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= Relational Event Model =

Conceptual background
The Relational Event Model (REM) has been originally introduced by Carter T. Butts for the analysis of social behavior over short time scales. REMs are statistical models that represent network data. REMs have their roots in the analyses of event histories, used for empirical research on interorganizational exchange and dependence. They are used to understand how social interactions and events occur and are shaped by social context, individual characteristics, or structural constraints. The unit of analysis in REMs is typically an event or a dyad. REMs can be applied to various research questions related to social interactions, network dynamics, and relational processes.

The conceptual background is broad, ranging from social network theory (to study how the connections between individuals shape social action), and symbolic interactionism (to study symbolic meaning to interpret social interaction), to event history analysis (to study the sequence and timing of social interaction). An important assumption in the original conceptualization of REM is undirectionality in social ties, instead focusing on the patterns of connections. This assumption was revised later to capture the complexities of social networks. In the last fifteen years, the original REM has been constantly evolving and multiple specifications of the original model are now available.

Evolution of REMs
REMs have evolved considerably since their initial conceptualization, marked by continuous development and refinement of methodological and analytical tools. Early works such as that by Butts were instrumental in setting the foundation for the REMs framework for social action and network analysis. Butts proposed a statistical approach to capturing dynamic and relational aspects of social behaviors. This provided an innovative perspective on understanding complex networks and their evolving structures.

The next phase in the evolution of REMs saw the development of more complex and refined models, as well as their application in a variety of domains. Works by DuBois et al. (2013), for example, presented hierarchical models for relational event sequences, adding a new level of complexity to the analysis. Similarly, Quintane & Carnabuci and Lerner & Lomi, and others applied REMs to explore dynamics in various organizational and social contexts. These studies enriched the field with their insights into the temporal dynamics of inter-organizational exchange, the role of brokers in the temporality of structural holes, and stability in organizational networks. Importantly, REMs were not confined to human social interaction but also extended to animal behaviour analysis, as evidenced by studies from Tranmer et al. (2015), and Patison et al. (2015).

In more recent years, the applicability of REMs has expanded further, with a range of novel and innovative uses. Lomi and Bianchi (2021) applied REMs to understand role switching and generalized exchange in a financial market. In the field of physics, Fortin et al. (2021) utilized REMs to explore the concept of 'Relational Event-Time in Quantum Mechanics'. These diverse applications underscore the versatility and adaptability of REMs in a variety of research contexts, marking a significant milestone in their evolution.

Core Properties of REMs
REMs exhibit core properties that define their approach to analyzing social action through modeling discrete relational events initiated by social actors. These properties offer a comprehensive framework for understanding dynamics within dynamic networks. The core properties include:


 * Sequentiality and Timing: In order to understand social action, REMs emphasize sequence and timing. It is possible to model how actions unfold over time by taking into consideration the temporal sequence of events.
 * Dynamic Network Perspective: By taking into account changes in network structures over time, REMs adopt a dynamic network perspective. These models capture the formation and dissolution of ties (edges) between actors, allowing researchers to analyze how actors behave within evolving network settings.
 * Endogenous and Exogenous Effects: REMs explain social interactions both endogenously and exogenously. The endogenous effect captures the influence of past event characteristics on future interactions. For instance, repetition or triadic closure may affect the probability of future interactions. Social interactions occur as a result of external factors, such as contextual factors or individual characteristics.
 * Temporal Dependency: REMs account for temporal dependency between events by considering the history of past interactions. Sequential structural signatures are used to model the probability of a single event occurring at any given time, given the previous interactions.
 * Estimating Network Effects: REMs enable the estimation of network effects with improved precision by incorporating information about the timing of events. As a result of this additional temporal information, a more accurate model of how specific actions or interactions contribute to the overall structure of the network can be developed.
 * Model Specification and Fit Assessment: REMs require careful model specification to ensure the accurate representation of social action dynamics. A standard method of assessing model fit may not be appropriate for REMs due to their combination of survival analysis and network model terms. Appropriate fit assessment techniques should be employed to avoid biased estimates.

As a result of focusing on these core properties, REMs offer a useful framework for studying social action within dynamic networks. They provide insight into how past interactions influence future interactions, the influence of contextual factors on interaction patterns, and the influence of individual characteristics on social ties. The use of REMs contributes to a deeper understanding of social dynamics and the temporal complexities of social networks.

Empirical Applications of REMs
REMs can be empirically applied to research questions concerning event based, sequential and dynamic phenomena, such as:


 * How do social networks develop over time?
 * What types of individual attributes make sending or receiving interactions more likely?
 * What types of exogenous contextual factors influence patterns of group interactions?
 * Do certain patterns of interactions influence the probability of future interactions?
 * What is the duration of an interaction effect and how does it wane?
 * Who are the key actors of social networks?

REMs have been largely used to analyze various types of networks, such as contact and interaction networks, networks of political action, conflict networks , and organizational networks.

