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摘要翻译：
在双向列联表中，我们有时会发现沿对角线单元格的频率相对于非对角线单元格更大（或更小），尤其是在具有常见的行和列类别的方表中。在这种情况下，对于每个对角线单元，通常用一个附加参数的准独立模型来拟合数据。一个比准独立模型更简单的模型是对所有对角线单元假定一个共同的附加参数。我们考虑用马尔可夫链蒙特卡罗(MCMC)方法检验对角效应的拟合优度。我们导出了一个马尔可夫基的显式形式，用于执行公共对角线效应的条件检验。一旦给出了马尔可夫基，MCMC过程就可以很容易地用代数统计技术实现。我们用一些实际数据集来说明这个过程。
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英文标题：
《A Markov Basis for Conditional Test of Common Diagonal Effect in
Quasi-Independence Model for Square Contingency Tables》
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作者：
Hisayuki Hara, Akimichi Takemura and Ruriko Yoshida
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最新提交年份：
2008
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
In two-way contingency tables we sometimes find that frequencies along the diagonal cells are relatively larger(or smaller) compared to off-diagonal cells, particularly in square tables with the common categories for the rows and the columns. In this case the quasi-independence model with an additional parameter for each of the diagonal cells is usually fitted to the data. A simpler model than the quasi-independence model is to assume a common additional parameter for all the diagonal cells. We consider testing the goodness of fit of the common diagonal effect by Markov chain Monte Carlo (MCMC) method. We derive an explicit form of a Markov basis for performing the conditional test of the common diagonal effect. Once a Markov basis is given, MCMC procedure can be easily implemented by techniques of algebraic statistics. We illustrate the procedure with some real data sets.
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PDF链接：
https://arxiv.org/pdf/802.2603
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