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

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

Journal of Multivariate Analysis, 2014, vol. 132, issue C, 9-24

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.

Keywords: Analysis of distance; Biplot; Canonical variate analysis; Categorical canonical variate analysis; Category level point; Discriminant analysis; Generalised biplot; Nonlinear biplot; Prediction region; Singular value decomposition (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2014.07.014

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