Modelling and inference of relational events
E. C. Wit${}^a$
${}^a$Faculty of Informatics, Università della Svizzera italiana, Lugano, CH
When asked to imagine a social network, one typically envisions a static graph $G=(V,E)$, where edges $(i,j)\in E$ indicate relationships between nodes. Early statistical network models, developed in the 1970s and formalized in the 1980s through exponential random graph models (ERGMs), are inherently static. With the increasing availability of temporal network data in the 1990s, extensions such as temporal ERGMs and stochastic actor-oriented models (SAOMs) were proposed. Building on the latter’s shift toward event-based representations, relational event models (REMs), introduced in 2008, conceptualize network dynamics as a multivariate point process. Specifically, interactions are modeled as a counting process of events $(i,j,t)$ occurring in continuous time, with conditional intensity

$${\lambda }_{ij}(t\mid {\mathscr{H}}_t)=Y(t){\lambda }_0(t)\exp \{{\beta }^{\top }{x}_{ij}(t,{\mathscr{H}}_t)\},$$

where ${\mathscr{H}}_t$ denotes the history of past events and $x_{ij}(\cdot )$ encodes time-varying covariates and endogenous network effects. This formulation connects directly to non-homogeneous Poisson processes and allows for fine-grained modeling of temporal dependence. REMs have proven highly flexible in applications ranging from ecological invasion processes and bike-sharing systems to communication networks and interbank lending. In this talk, I will describe recent methodological developments that improve estimation, scalability, and interpretability, making REMs increasingly practical for applied researchers. Keywords: Networks, Counting process, Inference