Fellows Ian E, Handcock Mark S
Fellows Statistics, San Diego, CA 92107 USA.
Department of Statistics, University of California, Los Angeles, Los Angeles, CA 90095-1554 USA.
Metron. 2023;81(1):21-35. doi: 10.1007/s40300-023-00246-3. Epub 2023 May 20.
Networked populations consist of inhomogeneous individuals connected via relational ties. The individuals typically vary in multivariate attributes. In some cases primary interest focuses on individual attributes and in others the understanding of the social structure of the ties. In many circumstances both are of interest, as is their relationship. In this paper we consider this last, most general, case. We model the joint distribution of social ties and individual attributes when the population is only partially observed. Of central interest is when the population is surveyed using a network sampling design. A second situation is when data about a subset of the ties and/or the individual attributes is unintentionally missing. Exponential-family random network models (ERNM)s are capable of specifying a joint statistical representation of both the ties of a network and individual attributes. This class of models allow the nodal attributes to be modeled as stochastic processes, expanding the range and realism of exponential-family approaches to network modeling. In this paper we develop a theory of inference for ERNMs when only part of the network is observed, as well as specific methodology for partially observed networks, including non-ignorable mechanisms for network-based sampling designs. In particular, we consider data collected via contact tracing, of considerable importance to infectious disease epidemiology and public health.
网络群体由通过关系纽带相连的异质个体组成。个体通常在多变量属性上存在差异。在某些情况下，主要关注点在于个体属性，而在其他情况下，则在于对纽带社会结构的理解。在许多情况下，两者都很重要，以及它们之间的关系。在本文中，我们考虑最后这种最一般的情况。当群体仅被部分观察到时，我们对社会纽带和个体属性的联合分布进行建模。核心关注点在于当使用网络抽样设计对群体进行调查时的情况。第二种情况是当关于部分纽带和/或个体属性的数据无意中缺失时。指数族随机网络模型（ERNM）能够指定网络纽带和个体属性的联合统计表示。这类模型允许将节点属性建模为随机过程，扩展了指数族网络建模方法的范围和现实性。在本文中，我们发展了一种在仅观察到部分网络时对ERNM进行推断的理论，以及针对部分观察到的网络的具体方法，包括基于网络抽样设计的不可忽略机制。特别是，我们考虑通过接触者追踪收集的数据，这对传染病流行病学和公共卫生具有相当重要的意义。
