关系数据矩阵中节点依赖性的测试
Testing for nodal dependence in relational data matrices
摘要：
关系数据通常表示为方阵，其条目记录了对象对之间的关系。许多分析这些数据的统计方法都假设对象之间在相互关联的方式上存在某种程度的相似性或依赖性。然而，这种依赖性的正式测试尚未开发。我们提供了一个测试这种依赖性使用的框架下的矩阵正态模型，一种类型的多元正态分布参数化的行和列特定的协方差阵。我们发展了一个似然比检验（LRT）的行和列依赖的基础上观察一个单一的关系数据矩阵。我们得到的LRT统计量的参考分布，从而提供了一个确切的测试在一个正方形的关系数据矩阵的行或列的相关性的存在。此外，我们提供了扩展的测试，以适应这些数据的共同特点，如未定义的对角线条目，非零均值，多个观察，并偏离正态性。
英文摘要：
Relational data are often represented as a square matrix, the entries of which record the relationships between pairs of objects. Many statistical methods for the analysis of such data assume some degree of similarity or dependence between objects in terms of the way they relate to each other. However, formal tests for such dependence have not been developed. We provide a test for such dependence using the framework of the matrix normal model, a type of multivariate normal distribution parameterized in terms of row- and column-specific covariance matrices. We develop a likelihood ratio test (LRT) for row and column dependence based on the observation of a single relational data matrix. We obtain a reference distribution for the LRT statistic, thereby providing an exact test for the presence of row or column correlations in a square relational data matrix. Additionally, we provide extensions of the test to accommodate common features of such data, such as undefined diagonal entries, a non-zero mean, multiple observations, and deviations from normality.
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