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Transformed statistics for tests of conditional independence in J×K×L contingency tables

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  • Taneichi, Nobuhiro
  • Sekiya, Yuri
  • Toyama, Jun

Abstract

Tests of the hypothesis of conditional independence in J×K×L contingency tables are considered. An expression to approximate the null distribution of the test statistics is derived. Using this expression, transformed statistics are obtained which converge to a chi-square limiting distribution faster than the original statistics do. Simulations are used to compare the transformed statistics with the original ones, and transformed statistics are proposed based on a Bartlett-type adjustment. Through this work and earlier ones, we cover testing hierarchical loglinear models in three-way tables except for a model having three interaction terms.

Suggested Citation

  • Taneichi, Nobuhiro & Sekiya, Yuri & Toyama, Jun, 2019. "Transformed statistics for tests of conditional independence in J×K×L contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 193-208.
    • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:193-208
    DOI: 10.1016/j.jmva.2018.12.001
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    References listed on IDEAS

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    1. Taneichi, Nobuhiro & Sekiya, Yuri, 2007. "Improved transformed statistics for the test of independence in rxs contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1630-1657, September.
    2. Sekiya, Yuri & Taneichi, Nobuhiro, 2004. "Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 199-223, November.
    3. Taneichi, Nobuhiro & Sekiya, Yuri & Suzukawa, Akio, 2002. "Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 335-359, May.
    4. Fujikoshi, Yasunori, 2000. "Transformations with Improved Chi-Squared Approximations," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 249-263, February.
    5. Nian-Sheng Tang & Man-Lai Tang, 2002. "Exact Unconditional Inference for Risk Ratio in a Correlated 2 × 2 Table with Structural Zero," Biometrics, The International Biometric Society, vol. 58(4), pages 972-980, December.
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