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Orthogonal rotation in PCAMIX

  • Marie ChaventEmail author
  • Vanessa Kuentz-Simonet
  • Jérôme Saracco
Regular Article

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”.

Keywords

Mixture of qualitative and quantitative data Principal component analysis Multiple correspondence analysis Rotation 

Mathematics Subject Classification

6207 (Data Analysis) 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Marie Chavent
    • 1
    • 2
    • 3
    Email author
  • Vanessa Kuentz-Simonet
    • 4
  • Jérôme Saracco
    • 2
    • 3
    • 5
  1. 1.IMB, CNRS, UMR, Université de BordeauxBordeauxFrance
  2. 2.Univ. Bordeaux, IMB, UMR 5251TalenceFrance
  3. 3.INRIATalenceFrance
  4. 4.Irstea, UR ADBXCestas CedexFrance
  5. 5.Institut Polytechnique de BordeauxBordeauxFrance

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