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Relating principal component analysis on merged data sets to a regression approach

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  • Meyners, Michael
  • Qannari, El Mostafa

Abstract

A method for calculating a consensus of several data matrices on the same samples using a PCA is based on a mathematical background. We propose a model to describe the data which might be obtained e. g. by means of a free choice profiling or a fixed vocabulary in a sensory profiling framework. A regression approach for this model leads to a Principal Component Analysis on Merged Data sets (PCAMD), which provides a simple method to calculate a consensus from the data. Since we use less restrictions on the variables under investigation, the model is claimed to be more general than the model induced by GPA respectively STATIS, which are widely accepted methods to analyse this kind of data. Furthermore, the PCAMD provides also additional opportunities to compare and interpret assessor performances with respect to the variables of the calculated consensus. An example from a sensory profiling study of cider is provided to illustrate these possibilities.

Suggested Citation

  • Meyners, Michael & Qannari, El Mostafa, 2001. "Relating principal component analysis on merged data sets to a regression approach," Technical Reports 2001,47, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200147
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    References listed on IDEAS

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    1. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    2. J. Gower, 1975. "Generalized procrustes analysis," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 33-51, March.
    3. Jos Berge, 1977. "Orthogonal procrustes rotation for two or more matrices," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 267-276, June.
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