Testing for Nodal Dependence in Relational Data Matrices

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. Howev...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 110; no. 511; pp. 1037 - 1046
Main Authors: Volfovsky, Alexander, Hoff, Peter D.
Format: Journal Article
Language:English
Published: United States Taylor & Francis 01.09.2015
Taylor & Francis Group, LLC
Taylor & Francis Ltd
Subjects:
Analysis of covariance
Correlation analysis
covariance
Data
data analysis
Hypothesis testing
Matrices
Matrix
Matrix normal
Maximum likelihood
Multivariate analysis
Networks
Normal distribution
Normality
Statistical methods
Statistics
Tests
Theory and Methods
Networks
Maximum likelihood
hypothesis testing
Matrix normal
ISSN:1537-274X, 0162-1459, 1537-274X
Online Access:Get full text
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Summary: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.
Bibliography:http://dx.doi.org/10.1080/01621459.2014.965777
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ISSN:1537-274X
0162-1459
1537-274X
DOI:10.1080/01621459.2014.965777