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Multiple factor analysis and clustering of a mixture of quantitative, categorical and frequency data

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  • Bécue-Bertaut, Monica
  • Pagès, Jérome

Abstract

Analysing and clustering units described by a mixture of sets of quantitative, categorical and frequency variables is a relevant challenge. Multiple factor analysis is extended to include these three types of variables in order to balance the influence of the different sets when a global distance between units is computed. Suitable coding is adopted to keep as close as possible to the approach offered by principal axes methods, that is, principal component analysis for quantitative sets, multiple correspondence analysis for categorical sets and correspondence analysis for frequency sets. In addition, the presence of frequency sets poses the problem of selecting the unit weighting, since this is fixed by the user (usually uniform) in principal component analysis and multiple correspondence analysis, but imposed by the table margin in correspondence analysis. The method's main steps are presented and illustrated by an example extracted from a survey that aimed to cluster respondents to a questionnaire that included both closed and open-ended questions.

Suggested Citation

  • Bécue-Bertaut, Monica & Pagès, Jérome, 2008. "Multiple factor analysis and clustering of a mixture of quantitative, categorical and frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3255-3268, February.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:3255-3268
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    References listed on IDEAS

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    1. Wang, Xiaogang & Qiu, Weiliang & Zamar, Ruben H., 2007. "CLUES: A non-parametric clustering method based on local shrinking," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 286-298, September.
    2. Escofier, B. & Pages, J., 1994. "Multiple factor analysis (AFMULT package)," Computational Statistics & Data Analysis, Elsevier, vol. 18(1), pages 121-140, August.
    3. Chae, Seong S. & Warde, William D., 2006. "Effect of using principal coordinates and principal components on retrieval of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1407-1417, March.
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