A degree-corrected Cox model for dynamic networks

TL;DR

This paper introduces a degree-corrected Cox model for dynamic networks that accounts for degree heterogeneity, improving estimation of homophily effects in continuous time directed network data.

Contribution

It develops a novel degree-corrected Cox model with local estimating equations for dynamic networks, addressing degree heterogeneity and providing theoretical guarantees.

Findings

The proposed method accurately estimates time-varying parameters.

Simulation studies show good finite sample performance.

Application to real data demonstrates practical utility.

Abstract

Continuous time network data have been successfully modeled by multivariate counting processes, in which the intensity function is characterized by covariate information. However, degree heterogeneity has not been incorporated into the model which may lead to large biases for the estimation of homophily effects. In this paper, we propose a degree-corrected Cox network model to simultaneously analyze the dynamic degree heterogeneity and homophily effects for continuous time directed network data. Since each node has individual-specific in- and out-degree effects in the model, the dimension of the time-varying parameter vector grows with the number of nodes, which makes the estimation problem non-standard. We develop a local estimating equations approach to estimate unknown time-varying parameters, and establish consistency and asymptotic normality of the proposed estimators by using the powerful martingale process theories. We further propose test statistics to test for trend and degree heterogeneity in dynamic networks. Simulation studies are provided to assess the finite sample performance of the proposed method and a real data analysis is used to illustrate its practical utility.