IDEAS home Printed from https://ideas.repec.org/a/wly/envmet/v37y2026i1ne70073.html

Improving and Evaluating Resistant Alternatives to Procrustes Analysis for Multivariate Dataset Matching

Author

Listed:
  • Xiaozhuo Tang
  • Donald A. Jackson

Abstract

Procrustes analysis (PA) is a widely used method for aligning and comparing two or more multivariate data matrices and has been applied across various fields. However, PA is based on the least sum of squares, which has long been recognized as highly sensitive to outliers. This study proposes two new resistant alternatives to PA, advances five previously developed resistant PA methods, and provides accompanying R code for their implementation. The performance of PA and seven resistant PA methods in matching datasets containing outliers was compared and evaluated through simulation studies. We simulated 180 scenarios, including 36 scenarios without outliers and 144 scenarios varying in error variability, proportion of outliers, magnitude of outliers, sample size, reflection, and correlation structure. Results showed that in the presence of outliers, PA performed poorly in identifying outliers and matching datasets across all scenarios, while resistant PA methods, especially our proposed Improved Least Trimmed Squares, demonstrated strong robustness and practical utility. Key factors affecting methods' performance included error variability, proportion of outliers, magnitude of outliers, and sample size. These resistant PA methods have broad applicability in fields such as ecology and evolution, where robust comparison of multivariate datasets is essential.

Suggested Citation

  • Xiaozhuo Tang & Donald A. Jackson, 2026. "Improving and Evaluating Resistant Alternatives to Procrustes Analysis for Multivariate Dataset Matching," Environmetrics, John Wiley & Sons, Ltd., vol. 37(1), January.
    • Handle: RePEc:wly:envmet:v:37:y:2026:i:1:n:e70073
    DOI: 10.1002/env.70073
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/env.70073
    Download Restriction: no
    File URL: https://libkey.io/10.1002/env.70073?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
    ---><---

    References listed on IDEAS

    as
    1. Peter Verboon & Willem Heiser, 1992. "Resistant orthogonal procrustes analysis," Journal of Classification, Springer;The Classification Society, vol. 9(2), pages 237-256, December.
    2. Francy Junio Gonçalves Lisboa & Pedro R Peres-Neto & Guilherme Montandon Chaer & Ederson da Conceição Jesus & Ruth Joy Mitchell & Stephen James Chapman & Ricardo Luis Louro Berbara, 2014. "Much beyond Mantel: Bringing Procrustes Association Metric to the Plant and Soil Ecologist’s Toolbox," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-9, June.
    Full references (including those not matched with items on IDEAS)

    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. Groenen, P.J.F. & Giaquinto, P. & Kiers, H.A.L., 2003. "Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models," Econometric Institute Research Papers EI 2003-09, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Unkel, S. & Trendafilov, N.T., 2010. "A majorization algorithm for simultaneous parameter estimation in robust exploratory factor analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3348-3358, December.
    3. Peter Verboon & Ivo Lans, 1994. "Robust canonical discriminant analysis," Psychometrika, Springer;The Psychometric Society, vol. 59(4), pages 485-507, December.
    4. Henk Kiers, 1997. "Weighted least squares fitting using ordinary least squares algorithms," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 251-266, June.
    5. Ian L. Dryden & Gary Walker, 1999. "Highly Resistant Regression and Object Matching," Biometrics, The International Biometric Society, vol. 55(3), pages 820-825, September.
    6. Justin L. Kern, 2017. "On the Correspondence Between Procrustes Analysis and Bidimensional Regression," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 35-48, April.

    More about this item

    Statistics

    Access and download statistics

    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:wly:envmet:v:37:y:2026:i:1:n:e70073. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/1180-4009/ .

    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.