标题： 多线性张量回归用于纵向关系数据 显示英文标题

标题： Multilinear tensor regression for longitudinal relational data

摘要： 关系数据（如社交网络中的数据）的一个基本方面是关系之间可能存在依赖性。特别是，一个节点对成员之间的关系可能会影响另一个节点对成员之间的关系。本文开发了一种回归模型，用于在纵向和多变量关系数据或其他可以表示为张量形式的数据背景下估计此类效应。该模型基于广义的多元张量回归模型，其中一种特殊情况是张量自回归模型，在这种模型中，一个时间点的关系张量被简洁地回归到之前时间点的关系上。这是通过分离的或Kronecker结构的回归参数以及分离的协方差模型实现的。在纵向多变量关系数据分析的背景下，展示了多元张量回归模型如何表示关系和网络数据中常见的模式，例如互惠性和传递性。 显示英文摘要

摘要： 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.