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For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper proposes three kinds of new models which have the structure of point-symmetry (PS), quasi point-symmetry and marginal point-symmetry for collapsed square tables. This paper also gives a decomposition of the PS model for collapsed square tables. The father's and his daughter's occupational mobility data are analyzed using new models. 相似文献
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For multiway contingency tables, Wall and Lienert (Biom. J. 18:259–264, 1976) considered the point-symmetry model. For square contingency tables, Tomizawa (Biom. J. 27:895–905, 1985) gave a theorem that the point-symmetry model holds if and only if both the quasi point-symmetry and the marginal point-symmetry
models hold. This paper proposes some quasi point-symmetry models and marginal point-symmetry models for multiway tables,
and extends Tomizawa’s (Biom. J. 27:895–905, 1985) theorem into multiway tables. We also show that for multiway tables the likelihood ratio statistic for testing goodness
of fit of the point-symmetry model is asymptotically equivalent to the sum of those for testing the quasi point-symmetry model
with some order and the marginal point-symmetry model with the corresponding order. An example is given. 相似文献
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