Relational hyperevent models for polyadic interaction networks

TL;DR

The study addresses polyadic, multicast interaction data by introducing Relational Hyperevent Models (RHEMs), which use hyperedge covariates defined on the sender and the entire receiver set to capture higher-order dependencies that dyadic REMs miss. The authors formalize the RHEM framework, discuss estimation via case-control sampling, and implement a comprehensive set of actor-attribute and network-history covariates. In an empirical reanalysis of Enron email data, RHEMs demonstrate significant higher-order effects (e.g., exact/unordered repetition, partial receiver-set repetition, and triadic patterns) and achieve superior fit compared to dyadic REMs, suggesting that ignoring these dependencies can misestimate effects. The results imply that hyperedge covariates enrich models of polyadic interaction, offering new avenues for theory and practical analysis of multicast communication networks.

Abstract

Polyadic, or "multicast" social interaction networks arise when one sender addresses multiple receivers simultaneously. Currently available relational event models (REM) are not well suited to the analysis of polyadic interaction networks because they specify event rates for sets of receivers as functions of dyadic covariates associated with the sender and one receiver at a time. Relational hyperevent models (RHEM) address this problem by specifying event rates as functions of hyperedge covariates associated with the sender and the entire set of receivers. For instance, hyperedge covariates can express the tendency of senders to repeatedly address the same pairs (or larger sets) of receivers - a simple and frequent pattern in polyadic interaction data which, however, cannot be expressed with dyadic covariates. In this article we demonstrate the potential benefits of RHEMs for the analysis of polyadic social interaction. We define and discuss practically relevant effects that are not available for REMs but may be incorporated in empirical specifications of RHEM. We illustrate the empirical value of RHEM, and compare them with related REM, in a reanalysis of the canonical Enron email data.

Figures (7)

• Figure 1: Stylized example illustrating unordered repetition. Left: history of a past event $e_1=(t_1,A,\{B,C,D,E\})$ displayed as a gray-shaded area; dashed lines connect the sender to the receivers. Right: a candidate hyperedge $h=(C,\{A,B,D,E\})$ for a future hyperevent. The past event $e_1$ increases the value of unordered repetition on $h$ at time $t>t_1$. In communication networks, unordered repetition could point to turn-taking among a stable set of conversation participants.
• Figure 2: Stylized example illustrating (sender-specific) partial receiver set repetition. Left: history of a past event $e_1=(t_1,A,\{B,C,D,E\})$. Right: a candidate hyperedge $h=(A,\{C,D,E,F\})$ for a future hyperevent. Among the four receivers in $h$, three have individually received the past event $e_1$. Among the six pairs of receivers in $h$, three have jointly received the past event $e_1$. Among the four triples of receivers in $h$, one has jointly received the past event $e_1$. The past event $e_1$ increases the value of sender-specific partial receiver set repetition of order $p=1,2,3$ on $h$ at $t>t_1$. If the sender of $h$ was another actor $G$, instead of $A$, then the past event would still increase the value of partial receiver set repetition, but it would not increase the value of the sender-specific variant.
• Figure 3: Stylized example illustrating the covariate "interaction among receivers". Left: history of a past event $e_1=(t_1,A,\{C,D,E\})$. Right: a candidate hyperedge $h=(F,\{A,B,C,D\})$ for a future hyperevent. The sender $F$ of $h$ sends an interaction to the sender $A$ of the past event $e_1$ and to two of its receivers ($C$ and $D$). The past event $e_1$ increases the value of the covariate interaction among receivers on $h$ at $t>t_1$ for $p=1,2$. For $p>2$ that covariate is zero since there are no three previous receivers that receive an interaction together with the previous sender.
• Figure 4: Stylized example illustrating reciprocation and out-in popularity. Left: history of two past events $e_1=(t_1,A,\{D,E,F\})$ and $e_2=(t_2,B,\{A,C\})$. Right: a candidate hyperedge $h=(D,\{A,B,C\})$ for a future hyperevent. The past event $e_1$ increases the value of the reciprocation covariate on $h$ at $t>t_1$, since $e_1$ has been sent by $A$, a receiver of $h$, among others to $D$, the sender of $h$. The past event $e_2$ does not increase reciprocation on $h$ -- but it increases out-in popularity on $h$, since $e_2$ has been send by $B$, a receiver of $h$.
• Figure 5: Stylized example illustrating transitive closure and cyclic closure. Left: history of two past events $e_1=(t_1,A,\{B,C\})$ and $e_2=(t_2,C,\{D,E\})$. Right: two candidate hyperedges $h=(A,\{D,E\})$ and $h'=(E,\{A,F\})$ for future hyperevents. The past events $e_1,e_2$ increase the value of transitive closure on $h$ at $t>t_1,t_2$, since $h$ transitively closes two paths: from $A$ over $C$ to $D$ and from $A$ over $C$ to $E$. The past events $e_1,e_2$ increase the value of cyclic closure on $h'$ at $t>t_1,t_2$, since $h'$ closes a cycle from $A$ to $C$ to $E$ to $A$.