Goodness of fit of relational event models

TL;DR

This paper introduces a new goodness-of-fit testing framework for relational event models, utilizing weighted martingale residuals and a Kolmogorov-Smirnov test, with applications to synthetic and real email data.

Contribution

It proposes an additive mixed-effect relational event model with a novel goodness-of-fit test based on weighted martingale residuals, enhancing model evaluation efficiency.

Findings

Effective goodness-of-fit assessment demonstrated on synthetic data.

Application to real email data shows practical utility.

Method implemented in R package mgcv.

Abstract

A type of dynamic network involves temporally ordered interactions between actors, where past network configurations may influence future ones. The relational event model can be used to identify the underlying dynamics that drive interactions among system components. Despite the rapid development of this model over the past 15 years, an ongoing area of research revolves around evaluating the goodness of fit of this model, especially when it incorporates time-varying and random effects. Current methodologies often rely on comparing observed and simulated events using specific statistics, but this can be computationally intensive, and requires various assumptions. We propose an additive mixed-effect relational event model estimated via case-control sampling, and introduce a versatile framework for testing the goodness of fit of such models using weighted martingale residuals. Our focus is on a Kolmogorov-Smirnov type test designed to assess if covariates are accurately modeled. Our approach can be easily extended to evaluate whether other features of network dynamics have been appropriately incorporated into the model. We assess the goodness of fit of various relational event models using synthetic data to evaluate the test's power and coverage. Furthermore, we apply the method to a social study involving 57,791 emails sent by 159 employees of a Polish manufacturing company in 2010. The method is implemented in the R package mgcv.