Range of correlation matrices for dependent Bernoulli random variables
Range of correlation matrices for dependent Bernoulli random variables
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DOI：
10.1093/biomet/93.1.197
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发表时间：
2006-03-01
期刊：
影响因子：
2.7
通讯作者：
Joe, H
中科院分区：
文献类型：
--
作者：
Chaganty, NR;Joe, H
如果存在具有均值向量p和相关矩阵R的多元二元分布，我们称(p，R)是相容的。本文研究了结构化相关矩阵和非结构化相关矩阵相容的充要条件。我们给出了与任何p不相容的相关矩阵的例子。利用我们的结果，我们表明Emrich&Piedmonte(1991)和QAQISH(2003)的参数二元模型允许二元变量之间的良好范围的相关性。我们还得到了赔率比矩阵与给定p相容的充要条件。我们的发现支持了普遍认为的赔率比比相关性更少的约束和更灵活的观点。
We say that a pair (p, R) is compatible if there exists a multivariate binary distribution with mean vector p and correlation matrix R. In this paper we study necessary and sufficient conditions for compatibility for structured and unstructured correlation matrices. We give examples of correlation matrices that are incompatible with any p. Using our results we show that the parametric binary models of Emrich & Piedmonte (1991) and Qaqish (2003) allow a good range of correlations between the binary variables. We also obtain necessary and sufficient conditions for a matrix of odds ratios to be compatible with a given p. Our findings support the popular belief that the odds ratios are less constrained and more flexible than the correlations.