Statistical approaches to dynamic networks in society

Networks encode relational structures between entities that do not generally abide by the conditional independence assumption employed in most statistical models. In particular, network analysis has gained traction in the past decades in the Social Sciences, where many applications originate. This cumulative dissertation is dedicated to studying dynamic networks with a focus on applications within the Social Sciences. The thesis is divided into four parts, with the first part providing the background on the contributing manuscripts and putting them into a general context. Each subsequent part is composed of two articles. More specifically, the second part provides an overview of methods to model dynamic networks as well as a substantively meaningful example of using dynamic networks as covariates to study infections during the first wave of the COVID-19 pandemic. The first article introduces two modeling frameworks, one based on Markov chains to study networks observed at discrete time points and another one building on counting processes if the network is continuously monitored in a fine-grained temporal resolution. We showcase the available methods, software implementations, and their applicability and interpretation for each framework by two data examples. The second article uses dynamic spatial and weighted networks as covariates to investigate how regional mobility and social connectivity affect COVID-19 infections in Germany. The third part focuses on studying networks observed at discrete points in time as the outcome of a Markov chain. In the first article encompassed in this part, building on the theorization and description of signed networks, starting with the structural balance theory of \citet{Heider_1946}, and the Temporal Exponential Random Graph model of \citet{Hanneke2010} the Signed Exponential Random Graph Model (SERGM) for the study of dynamic signed networks is introduced. With the theoretical foundation of structural balance theory in mind, novel simultaneous statistics are proposed that provide better performance than operationalizing them by lagged covariates, as commonly done by other authors. The second article examines the co-inventorship of patents viewed as a bipartite network. Here one mode comprises the inventors, and the second mode is composed of all patents on which the inventors collaborate. In particular, we propose a bipartite variant of the TERGM with varying actor compositions, differentiating between inventors that already submitted patents and those that did not while accounting for pairwise statistics of inventors. Finally, in the fourth part of the dissertation, we analyze event data observed in continuous and discrete time. Within the first article, a tie-oriented model for longitudinal event network data is proposed to explore the international trade of combat aircraft. Motivated by the observation that automated or human-coded events often suffer from non-negligible false-discovery rates in event identification, the second article offers the Relational Event Model for Spurious Events (REMSE) as a flexible solution for modeling data while controlling for spurious events. Moreover, it is possible to use the REMSE to assess the robustness of any Relational Event Model specification for the studied event data