Project
Exploring Hidden Patterns in Relational Event History Data: an extension of Hidden Markov Model for the Relational Event Model

Relational Event History (REH) data refers to longitudinal data that captures the occurrence and timing of relational events between actors or entities within a network over a specific period of time. Examples of REH data sources include email data, communication records, and social networks like Facebook. Each event (e.g., emails) in REH data includes essential details such as the sender, receiver, and the precise message time (or order of the event).

These data can be collected using methods such as sociometric badges, digital communication (email), video monitoring, and other relevant tools. To illustrate, Table 1 provides an instance of face-to-face contacts between employees as part of the REH data analysis [1].

Table 1. The first 5 events from a relational event history

Time	Sender	Receiver
08:00	1	2
08:12	1	3
08:15	4	6
08:16	4	6
08:37	10	7

These events represent interactions, exchanges, or any form of relational activities between individuals or entities within a social or organizational context. Relational Event Model (REM) is a specialized well-established toolkit for analyzing and modeling REH data. The REM stands as a valuable statistical framework for analyzing and modeling event sequences within relational data without the need for data aggregation over observational periods. By avoiding data aggregation, REM retains the crucial temporal aspect of the data. This feature makes REM particularly suitable for studying how social interactions evolve over time and understanding the dynamic patterns of events.

REM considers the timing, direction, and characteristics of events, and it takes into account the dependencies and interrelationships between actors, and parameterizes the interaction rates between actors as a function of exogenous and endogenous statistics, given the event history [3]. Exogenous predictors involve external variables such as personality traits, tenure, age, education, location, hierarchy, or environmental context. By incorporating exogenous predictors, we can explore questions like the influence of extraversion or similarity in age/gender on the likelihood of future interactions. Endogenous predictors capture past interaction characteristics, like past interaction volume, shared interaction partners, Inertia or reciprocity. Including endogenous predictors enables investigation of research questions related to social interaction processes and the event history, such as the impact of past interactions on the timing of subsequent interactions. Given s(sender), and r(receiver), we can write the event rate λ(s,r,t), of directed pair (s,r) at time t as a log linear function of endogenous and exogenous variables. This can be mathematically represented, as demonstrated by, for example, the following predictor set

 I = {Intercept, Inertia, Reciprocity, SameBuilding}

(which describes the influence of statistics on the email occurrence rate, for example), as follows:

λ(s,r,t)=exp⁡(Intercept+Inertia.Xinertias,r,t+Reciprocity.XReciprocitys,r,t+SameBuilding.XSameBuildings,r,t)

Where i are coefficients that represent the impact of predictor Xis,r,t on the event rate. The set of variables in I can be altered based on the specific problem to capture potential system dynamics.

Using REM, we can effectively address questions concerning the impact of external factors and past interaction characteristics to study phenomena as diverse as reciprocity in food-sharing among birds, social disruption in herds of cows, cooperation in organizational networks, and multiple event histories from classroom conversations.

In certain scenarios, it is reasonable to expect that social dynamics may undergo changes, leading to corresponding variations in the parameters used to represent these dynamics. Nevertheless, the conventional REM would assume a constant effect for each statistic over the entire observation period. For many applications, this assumption may not hold. For instance, in critical situations that might happen in a surgery room, the communication dynamics between the surgeons might undergo changes due to issues or emergency situations. This underscores the necessity for employing models that can detect if and when event dynamics experience changes over time. To address this purpose, [3] identified time zones where change points occurred, enhancing the understanding of instantaneous changes in communication behavior over time and how astronauts and control teams in Apollo 13 mission adapt their interactions to cope with critical situations. They achieved this by introducing a novel change point detection algorithm based on Bayesian model, which significantly improved the comprehension of these instantaneous changes.

However, changepoint processes have a limitation: data points in different inferred segments cannot be allocated to the same component. Once a component is left, it cannot be revisited [4]. Nevertheless, for instance, when considering the communication dynamics of a surgical team, the pattern might revert to routine interactions after a critical situation, and this pattern may repeat over time. To address this challenge, we aim to leverage the potential of Hidden Markov Models (HMMs) to effectively model the complexities of the temporal relationships and dependencies within the REM data. HMMs, being probabilistic models, offer a robust approach to modeling sequential data, like event sequences in relational data, through the incorporation of hidden states that reveal underlying patterns and processes.

In this proposal we anticipate a significant breakthrough in our ability to analyze relational event data by integrating HMMs into REM. Our approach goes beyond merely detecting abrupt changes, as we strive to uncover the intricate temporal patterns that encompass gradual transitions, periodic behavior, and combinations of different patterns [5]. By considering shifts from one state to another, much like the transitions between critical and non-critical situations observed in the communication data of the Apollo 13 mission, we can explore various states within communication patterns of the astronaut teams. Similarly, in a surgical team context, we can explore communication patterns when patient loads, patient conditions, or other related factors change within a healthcare team. This comprehensive understanding of the underlying dynamics will provide valuable insights into the complexities of social interactions.

Supervisors
Dr. E.A. Aarts
Dr. M.S.K Shafiee Kamalabad
Dr. Daniel Oberski

Period
2023-2027