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Testing for Nodal Dependence in Relational Data Matrices

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  • Alexander Volfovsky
  • Peter D. Hoff

Abstract

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 nonzero mean, multiple observations, and deviations from normality. Supplementary materials for this article are available online.

Suggested Citation

  • Alexander Volfovsky & Peter D. Hoff, 2015. "Testing for Nodal Dependence in Relational Data Matrices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1037-1046, September.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:511:p:1037-1046
    DOI: 10.1080/01621459.2014.965777
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    Cited by:

    1. Hafner, Christian M. & Linton, Oliver B. & Tang, Haihan, 2020. "Estimation of a multiplicative correlation structure in the large dimensional case," Journal of Econometrics, Elsevier, vol. 217(2), pages 431-470.
    2. Hoff, Peter D., 2016. "Limitations on detecting row covariance in the presence of column covariance," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 249-258.
    3. Volfovsky, Alexander & Airoldi, Edoardo M., 2016. "Sharp total variation bounds for finitely exchangeable arrays," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 54-59.

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