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Singular value decomposition of matched matrices

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  • Michael Greenacre

Abstract

We consider the joint analysis of two matched matrices which have common rows and columns, for example multivariate data observed at two time points or split according to a dichotomous variable. Methods of interest include principal components analysis for interval-scaled data, correspondence analysis for frequency data, log-ratio analysis of compositional data and linear biplots in general, all of which depend on the singular value decomposition. A simple result in matrix algebra shows that by setting up two matched matrices in a particular block format, matrix sum and difference components can be analysed using a single application of the singular value decomposition algorithm. The methodology is applied to data from the International Social Survey Program comparing male and female attitudes on working wives across eight countries. The resulting biplots optimally display the overall cross-cultural differences as well as the male-female differences. The case of more than two matched matrices is also discussed.

Suggested Citation

  • Michael Greenacre, 2003. "Singular value decomposition of matched matrices," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1101-1113.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:10:p:1101-1113
    DOI: 10.1080/0266476032000107132
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    References listed on IDEAS

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    1. Michael Greenacre & José G. Clavel, 1998. "Correspondence analysis of two transition tables," Economics Working Papers 298, Department of Economics and Business, Universitat Pompeu Fabra.
    2. John Aitchison & Michael Greenacre, 2002. "Biplots of compositional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 375-392, October.
    3. Michael Greenacre, 2008. "Correspondence analysis of raw data," Economics Working Papers 1112, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2009.
    4. 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.
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    4. Zárraga, A. & Goitisolo, B., 2009. "Simultaneous analysis and multiple factor analysis for contingency tables: Two methods for the joint study of contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3171-3182, June.
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