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arXiv · 1112.0301

Orthogonal rotation in PCAMIX

M. Chavent·K. Vanessa·J. Saracco
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Abstract

Kiers (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 (PCA) 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 computationaly 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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M. Chavent, K. Vanessa, J. Saracco. 2011-12-01. Orthogonal rotation in PCAMIX. https://doi.org/10.1007/s11634-012-0105-3

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