Non-parametric estimation of reciprocity and triadic effects in relational event networks

Abstract

Relational event networks arise naturally from social interactions: interactions can be considered time-stamped edges between vertices of social actors. By studying the factors that influence the interaction inter-arrival times we can get insight in the drivers of interaction dynamics. Relational event models provide a succinct way to analyse a broad family of interactional patterns and their influence on network dynamics. These models can easily incorporate a wide range of mechanisms involving both endogenous and exogenous network effects. It has been typical for quantitive models to assume that endogenous network mechanisms, such as reciprocity or triadic effects, remain stable over time. However, a number of studies argued that reciprocity has a strong tendency to decay over time.This paper proposes to model the dynamic structure of reciprocal and triadic effects in relational event networks via stratified baseline hazards. This avoids having to define arbitrary temporal windows for what can be considered reciprocity or triadic closure. A two-step estimation framework is used, based on the stratified Cox proportional hazards model, followed by non-parametric estimation of the stratified cumulative hazard functions. This framework is illustrated by a simulation study and its application to two studies involving email communication and classroom interactions.