Orthogonal rotation in PCAMIX |
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Authors: | Marie Chavent Vanessa Kuentz-Simonet Jér?me Saracco |
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Institution: | 1. IMB, CNRS, UMR, Universit?? de Bordeaux, 5251, Bordeaux, France 2. Univ. Bordeaux, IMB, UMR 5251, 33400, Talence, France 3. INRIA, 33400, Talence, France 4. Irstea, UR ADBX, 33612, Cestas Cedex, France 5. Institut Polytechnique de Bordeaux, Bordeaux, France
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Abstract: | Kiers (Psychometrika 56:197–212, 1991) considered the orthogonal rotation in PCAMIX, a principal component method for a mixture of qualitative and quantitative
variables. PCAMIX includes the ordinary principal component analysis and multiple correspondence analysis (MCA) as special
cases. In this paper, we give a new presentation of PCAMIX where the principal components and the squared loadings are obtained
from a Singular Value Decomposition. The loadings of the quantitative variables and the principal coordinates of the categories
of the qualitative variables are also obtained directly. In this context, we propose a computationally efficient procedure
for varimax rotation in PCAMIX and a direct solution for the optimal angle of rotation. A simulation study shows the good
computational behavior of the proposed algorithm. An application on a real data set illustrates the interest of using rotation
in MCA. All source codes are available in the R package “PCAmixdata”. |
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