Orthogonal rotation in PCAMIX

Marie Chavent (1, 2) , K. Vanessa (3) , Jérôme Saracco (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 UR ADBX - Aménités et dynamiques des espaces ruraux

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".

Mots clés: MIXTURE OF QUALITATIVE AND QUANTITATIVE DATA MULTIPLE CORRESPONDENCE ANALYSIS

Domaines: Calcul [stat.CO]

Marie Chavent, K. Vanessa, Jérôme Saracco. Orthogonal rotation in PCAMIX. Advances in Data Analysis and Classification, 2012, 6, pp.131-146. ⟨10.1007/s11634-012-0105-3⟩. ⟨hal-00764427⟩