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Measures of fit in principal component and canonical variate analyses

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  • Sugnet Gardner-Lubbe
  • Niël Le Roux
  • John Gowers

Abstract

Treating principal component analysis (PCA) and canonical variate analysis (CVA) as methods for approximating tables, we develop measures, collectively termed predictivity, that assess the quality of fit independently for each variable and for all dimensionalities. We illustrate their use with data from aircraft development, the African timber industry and copper froth measurements from the mining industry. Similar measures are described for assessing the predictivity associated with the individual samples (in the case of PCA and CVA) or group means (in the case of CVA). For these measures to be meaningful, certain essential orthogonality conditions must hold that are shown to be satisfied by predictivity.

Suggested Citation

  • Sugnet Gardner-Lubbe & Niël Le Roux & John Gowers, 2008. "Measures of fit in principal component and canonical variate analyses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 947-965.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:9:p:947-965
    DOI: 10.1080/02664760802185399
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    References listed on IDEAS

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    1. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
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    Cited by:

    1. la Grange, Anthony & le Roux, Niël & Gardner-Lubbe, Sugnet, 2009. "BiplotGUI: Interactive Biplots in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 30(i12).
    2. Laura Vicente-Gonzalez & Jose Luis Vicente-Villardon, 2022. "Partial Least Squares Regression for Binary Responses and Its Associated Biplot Representation," Mathematics, MDPI, vol. 10(15), pages 1-23, July.

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