Abstract
For multi-way tables with same categories, Bhapkar and Darroch [4] and Agresti [2], p. 440, considered the general order quasi-symmetry model and the ordinal quasi-symmetry model, respectively. Yamamoto, Iwashita and Tomizawa [16] considered the three kinds of linear ordinal quasi-symmetry models, which are special cases of the first and second order quasi-symmetry models. For multi-way tables with same ordinal categories, the present paper proposes the general linear ordinal quasi-symmetry models, which are special cases of the general order quasi-symmetry model, and gives new decomposition of the symmetry model. Moreover it is shown that the likelihood ratio statistic for testing goodness-of-fit of the symmetry model is asymptotically equivalent to the sum of those for testing goodness-of-fit of the decomposed models.
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Tahata, K., Yamamoto, H. & Tomizawa, S. Linear ordinal quasi-symmetry model and decomposition of symmetry for multi-way tables. Math. Meth. Stat. 20, 158–164 (2011). http://doi.org/10.3103/S1066530711020050
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DOI: http://doi.org/10.3103/S1066530711020050