Testing for nodal dependence in relational data matrices.

Published

Journal Article

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. Supplementary materials for this article are available online.

Full Text

Duke Authors

Cited Authors

  • Volfovsky, A; Hoff, PD

Published Date

  • January 2015

Published In

Volume / Issue

  • 110 / 511

Start / End Page

  • 1037 - 1046

PubMed ID

  • 27087713

Pubmed Central ID

  • 27087713

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1080/01621459.2014.965777

Language

  • eng