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Correspondence analysis of square asymmetric matrices

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  • Michael Greenacre

Abstract

The application of correspondence analysis to square asymmetric tables is often unsuccessful because of the strong role played by the diagonal entries of the matrix, obscuring the data off the diagonal. A simple modification of the centring of the matrix, coupled with the corresponding change in row and column masses and row and column metrics, allows the table to be decomposed into symmetric and skew symmetric components, which can then be analysed separately. The symmetric and skew symmetric analyses can be performed by using a simple correspondence analysis program if the data are set up in a special block format. The methodology is demonstrated on a social mobility table from the first democratically elected Parliament in Germany, the Frankfurter Nationalversammlung. The table cross‐tabulates the jobs of parliamentarians when first entering the labour market and their jobs in May 1848 when the Parliament started its first session.

Suggested Citation

  • Michael Greenacre, 2000. "Correspondence analysis of square asymmetric matrices," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(3), pages 297-310.
  • Handle: RePEc:bla:jorssc:v:49:y:2000:i:3:p:297-310
    DOI: 10.1111/1467-9876.00193
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    File URL: https://doi.org/10.1111/1467-9876.00193
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    Cited by:

    1. Michael Greenacre, 2003. "Singular value decomposition of matched matrices," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1101-1113.
    2. Nora Lado & Anna Torres & Oscar Licandro, 2006. "Changes in the Importance of Bank Attributes Provoked by a Financial Crisis: A Dynamic Analysis of the Uruguayan Case," Economics Working Papers ECO2006/4, European University Institute.
    3. Iodice D'Enza, Alfonso & Palumbo, Francesco & Greenacre, Michael, 2008. "Exploratory data analysis leading towards the most interesting simple association rules," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3269-3281, February.
    4. Giuseppe Bove & Akinori Okada, 2018. "Methods for the analysis of asymmetric pairwise relationships," 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. 12(1), pages 5-31, March.
    5. Tiziano CAMPORESI & Gelsomina CATALANO & Massimo FLORIO & Francesco GIFFONI, 2016. "A Professional Premium for LHC Students: Perceptions from within," Departmental Working Papers 2016-07, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano, revised 08 Jun 2016.
    6. Michael Greenacre, 2001. "Analysis of matched matrices," Economics Working Papers 539, Department of Economics and Business, Universitat Pompeu Fabra.

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