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Measures of fit in principal component and canonical variate analyses

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  • Sugnet Gardner-Lubbe
  • Ni�l Le Roux
  • John Gowers
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    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.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Journal of Applied Statistics.

    Volume (Year): 35 (2008)
    Issue (Month): 9 ()
    Pages: 947-965

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    Handle: RePEc:taf:japsta:v:35:y:2008:i:9:p:947-965

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    Related research

    Keywords: biplots; canonical variate analysis; measures of fit; prediction; principal component analysis;

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    Cited by:
    1. Anthony la Grange & Niël le Roux & Sugnet Gardner-Lubbe, . "BiplotGUI: Interactive Biplots in R," Journal of Statistical Software, American Statistical Association, vol. 30(i12).

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