Star graphs induce tetrad correlations: for Gaussian as well as for binary variables
Star graphs induce tetrad correlations: for Gaussian as well as for binary variables
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星图引发四分体相关性：对于高斯变量以及二元变量
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
G. M. Marchetti
中科院分区：
文献类型：
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作者：
N. Wermuth;G. M. Marchetti
当任务被设计用于测量一种能力或态度时，对于高斯分布，历史上就已经得到了四元组相关。这样一个单一的未观测变量可能会在任务之间产生所观测到的线性递增的相关性。我们将这种生成过程与一种特定类型的有向图（星图）以及可追踪回归的概念联系起来。推导出了存在单个潜在变量的四元组相关条件。这些条件不仅对于联合高斯分布中的正相关性是必要的，对于联合二元分布中的正相关性也是必要的。给出了三个关于二元项目的应用。
Tetrad correlations were obtained historically for Gaussian distributions when tasks are designed to measure an ability or attitude so that a single unobserved variable may generate the observed, linearly increasing dependences among the tasks. We connect such generating processes to a particular type of directed graph, the star graph, and to the notion of traceable regressions. Tetrad correlation conditions for the existence of a single latent variable are derived. These are needed for positive dependences not only in joint Gaussian but also in joint binary distributions. Three applications with binary items are given.