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Hierarchical subspace models for contingency tables

Author

Listed:
  • Hara, Hisayuki
  • Sei, Tomonari
  • Takemura, Akimichi

Abstract

For the statistical analysis of multiway contingency tables, we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom than the usual hierarchical model, while preserving the localization property of the inference in the hierarchical model. This approach also enables us to evaluate the localization property of a given log-affine model. We discuss estimation and exact tests of the proposed model and illustrate the advantage of the proposed modeling with some data sets.

Suggested Citation

  • Hara, Hisayuki & Sei, Tomonari & Takemura, Akimichi, 2012. "Hierarchical subspace models for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 19-34, January.
    • Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:19-34
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    References listed on IDEAS

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    1. Hara, Hisayuki & Takemura, Akimichi & Yoshida, Ruriko, 2009. "A Markov basis for conditional test of common diagonal effect in quasi-independence model for square contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1006-1014, February.
    2. Hojsgaard, Soren, 2003. "Split models for contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 621-645, April.
    3. Kuriki, Satoshi, 2005. "Asymptotic distribution of inequality-restricted canonical correlation with application to tests for independence in ordered contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 420-449, June.
    4. Søren Højsgaard, 2004. "Statistical Inference in Context Specific Interaction Models for Contingency Tables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 143-158, March.
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