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September 2015 Multilinear tensor regression for longitudinal relational data
Peter D. Hoff
Ann. Appl. Stat. 9(3): 1169-1193 (September 2015). DOI: 10.1214/15-AOAS839

Abstract

A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations. In particular, the relations between members of one pair of nodes may have an effect on the relations between members of another pair. This article develops a type of regression model to estimate such effects in the context of longitudinal and multivariate relational data, or other data that can be represented in the form of a tensor. The model is based on a general multilinear tensor regression model, a special case of which is a tensor autoregression model in which the tensor of relations at one time point are parsimoniously regressed on relations from previous time points. This is done via a separable, or Kronecker-structured, regression parameter along with a separable covariance model. In the context of an analysis of longitudinal multivariate relational data, it is shown how the multilinear tensor regression model can represent patterns that often appear in relational and network data, such as reciprocity and transitivity.

Citation

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Peter D. Hoff. "Multilinear tensor regression for longitudinal relational data." Ann. Appl. Stat. 9 (3) 1169 - 1193, September 2015. https://doi.org/10.1214/15-AOAS839

Information

Received: 1 November 2014; Revised: 1 May 2015; Published: September 2015
First available in Project Euclid: 2 November 2015

zbMATH: 06525982
MathSciNet: MR3418719
Digital Object Identifier: 10.1214/15-AOAS839

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.9 • No. 3 • September 2015
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