IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v89y2002i2p423-436.html
   My bibliography  Save this article

Goodness of fit of biplots and correspondence analysis

Author

Listed:
  • K. Ruben Gabriel

Abstract

The present paper examines proportional goodness of fit to variables recorded on individuals, the variances and covariances of the variables, and the form and distances between individuals. No single plot displays all three optimally in the sense of least squares. However, even aspects which are non-optimally fitted by biplots and Benzecri plots often closely preserve the optimal fit. This is shown by means of a preservation-of-fit function which depends on the type of display and on the ratio of the second to the first singular value of the data matrix. This function is never below 0·5, so at least half the fit is always preserved, and it is close to 1 unless the ratio of the singular values is small. That explains the frequently observed similarity of the various biplots and the Benzecri plot and the fact that they usually lead to the same conclusions. It follows that in many applications it is reasonable to use either the symmetric biplot or the Benzecri plot or a compromise maximin preservation plot, and that the difference between these three is usually unimportant. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • K. Ruben Gabriel, 2002. "Goodness of fit of biplots and correspondence analysis," Biometrika, Biometrika Trust, vol. 89(2), pages 423-436, June.
  • Handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:423-436
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rozkrut Dominik, 2014. "Measuring Eco-Innovation: Towards Better Policies to Support Green Growth," Folia Oeconomica Stetinensia, Sciendo, vol. 14(1), pages 137-148, June.
    2. Jan Graffelman, 2005. "Enriched biplots for canonical correlation analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(2), pages 173-188.
    3. Michael Greenacre & Paul Lewi, 2005. "Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data," Economics Working Papers 908, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 2007.
    4. Michael Greenacre & Paul Lewi, 2009. "Distributional Equivalence and Subcompositional Coherence in the Analysis of Compositional Data, Contingency Tables and Ratio-Scale Measurements," Journal of Classification, Springer;The Classification Society, vol. 26(1), pages 29-54, April.
    5. Ulrich Kohler & Magdalena Luniak, 2005. "Data inspection using biplots," Stata Journal, StataCorp LP, vol. 5(2), pages 208-233, June.
    6. Michael Greenacre, 2006. "Tying up the loose ends in simple correspondence analysis," Economics Working Papers 940, Department of Economics and Business, Universitat Pompeu Fabra.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:423-436. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.