Testing and Modeling Dependencies Between a Network and Nodal Attributes

Abstract

Network analysis is often focused on characterizing the dependencies between network relations and node-level attributes. Potential relationships are typically explored by modeling the network as a function of the nodal attributes or by modeling the attributes as a function of the network. These methods require specification of the exact nature of the association between the network and attributes, reduce the network data to a small number of summary statistics, and are unable provide predictions simultaneously for missing attribute and network information. Existing methods that model the attributes and network jointly also assume the data are fully observed. In this article we introduce a unified approach to analysis that addresses these shortcomings. We use a previously developed latent variable model to obtain a low dimensional representation of the network in terms of node-specific network factors. We introduce a novel testing procedure to determine if dependencies exist between the network factors and attributes as a surrogate for a test of dependence between the network and attributes. We also present a joint model for the network relations and attributes, for use if the hypothesis of independence is rejected, that can capture a variety of dependence patterns and be used to make inference and predictions for missing observations.

Social network spatial model

“…In particular, they put forward a class of exponential-family random network models that logistically model the full network, including both the random connection and random attributes. Fosdick and Hoff (2015) further extend such work, focusing on latent variable models for jointly modeling dependencies between a network and nodal attributes. In their work, Fosdick and Hoff allow node-specific network factors to impact the modeling of the network.…”

Equivariant and Scale-Free Tucker Decomposition Models

“…Xu et al (2012) develop a prior over the array normal model in which the mode-specific covariance matrices are functions of a potentially infinite set of latent features. In a similar vein, Fosdick and Hoff (2012) develop a version of factor analysis based on the array normal model. The Tucker product has also been used to construct priors in applications where it is the parameters in the model that are arrays: Bhattacharya and Dunson (2012) use a Tucker product to develop a prior over probability distributions for multivariate categorical data, and Volfovsky and Hoff (2012) use a collection of connected array normal distributions as a prior over parameter arrays in ANOVA decompositions.…”

Observation of tolerance in dynamic social networks using mobile phone data

“…In addition, they do not break connections like dynamic NEM's [11,15].  Nodal Attribute Models (NAM): Unlike the previous two models, a NAM does not rely on network structure and creates connections based explicitly on the attributes of two given nodes [2,19,9]. This research belongs to the category of Dynamic Network Evolution Models.…”