Testing for Nodal Correlation in Relational Data

• Activity Number: 431
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Alexander Volfovsky*+ and Peter David Hoff
• Companies: University of Washington and University of Washington
• Keywords: matrix normal ; social network ; relational data ; hypothesis test ; separable

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 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 for square data matrices using the framework of the matrix normal model, a type of multivariate normal distribution with a separable covariance matrix. We show that observation of a single matrix is sufficient for the likelihood function to be bounded and therefore for the likelihood ratio statistic to be finite. We obtain a reference distribution for the test statistic thereby providing an exact level-alpha test for the presence of row or column correlations in a square relational data matrix. Additionally, we discuss modifications of the test to accommodate common features of such data, such as missing diagonal entries, a non-zero mean, and multiple observations.