IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v42y2015i2p371-379.html
   My bibliography  Save this article

Marginal asymmetry model for square contingency tables with ordered categories

Author

Listed:
  • Kouji Tahata
  • Takuya Yoshimoto

Abstract

For the analysis of square contingency tables with ordered categories, this paper proposes a model which indicates the structure of marginal asymmetry. The model states that the absolute values of logarithm of ratio of the cumulative probability that an observation will fall in row category i or below and column category i +1 or above to the corresponding cumulative probability that the observation falls in column category i or below and row category i +1 or above are constant for every i . We deal with the estimation problem for the model parameter and goodness-of-fit tests. Also we discuss the relationships between the model and a measure which represents the degree of departure from marginal homogeneity. Examples are given.

Suggested Citation

  • Kouji Tahata & Takuya Yoshimoto, 2015. "Marginal asymmetry model for square contingency tables with ordered categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 371-379, February.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:2:p:371-379
    DOI: 10.1080/02664763.2014.951603
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2014.951603
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2014.951603?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. Sadao Tomizawa, 1995. "A Generalization of the Marginal Homogeneity Model for Square Contingency Tables With Ordered Categories," Journal of Educational and Behavioral Statistics, , vol. 20(4), pages 349-360, December.
    2. Kouji Tahata & Sadao Tomizawa, 2008. "Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories," 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. 2(3), pages 295-311, December.
    3. Chi Tim Ng & Johan Lim & Kyu S. Hahn, 2011. "Testing stochastic orders in tails of contingency tables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1133-1149, March.
    4. Kouji Tahata, 2012. "Quasi-asymmetry model for square tables with nominal categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 723-729, August.
    5. Sadao Tomizawa & Nobuko Miyamoto & Ryo Funato, 2004. "Conditional Difference Asymmetry Model for Square Contingency Tables with Nominal Categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(3), pages 271-277.
    6. Bartolucci, F. & Scaccia, L., 2004. "Testing for positive association in contingency tables with fixed margins," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 195-210, August.
    7. Nobuko Miyamoto & Kouji Tahata & Hirokazu Ebie & Sadao Tomizawa, 2006. "Marginal inhomogeneity models for square contingency tables with nominal categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(2), pages 203-215.
    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. Kouji Tahata, 2012. "Quasi-asymmetry model for square tables with nominal categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 723-729, August.
    2. Satoru Shinoda & Kouji Tahata & Kouji Yamamoto & Sadao Tomizawa, 2021. "Marginal Continuation odds Ratio Model and Decomposition of Marginal Homogeneity Model for Multi-way Contingency Tables," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 304-324, November.
    3. Bartolucci, Francesco & Scaccia, Luisa & Farcomeni, Alessio, 2012. "Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4067-4080.
    4. Jeremy E. Reynolds, 2014. "Prevailing Preferences," ILR Review, Cornell University, ILR School, vol. 67(3), pages 1017-1041, July.
    5. Ivy Liu & Alan Agresti, 2005. "The analysis of ordered categorical data: An overview and a survey of recent developments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 1-73, June.
    6. Linda J. Young & M. Kateri & A. Agresti, 2013. "Bayesian inference about odds ratio structure in ordinal contingency tables," Environmetrics, John Wiley & Sons, Ltd., vol. 24(5), pages 281-288, August.
    7. Manuela Cazzaro & Roberto Colombi, 2006. "Maximum Likelihood Inference for Log-linear Models Subject to Constraints of Double Monotone Dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(2), pages 177-190, August.
    8. Shuji Ando, 2019. "A Bivariate Index for Visually Measuring Marginal Inhomogeneity in Square Tables," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(5), pages 58-65, September.
    9. Bayo Lawal, 2008. "On fitting the conditional difference asymmetry models to square contingency tables with nominal categories," Quality & Quantity: International Journal of Methodology, Springer, vol. 42(5), pages 605-612, October.
    10. Alan Agresti, 2014. "Two Bayesian/frequentist challenges for categorical data analyses," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 125-132, August.
    11. Manuela Cazzaro & Roberto Colombi, 2006. "Maximum Likelihood Inference for Log-linear Models Subject to Constraints of Double Monotone Dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(2), pages 177-190, August.
    12. Chi Tim Ng & Johan Lim & Kyu S. Hahn, 2011. "Testing stochastic orders in tails of contingency tables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1133-1149, March.

    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:japsta:v:42:y:2015:i:2:p:371-379. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.