IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/10381.html
   My bibliography  Save this paper

Oblique rotation in correspondence analysis: a step forward in the simplest interpretation

Author

Listed:
  • Lorenzo-Seva, U.
  • van de Velden, M.
  • Kiers, H.A.L.

Abstract

Correspondence analysis (CA) is a popular method that can be used to analyze relationships between categorical variables. It is closely related to several popular multivariate analysis methods such as canonical correlation analysis and principal component analysis. Like principal component analysis, CA solutions can be rotated orthogonally as well as obliquely to simple structure, without affecting the total amount of explained inertia. However, some specific aspects of CA prevent standard rotation procedures from being applied in a straightforward fashion. In particular, the role played by weights assigned to points and dimensions, and the duality of CA solutions, are unique to CA. For orthogonal simple structure rotation, recently procedures have been proposed. In this paper, we construct oblique rotation methods for CA that takes into account these specific difficulties. We illustrate the benefits of our oblique rotation procedure by means of two illustrative examples.

Suggested Citation

  • Lorenzo-Seva, U. & van de Velden, M. & Kiers, H.A.L., 2007. "Oblique rotation in correspondence analysis: a step forward in the simplest interpretation," Econometric Institute Research Papers EI 2007-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:10381
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/10381/Ei-2007-25.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. P. Bentler, 1977. "Factor simplicity index and transformations," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 277-295, June.
    2. Michel Tenenhaus & Forrest Young, 1985. "An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 91-119, March.
    3. Henry Kaiser, 1974. "An index of factorial simplicity," Psychometrika, Springer;The Psychometric Society, vol. 39(1), pages 31-36, March.
    4. R. Jennrich & P. Sampson, 1966. "Rotation for simple loadings," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 313-323, September.
    5. Douglas Clarkson & Robert Jennrich, 1988. "Quartic rotation criteria and algorithms," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 251-259, June.
    6. Robert Jennrich, 2002. "A simple general method for oblique rotation," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 7-19, March.
    7. Michel Velden & Henk A.L. Kiers, 2005. "Rotation in Correspondence Analysis," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 251-271, September.
    8. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    9. Michael Greenacre, 2006. "Tying up the loose ends in simple correspondence analysis," Economics Working Papers 940, Department of Economics and Business, Universitat Pompeu Fabra.
    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. Lorenzo-Seva, Urbano & van de Velden, Michel & Kiers, Henk A. L., 2009. "CAR: A MATLAB Package to Compute Correspondence Analysis with Rotations," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i08).
    2. repec:jss:jstsof:31:i08 is not listed on IDEAS
    3. Urbano Lorenzo-Seva, 2003. "A factor simplicity index," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 49-60, March.
    4. Giovanni Franco, 2014. "Toward a simple structure: a comparison of different rotation techniques," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(3), pages 1785-1797, May.
    5. Thomas Despois & Catherine Doz, 2023. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 533-555, June.
    6. Urbano Lorenzo-Seva, 2000. "The weighted oblimin rotation," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 301-318, September.
    7. Robert Boik, 2008. "Newton Algorithms for Analytic Rotation: an Implicit Function Approach," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 231-259, June.
    8. Marie Chavent & Vanessa Kuentz-Simonet & Jérôme Saracco, 2012. "Orthogonal rotation in PCAMIX," 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(2), pages 131-146, July.
    9. 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.
    10. Xinyi Liu & Gabriel Wallin & Yunxiao Chen & Irini Moustaki, 2023. "Rotation to Sparse Loadings Using $$L^p$$ L p Losses and Related Inference Problems," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 527-553, June.
    11. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," Working Papers halshs-03626503, HAL.
    12. Liu, Xinyi Lin & Wallin, Gabriel & Chen, Yunxiao & Moustaki, Irini, 2023. "Rotation to sparse loadings using Lp losses and related inference problems," LSE Research Online Documents on Economics 118349, London School of Economics and Political Science, LSE Library.
    13. Hironori Satomura & Kohei Adachi, 2013. "Oblique Rotaton in Canonical Correlation Analysis Reformulated as Maximizing the Generalized Coefficient of Determination," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 526-537, July.
    14. Henk Kiers, 1991. "Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 197-212, June.
    15. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," PSE Working Papers halshs-03626503, HAL.
    16. Urbano Lorenzo-Seva & Antoni Rodríguez-Fornells, 2006. "Acquiescent Responding in Balanced Multidimensional Scales and Exploratory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 769-777, December.
    17. Rodríguez-Fuentes, Carlos Javier & Hernández-López, Montserrat, 1997. "Análisis de diferencias estructurales interregionales determinantes en el impacto de la política monetaria," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 7, pages 141-157, Junio.
    18. Hauck, Jana & Suess-Reyes, Julia & Beck, Susanne & Prügl, Reinhard & Frank, Hermann, 2016. "Measuring socioemotional wealth in family-owned and -managed firms: A validation and short form of the FIBER Scale," Journal of Family Business Strategy, Elsevier, vol. 7(3), pages 133-148.
    19. Tina Vohra & Mandeep Kaur, 2018. "Determining Reasons for Lower Participation of Women in Indian Stock Market: A Comparative Study of Stock Investors and Non-investors," Jindal Journal of Business Research, , vol. 7(2), pages 87-102, December.
    20. Lyndon Lim & Elaine Chapman, 2022. "Development and Preliminary Validation of the Moral Reasoning Questionnaire for Secondary School Students," SAGE Open, , vol. 12(1), pages 21582440221, March.
    21. Boik, Robert J., 2008. "An implicit function approach to constrained optimization with applications to asymptotic expansions," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 465-489, March.

    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:ems:eureir:10381. 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: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

    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.