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Generalized Cramér’s coefficient via f-divergence for contingency tables

Author

Listed:
  • Wataru Urasaki

    (Tokyo University of Science)

  • Tomoyuki Nakagawa

    (Tokyo University of Science)

  • Tomotaka Momozaki

    (Tokyo University of Science)

  • Sadao Tomizawa

    (Tokyo University of Science
    Meisei University)

Abstract

Various measures in two-way contingency table analysis have been proposed to express the strength of association between row and column variables in contingency tables. Tomizawa et al. (2004) proposed more general measures, including Cramér’s coefficient, using the power-divergence. In this paper, we propose measures using the f-divergence that has a wider class than the power-divergence. Unlike statistical hypothesis tests, these measures provide quantification of the association structure in contingency tables. The contribution of our study is proving that a measure applying a function that satisfies the condition of the f-divergence has desirable properties for measuring the strength of association in contingency tables. With this contribution, we can easily construct a new measure using a divergence that has essential properties for the analyst. For example, we conducted numerical experiments with a measure applying the $$\theta$$ θ -divergence. Furthermore, we can give further interpretation of the association between the row and column variables in the contingency table, which could not be obtained with the conventional one. We also show a relationship between our proposed measures and the correlation coefficient in a bivariate normal distribution of latent variables in the contingency tables.

Suggested Citation

  • Wataru Urasaki & Tomoyuki Nakagawa & Tomotaka Momozaki & Sadao Tomizawa, 2024. "Generalized Cramér’s coefficient via f-divergence for 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. 18(4), pages 893-910, December.
    • Handle: RePEc:spr:advdac:v:18:y:2024:i:4:d:10.1007_s11634-023-00560-8
    DOI: 10.1007/s11634-023-00560-8
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    References listed on IDEAS

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