Orthogonal rotation in PCAMIX

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.