Temporal network analysis via a degree-corrected Cox model

TL;DR

This paper introduces a novel degree-corrected Cox model for directed temporal networks that captures time-varying degree heterogeneity and homophily effects, with a focus on high-dimensional inference and model diagnostics.

Contribution

It develops a new statistical model and estimation method for analyzing dynamic networks with time-varying effects, addressing high-dimensional challenges.

Findings

Establishes consistency and asymptotic normality of estimators.

Provides tests for temporal variation and degree heterogeneity.

Demonstrates effectiveness through simulations and real data analysis.

Abstract

Temporal dynamics, characterised by time-varying degree heterogeneity and homophily effects, are often exhibited in many real-world networks. As observed in an MIT Social Evolution study, the in-degree and out-degree of the nodes show considerable heterogeneity that varies with time. Concurrently, homophily effects, which explain why nodes with similar characteristics are more likely to connect with each other, are also time-dependent. To facilitate the exploration and understanding of these dynamics, we propose a novel degree-corrected Cox model for directed networks, where the way for degree-heterogeneity or homophily effects to change with time is left completely unspecified. Because each node has individual-specific in- and out-degree parameters that vary over time, the number of unknown parameters grows with the number of nodes, leading to a high-dimensional estimation problem. Therefore, it is highly nontrivial to make inference. We develop a local estimating equations approach to estimate the unknown parameters and establish the consistency and asymptotic normality of the proposed estimators in the high-dimensional regime. We further propose test statistics to check whether temporal variation or degree heterogeneity is present in the network and develop a graphically diagnostic method to evaluate goodness-of-fit for dynamic network models. Simulation studies and two real data analyses are provided to assess the finite sample performance of the proposed method and illustrate its practical utility.