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The analysis of distance of grouped data with categorical variables: Categorical canonical variate analysis

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  • Le Roux, Niël J.
  • Gardner-Lubbe, Sugnet
  • Gower, John C.

Abstract

We use generalised biplots to develop the important special case of (i) when all variables are categorical and (ii) the samples fall into K recognised groups. We term this Categorical Canonical Variate Analysis (CatCVA), because it has similar characteristics to Rao’s Canonical Variate Analysis (CVA), especially its visual aspects. It allows centroids of groups to be exhibited in increasing numbers of dimensions, together with information on within-group sample variation. Variables are represented by category-level-points (CLPs) which are a counterpart of numerically calibrated biplot axes for quantitative variables. Mechanisms are provided for relating the samples to their category levels, for giving convex regions to help predict categories, and for adding new samples. Inter-sample distance may be measured by any Euclidean embeddable distance. Computation is minimised by working in the K−1 dimensional space containing the group centroids.

Suggested Citation

  • Le Roux, Niël J. & Gardner-Lubbe, Sugnet & Gower, John C., 2014. "The analysis of distance of grouped data with categorical variables: Categorical canonical variate analysis," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 9-24.
    • Handle: RePEc:eee:jmvana:v:132:y:2014:i:c:p:9-24
    DOI: 10.1016/j.jmva.2014.07.014
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    References listed on IDEAS

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    1. Gardner, Sugnet & Gower, John C. & le Roux, N.J., 2006. "A synthesis of canonical variate analysis, generalised canonical correlation and Procrustes analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 107-134, January.
    2. J. Gower & P. Legendre, 1986. "Metric and Euclidean properties of dissimilarity coefficients," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 5-48, March.
    3. John Gower & Niel Roux & Sugnet Gardner-Lubbe, 2014. "The Canonical Analysis of Distance," Journal of Classification, Springer;The Classification Society, vol. 31(1), pages 107-128, April.
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    1. John C. Gower & Niël J. Le Roux & Sugnet Gardner-Lubbe, 2022. "Properties of individual differences scaling and its interpretation," Statistical Papers, Springer, vol. 63(4), pages 1221-1245, August.

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