IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v28y2013i6p2449-2464.html
   My bibliography  Save this article

Generalized joint Procrustes analysis

Author

Listed:
  • Kohei Adachi

Abstract

In this paper, we propose a generalized version of Adachi’s (Psychometrika 74:667–683, 2009 ) Joint Procrustes Analysis (GJPA), in order to transform the principal component score and loading matrices obtained for multiple data sets of the same size. The transformation is made so that multiple score and loading matrices are optimally matched to two unknown target matrices, respectively, without affecting the fit of the score and loading matrices to data sets, and without any constraint imposed on the transformation, except for its being nonsingular. The resulting transformed score and loading matrices can reasonably be compared across data sets. A simulation study is performed for assessing an alternate least-squares algorithm for GJPA. Additional procedures for interpreting GJPA solutions are also presented and they are illustrated with a real data example. Finally, GJPA is reconsidered in the contexts of three-way data analysis and canonical correlation analysis. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Kohei Adachi, 2013. "Generalized joint Procrustes analysis," Computational Statistics, Springer, vol. 28(6), pages 2449-2464, December.
  • Handle: RePEc:spr:compst:v:28:y:2013:i:6:p:2449-2464
    DOI: 10.1007/s00180-013-0413-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-013-0413-x
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00180-013-0413-x?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. Dahl, Tobias & Naes, Tormod, 2006. "A bridge between Tucker-1 and Carroll's generalized canonical analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3086-3098, July.
    2. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    3. Kohei Adachi, 2011. "Three-Way Tucker2 Component Analysis Solutions of Stimuli × Responses × Individuals Data with Simple Structure and the Fewest Core Differences," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 285-305, April.
    4. Casper Albers & John Gower, 2010. "A general approach to handling missing values in Procrustes analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(4), pages 223-237, December.
    5. John Geer, 1984. "Linear relations amongk sets of variables," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 79-94, March.
    6. Jacques Bénasséni & Mohammed Bennani Dosse, 2012. "Analyzing multiset data by the Power STATIS-ACT method," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(1), pages 49-65, April.
    7. Roger Millsap & William Meredith, 1988. "Component analysis in cross-sectional and longitudinal data," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 123-134, March.
    8. Kohei Adachi, 2009. "Joint Procrustes Analysis for Simultaneous Nonsingular Transformation of Component Score and Loading Matrices," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 667-683, December.
    9. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    10. J. Gower, 1975. "Generalized procrustes analysis," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 33-51, March.
    11. Jos Berge, 1977. "Orthogonal procrustes rotation for two or more matrices," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 267-276, June.
    12. Michel Velden & Yoshio Takane, 2012. "Generalized canonical correlation analysis with missing values," Computational Statistics, Springer, vol. 27(3), pages 551-571, September.
    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. Kensuke Okada & Shin-ichi Mayekawa, 2018. "Post-processing of Markov chain Monte Carlo output in Bayesian latent variable models with application to multidimensional scaling," Computational Statistics, Springer, vol. 33(3), pages 1457-1473, September.

    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. Meyners, Michael & Qannari, El Mostafa, 2001. "Relating principal component analysis on merged data sets to a regression approach," Technical Reports 2001,47, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Dahl, Tobias & Naes, Tormod, 2006. "A bridge between Tucker-1 and Carroll's generalized canonical analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3086-3098, July.
    3. Kensuke Okada & Shin-ichi Mayekawa, 2018. "Post-processing of Markov chain Monte Carlo output in Bayesian latent variable models with application to multidimensional scaling," Computational Statistics, Springer, vol. 33(3), pages 1457-1473, September.
    4. Ikemoto, Hiroki & Adachi, Kohei, 2016. "Sparse Tucker2 analysis of three-way data subject to a constrained number of zero elements in a core array," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 1-18.
    5. Kohei Adachi, 2011. "Three-Way Tucker2 Component Analysis Solutions of Stimuli × Responses × Individuals Data with Simple Structure and the Fewest Core Differences," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 285-305, April.
    6. Mariela González-Narváez & María José Fernández-Gómez & Susana Mendes & José-Luis Molina & Omar Ruiz-Barzola & Purificación Galindo-Villardón, 2021. "Study of Temporal Variations in Species–Environment Association through an Innovative Multivariate Method: MixSTATICO," Sustainability, MDPI, vol. 13(11), pages 1-25, May.
    7. D'Urso, Pierpaolo & Giordani, Paolo, 2003. "A least squares approach to Principal Component Analysis for interval valued data," Economics & Statistics Discussion Papers esdp03013, University of Molise, Department of Economics.
    8. Rizzi, Alfredo & Vichi, Maurizio, 1995. "Representation, synthesis, variability and data preprocessing of a three-way data set," Computational Statistics & Data Analysis, Elsevier, vol. 19(2), pages 203-222, February.
    9. Modroño Herrán, Juan Ignacio & Fernández Aguirre, María Carmen & Landaluce Calvo, M. Isabel, 2003. "Una propuesta para el análisis de tablas múltiples," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    10. Kohei Adachi, 2009. "Joint Procrustes Analysis for Simultaneous Nonsingular Transformation of Component Score and Loading Matrices," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 667-683, December.
    11. Michel Tenenhaus & Arthur Tenenhaus & Patrick J. F. Groenen, 2017. "Regularized Generalized Canonical Correlation Analysis: A Framework for Sequential Multiblock Component Methods," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 737-777, September.
    12. Henk Kiers, 1997. "Techniques for rotating two or more loading matrices to optimal agreement and simple structure: A comparison and some technical details," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 545-568, December.
    13. Pietro Lovaglio & Giorgio Vittadini, 2013. "Multilevel dimensionality-reduction methods," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 183-207, June.
    14. Meyners, M. & Kunert, Joachim & Qannari, El Mostafa, 1998. "Comparing Generalized Procrustes Analysis and STATIS," Technical Reports 1998,35, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    15. Tom Frans Wilderjans & Eva Gaer & Henk A. L. Kiers & Iven Mechelen & Eva Ceulemans, 2017. "Principal Covariates Clusterwise Regression (PCCR): Accounting for Multicollinearity and Population Heterogeneity in Hierarchically Organized Data," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 86-111, March.
    16. Piotr Tarka, 2018. "An overview of structural equation modeling: its beginnings, historical development, usefulness and controversies in the social sciences," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 313-354, January.
    17. Veldscholte, Carla M. & Kroonenberg, Pieter M. & Antonides, Gerrit, 1998. "Three-mode analysis of perceptions of economic activities in Eastern and Western Europe1," Journal of Economic Psychology, Elsevier, vol. 19(3), pages 321-351, June.
    18. Henk Kiers & Jos Berge, 1994. "The Harris-Kaiser independent cluster rotation as a method for rotation to simple component weights," Psychometrika, Springer;The Psychometric Society, vol. 59(1), pages 81-90, March.
    19. Henk Kiers, 1997. "Three-mode orthomax rotation," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 579-598, December.
    20. Bennani Dosse, Mohammed & Kiers, Henk A.L. & Ten Berge, Jos M.F., 2011. "Anisotropic generalized Procrustes analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1961-1968, May.

    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:compst:v:28:y:2013:i:6:p:2449-2464. 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.