Section: New Results

Orthogonal rotation in PCAMIX

Participants : Marie Chavent, Jérôme Saracco.

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 work, 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”.

These results have been obtained in collaboration with Vanessa Kuentz of IRSTEA (UR ABDX).

It has been published in Advances in Data Analysis and Classification [15] and presented in the context of application in cultural sociology in the Premières Rencontres R [42] .