IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v14y2020i3d10.1007_s11634-019-00374-7.html
   My bibliography  Save this article

Familywise decompositions of Pearson’s chi-square statistic in the analysis of contingency tables

Author

Listed:
  • Rosaria Lombardo

    (University of Campania “Luigi Vanvitelli”)

  • Yoshio Takane

    (University of Victoria)

  • Eric J. Beh

    (University of Newcastle)

Abstract

Pearson’s chi-square statistic is well established for testing goodness-of-fit of various hypotheses about observed frequency distributions in contingency tables. A general formula for ANOVA-like decompositions of Pearson’s statistic is given under the independence assumption along with their extensions to higher-order tables. Mathematically, it makes the terms in the partitions and orthogonality among them obvious. Practically, it enables simultaneous analyses of marginal and joint probabilities in contingency tables under a variety of hypotheses about the marginal probabilities. Specifically, this framework accommodates the specification of theoretically driven probabilities as well as the well known cases in which the marginal probabilities are fixed or estimated from the data. The former allows tests of prescribed marginal probabilities, while the latter allows tests of the associations among variables after eliminating the marginal effects. Mixtures of these two cases are also permitted. Examples are given to illustrate the tests.

Suggested Citation

  • Rosaria Lombardo & Yoshio Takane & Eric J. Beh, 2020. "Familywise decompositions of Pearson’s chi-square statistic in the analysis of contingency tables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(3), pages 629-649, September.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:3:d:10.1007_s11634-019-00374-7
    DOI: 10.1007/s11634-019-00374-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-019-00374-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11634-019-00374-7?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.

    References listed on IDEAS

    as
    1. Sébastien Loisel & Yoshio Takane, 2016. "Partitions of Pearson’s Chi-square statistic for frequency tables: a comprehensive account," Computational Statistics, Springer, vol. 31(4), pages 1429-1452, December.
    2. Peter Heijden & Jan Leeuw, 1985. "Correspondence analysis used complementary to loglinear analysis," Psychometrika, Springer;The Psychometric Society, vol. 50(4), pages 429-447, December.
    3. André Carlier & Pieter Kroonenberg, 1996. "Decompositions and biplots in three-way correspondence analysis," Psychometrika, Springer;The Psychometric Society, vol. 61(2), pages 355-373, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michailidis, George & de Leeuw, Jan, 2000. "Multilevel homogeneity analysis with differential weighting," Computational Statistics & Data Analysis, Elsevier, vol. 32(3-4), pages 411-442, January.
    2. Rosaria Lombardo & Eric J. Beh & Luis Guerrero, 2019. "Analysis of three-way non-symmetrical association of food concepts in cross-cultural marketing," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(5), pages 2323-2337, September.
    3. Giuseppe Bove & Akinori Okada, 2018. "Methods for the analysis of asymmetric pairwise relationships," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(1), pages 5-31, March.
    4. repec:jss:jstsof:34:i10 is not listed on IDEAS
    5. Ip, Edward H. & Wang, Yuchung J. & Yeh, Yeong-nan, 2004. "Structural decompositions of multivariate distributions with applications in moment and cumulant," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 119-134, April.
    6. Antonello D’Ambra & Pietro Amenta, 2011. "Correspondence Analysis with Linear Constraints of Ordinal Cross-Classifications," Journal of Classification, Springer;The Classification Society, vol. 28(1), pages 70-92, April.
    7. Brzezińska Justyna, 2020. "The Analysis of the Structure of University Positions in Poland Using Classification Methods," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 24(1), pages 71-81, March.
    8. Alzbeta Kucharcikova & Martin Miciak & Eva Malichova & Maria Durisova & Emese Tokarcikova, 2019. "The Motivation of Students at Universities as a Prerequisite of the Education’s Sustainability within the Business Value Generation Context," Sustainability, MDPI, vol. 11(20), pages 1-25, October.
    9. D'Ambra, Luigi & Amenta, Pietro & D'Ambra, Antonello & de Tibeiro, Jules S., 2021. "A study of the family service expenditures and the socio-demographic characteristics via fixed marginals correspondence analysis," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    10. Vivien, Myrtille & Sabatier, Robert, 2004. "A generalization of STATIS-ACT strategy: DO-ACT for two multiblocks tables," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 155-171, May.
    11. Valero-Mora, Pedro M. & Young, Forrest W. & Friendly, Michael, 2003. "Visualizing categorical data in ViSta," Computational Statistics & Data Analysis, Elsevier, vol. 43(4), pages 495-508, August.
    12. Becue-Bertaut, Monica & Pages, Jerome, 2004. "A principal axes method for comparing contingency tables: MFACT," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 481-503, April.
    13. Fithian, William & Josse, Julie, 2017. "Multiple correspondence analysis and the multilogit bilinear model," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 87-102.

    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:spr:advdac:v:14:y:2020:i:3:d:10.1007_s11634-019-00374-7. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.