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Asymmetry models for square contingency tables: exact tests via algebraic statistics

机译：方形列联表的不对称模型：通过代数统计的精确检验

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摘要

Square contingency tables with the same row and column classification occur frequently in a wide range of statistical applications, e.g. whenever the members of a matched pair are classified on the same scale, which is usually ordinal. Such tables are analysed by choosing an appropriate loglinear model. We focus on the models of symmetry, triangular, diagonal and ordinal quasi symmetry. The fit of a specific model is tested by the chi-squared test or the likelihood-ratio test, where p-values are calculated from the asymptotic chi-square distribution of the test statistic or, if this seems unjustified, from the exact conditional distribution. Since the calculation of exact p-values is often not feasible, we propose alternatives based on algebraic statistics combined with MCMC methods.
机译：具有相同行和列分类的方列联列表在各种统计应用中经常出现，例如每当匹配对的成员以相同的等级进行分类时（通常是有序的）。通过选择适当的对数线性模型来分析此类表。我们专注于对称，三角形，对角线和序数准对称的模型。特定模型的拟合度通过卡方检验或似然比检验进行检验，其中p值是根据检验统计量的渐近卡方分布或（如果似乎不合理的话）根据确切的条件分布来计算的。由于精确的p值的计算通常不可行，因此我们提出了基于代数统计和MCMC方法的替代方案。

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