting decomposition of variance components. Accordingly, the Procrustes analysis provides not only a measure of general fit between configurations, but also values for individual objects enabling more elaborate validations. As such, the Mantel test and Procrustes analysis can be used as statistical validation tools in informetric studies and thus help choosing suitable proximity measures.

Suggested Citation

  • Jesper W. Schneider & Pia Borlund, 2007. "Matrix comparison, Part 2: Measuring the resemblance between proximity measures or ordination results by use of the mantel and procrustes statistics," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 58(11), pages 1596-1609, September.
  • Handle: RePEc:bla:jamist:v:58:y:2007:i:11:p:1596-1609
    DOI: 10.1002/asi.20642
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    Cited by:

    1. Hung-Wen Yeh & Byron Gajewski & David Perdue & Angel Cully & Lance Cully & K. Greiner & Won Choi & Christine Daley, 2014. "Sorting it out: pile sorting as a mixed methodology for exploring barriers to cancer screening," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(5), pages 2569-2587, September.
    2. Barbara E. Marschallek & Thomas Jacobsen, 2022. "Smooth and Hard or Beautiful and Elegant? Experts’ Conceptual Structure of the Aesthetics of Materials," SAGE Open, , vol. 12(2), pages 21582440221, May.
    3. Copiello, Sergio, 2019. "Peer and neighborhood effects: Citation analysis using a spatial autoregressive model and pseudo-spatial data," Journal of Informetrics, Elsevier, vol. 13(1), pages 238-254.
    4. Wildgaard, Lorna, 2016. "A critical cluster analysis of 44 indicators of author-level performance," Journal of Informetrics, Elsevier, vol. 10(4), pages 1055-1078.
    5. Nikolaj Bak & Lars K Hansen, 2016. "Data Driven Estimation of Imputation Error—A Strategy for Imputation with a Reject Option," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-13, October.
    6. Tom Broekel & Pierre-Alexandre Balland & Martijn Burger & Frank van Oort, 2013. "Modeling Knowledge Networks in Economic Geography: A Discussion of Four Empirical Strategies," Papers in Evolutionary Economic Geography (PEEG) 1325, Utrecht University, Department of Human Geography and Spatial Planning, Group Economic Geography, revised Dec 2013.
    7. Stoyanov, Slavi & Jablokow, Kathryn & Rosas, Scott R. & Wopereis, Iwan G.J.H. & Kirschner, Paul A., 2017. "Concept mapping—An effective method for identifying diversity and congruity in cognitive style," Evaluation and Program Planning, Elsevier, vol. 60(C), pages 238-244.
    8. Tom Broekel & Pierre-Alexandre Balland & Martijn Burger & Frank Oort, 2014. "Modeling knowledge networks in economic geography: a discussion of four methods," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(2), pages 423-452, September.

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