Modelling Interaction Duration in Relational Event Models

TL;DR

A novel Duration Relational Event Model (DuREM) is introduced that incorporates the temporal duration of events into the analysis and extends the traditional relational event model by also modelling when events will end based on past event history and covariates.

Abstract

The study of relational events, which are interactions occurring between actors over time, has gained significant traction recently. Traditional relational event models typically focus on modelling the occurrence and sequence of events without considering their duration even though duration information is frequently available in empirical relational event data. We introduce a novel Duration Relational Event Model (DuREM) that incorporates the temporal duration of events into the analysis. The proposed model extends the existing framework by (i) allowing the inclusion of past event durations in the endogenous statistics to account for how the duration of past events affects the rate of future interactions, and (ii) extending the traditional relational event model by also modelling when events will end based on past event history and covariates. This is achieved by extending the risk set to include both ongoing events at risk of ending and idle dyads at risk of starting new events. The methodology is implemented in a new R package `durem'. Two case studies concerning team dynamics and inter-personal violence are presented to illustrate the applicability of the model.

Figures (5)

• Figure 1: Representation of sequence of start and end relational events for dyads $d_1$, $d_2$, and $d_3$.
• Figure 2: In the first case study, the weight of past events is determined by the time since the events and their duration. The figures display event weight $w$ for the estimated $\psi^s$, $\psi^e$ and $\tau$ values.
• Figure 3: Profile log-Likelihood for DuREM over a grid of $\psi$ parameters for the street fight data. The red dot indicates the MLE.
• Figure 4: Maximum likelihood estimates of DuREM start-rate parameters ($\boldsymbol{\beta^s}$) at different values of parameters $\psi^s,\psi^e$. Numerical labels on contour lines provide specific values of $\hat{\boldsymbol{\beta^s}}$, illustrating the magnitude of changes. The red dot represents the MLEs $\hat{\boldsymbol{\beta^s}}$.The colours represent the magnitude of the contours in that region with blue indicating higher magnitudes and yellow, lower.
• Figure 5: Maximum likelihood estimates of DuREM end-rate parameters ($\boldsymbol{\beta^e}$) at different values of parameters $\psi^s,\psi^e$. Numerical labels on contour lines provide specific values of $\hat{\boldsymbol{\beta^e}}$, illustrating the magnitude of changes. The red dot represents the MLEs $\hat{\boldsymbol{\beta^e}}$. The colours represent the magnitude of the contours in that region with blue indicating higher magnitudes and yellow, lower.