Reliability of relational event model estimates under sampling: How to fit a relational event model to 360 million dyadic events

Abstract

We assess the reliability of relational event model parameters estimated under two sampling schemes:(1) uniform sampling from the observed events and (2) case-control sampling which samples non-events, or null dyads ("controls"), from a suitably defined risk set. We experimentally determine the variability of estimated parameters as a function of the number of sampled events and controls per event, respectively. Results suggest that relational event models can be reliably fitted to networks with more than 12 million nodes connected by more than 360 million dyadic events by analyzing a sample of some tens of thousands of events and a small number of controls per event. Using data that we collected on the Wikipedia editing network, we illustrate how network effects commonly included in empirical studies based on relational event models need widely different sample sizes to be estimated reliably. For our analysis we use an open-source software which implements the two sampling schemes, allowing analysts to fit and analyze relational event models to the same or other data that may be collected in different empirical settings, varying sample parameters or model specification.hampered by runtime complexity (Foucault Welles et al. 2014) -a problem that is rooted in the likelihood function which normalizes event rates on dyads that experience events by the rates on all dyads that could have possibly experienced an event at the given point in time. The corresponding risk set can be huge, since its size is often quadratic in the number of nodes. For example, in Wikipedia -the setting for the data that we examine in the empirical part of this paper -more than 6 million users contribute to one or several of more than 5 million encyclopedic articles, giving rise to more than 360 million dyadic events. Thus, at given points in time a dyadic event could occur on more than 30 trillion (3 × 10 13 ) dyads. Computing explanatory variables (statistics) for each of these dyads is unfeasible even for a single observed event -much less so for all 360 million events. Such problems are rather typical since -as mentioned above -large quantities of information on relational events are often collected with automatic data-collection technologies which in turn can easily yield large, or very large networks.Empirical studies applying REM, therefore, have often been limited to networks with a rather small number of nodes (Foucault Welles et al. 2014;Lerner et al. 2013;Vu et al. 2017). Exceptions include studies exploiting a "sparsity condition," namely that a single observed event changes the values of some statistics not for all dyads in the risk set but only for a limited subset (Perry and Wolfe 2013;Hunter et al. 2011). For instance, an observed event on a dyad (a, b) changes the out-degree statistic only for all dyads with source aimplying update costs that are linear, rather than quadratic in the number of nodes. This approach, however, requires to develop specific estimation algorithms for different model statistics. Moreover, it does not...

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