Group interaction processes and dynamics
The first example of a research domain where REMs can be applied regards group interactions and dynamics, where an innovative approach has been developed using REMs to facilitate the examination of group processes. In particular, Pilny and colleagues tried to comprehend the diverse patterns group members engage in during interactions using REMs. The authors argued that REMs offer a means to address the challenges associated with measuring and methodically analyzing the intricate concept of group interaction processes. By employing longitudinal statistics, REMs enable the incorporation of past relational events, individual attributes, and environmental factors.

Together with this, the increasing availability of data on team dynamics has made the relational event framework an efficient method also for enhancing the understanding of team processes using continuous-time data. In particular, some studies have also sought to elucidate the dynamics of work team processes through the analysis of relational event patterns. These studies focus on the idea that it’s necessary to study team processes as a continuous movie rather than a limited series of snapshots and they demonstrate that different temporal patterns and individuals’ perceptions about team processes are indicative of different team characteristics.

Organizational communication
Organizational communication is another domain where REMs find utility, particularly when focusing on behavioral interactions rather than network structures. By examining the content and frequency of communication events, REMs offer valuable insights into enhancing communication within an organization. Foucault Welles and colleagues leveraged the relational event network and its time-stamped data to track the dynamic evolution of online communication networks, positing that when individuals engage in communications, these can be seen as relational events that, when aggregated, form a network. REMS prove instrumental in analyzing such networks for several reasons, including their ability to explicitly identify the time-dependent nature of network communication patterns and investigate the influence of past relational events on future ones.

Problem-solving
Researchers can utilize REMs also to identify key problem-solvers and problem-solving networks, thereby providing insights into enhancing organizational problem-solving capabilities. In a noteworthy study, Quintane and colleagues investigated a free/open-source software development project, examining the effort contributed by project contributors through the relational events that connect them. This analysis shed light on the underlying dynamics of problem-solving within the project.

Organizational learning
Vu, Pattinson, and Robins used REMs to study organizational learning events and their impact on group dynamics. This approach enables a comprehensive understanding of the interplay between learning events and group dynamics, facilitating insights into the organizational learning process.

Leadership
REMs can identify crucial leadership events and elucidate the factors that contribute to their success. This analytical framework offers insights into how organizations can foster effective leadership and facilitate the formation of hierarchical structures. A recent study conducted by Lerner and Lomi showcased the application of relational event models in examining how dyadic interactions contribute to the emergence of extra-dyadic dependence structures that can be interpreted as hierarchies.

Collaboration and conflict
REMs offer valuable insights into how organizations can cultivate effective collaboration and manage conflicts. In their empirical research centered around the production of Wikipedia articles, Lerner and Lomi demonstrated the utility of REMs in analyzing patterns of agreement and disagreement among group members. This approach enables the prediction of the probability that an individual expresses personal disagreement and/or personal agreement towards another person, providing further understanding of collaboration dynamics within groups.

Other areas of application
Other areas where REMs have been applied include animal social networks and interactions. Tranmer et al. (2015) examined the social network of 12 jackdaws to test whether the birds relied on memory to reciprocate food transfers. Patison et al. (2015) applied REMs to a data set of interactions between familiar and unfamiliar steers to investigate the process of social disruption, relationship formation, the integration process of unfamiliar animals and group building dynamics.

Lomi & Bianchi (2021) used REMs to study generalized exchange in financial markets using data of online trading in a major European interbank market for liquidity.

REMs have also been used to study quantum mechanics (Fortin et al., 2022) to expand the quantum theory of gravity by proposing a relational reconstruction of the event-time, ordering the detection of the definite values of the system’s observables to make quantum mechanics compatible with relativity.

Pros and Cons of REMs
Here are some advantages and disadvantages of using REMs in research :

Advantages of REMs
(1) Captures Temporal Dynamics: REMs are ideal models for capturing the temporal dynamics of interactions among individuals or groups. This allows researchers to understand how past interactions influence future events, providing a better understanding of the evolution of relationships over time.

(2) Allows for Fine-Grained Analysis: REMs allow for the analysis of individual interactions, providing a more detailed and nuanced understanding of the relationships being studied.

Disadvantages of REMs
(1) Small Sample Size: REMs require a typically large number of events to be observed, which can be difficult to achieve in certain research studies with small sample sizes.

(2) Complex Model: REMs are a complex model that requires specialized software to implement. This can be a barrier for some researchers who may not have the necessary expertise or resources.

REMs can be a useful model when the research question involves understanding the impact of specific events or behaviors on network dynamics over time. However, it is important to consider the assumptions and limitations of the model, as well as its suitability for the specific research question at hand. In the stream of longitudinal social network analysis, compared to REMs, the Stochastic Actor-Oriented Model (SAOM) and the Temporal Exponential Random Graph Model (TERGM) may be more appropriate for other specific types of research questions or data structures.