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Marginal asymmetry model for square contingency tables with ordered categories

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  • 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
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    References listed on IDEAS

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    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.
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