Multiple Correspondence Analysis via Polynomial Transformations of Ordered Categorical Variables |
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Authors: | Rosaria Lombardo Jacqueline J Meulman |
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Institution: | (1) University of Bonn, Bonn, Germany; |
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Abstract: | We present an alternative approach to Multiple Correspondence Analysis (MCA) that is appropriate when the data consist of
ordered categorical variables. MCA displays objects (individuals, units) and variables as individual points and sets of category
points in a low-dimensional space. We propose a hybrid decomposition on the basis of the classical indicator super-matrix,
using the singular value decomposition, and the bivariate moment decomposition by orthogonal polynomials. When compared to
standard MCA, the hybrid decomposition will give the same representation of the categories of the variables, but additionally,
we obtain a clear association interpretation among the categories in terms of linear, quadratic and higher order components.
Moreover, the graphical display of the individual units will show an automatic clustering. |
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Keywords: | |
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