IDEAS home Printed from https://ideas.repec.org/a/taf/lstaxx/v44y2015i18p3978-3996.html
   My bibliography  Save this article

Independence in Contingency Tables Using Simplicial Geometry

Author

Listed:
  • Juan José Egozcue
  • Vera Pawlowsky-Glahn
  • Matthias Templ
  • Karel Hron

Abstract

Frequently, contingency tables are generated in a multinomial sampling. Multinomial probabilities are then organized in a table assigning probabilities to each cell. A probability table can be viewed as an element in the simplex. The Aitchison geometry of the simplex identifies independent probability tables as a linear subspace. An important consequence is that, given a probability table, the nearest independent table is obtained by orthogonal projection onto the independent subspace. The nearest independent table is identified as that obtained by the product of geometric marginals, which do not coincide with the standard marginals, except in the independent case. The original probability table is decomposed into orthogonal tables, the independent and the interaction tables. The underlying model is log-linear, and a procedure to test independence of a contingency table, based on a multinomial simulation, is developed. Its performance is studied on an illustrative example.

Suggested Citation

  • Juan José Egozcue & Vera Pawlowsky-Glahn & Matthias Templ & Karel Hron, 2015. "Independence in Contingency Tables Using Simplicial Geometry," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(18), pages 3978-3996, September.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:18:p:3978-3996
    DOI: 10.1080/03610926.2013.824980
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/03610926.2013.824980
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/03610926.2013.824980?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Wilfredo L. Maldonado & Juan José Egozcue & Vera Pawlowsky‐Glahn, 2021. "No‐arbitrage matrices of exchange rates: Some characterizations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 17(4), pages 375-389, December.
    2. Juan José Egozcue & Vera Pawlowsky-Glahn, 2019. "Compositional data: the sample space and its structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 599-638, September.

    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:taf:lstaxx:v:44:y:2015:i:18:p:3978-3996. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/lsta .

    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.