Discovering trends of social interaction behavior over time: An introduction to relational event modeling

Real-life social interactions occur in continuous time and are driven by complex mechanisms. Each interaction is not only affected by the characteristics of individuals or the environmental context but also by the history of interactions. The relational event framework provides a flexible approach to studying the mechanisms that drive how a sequence of social interactions evolves over time. This paper presents an introduction of this new statistical framework and two of its extensions for psychological researchers. The relational event framework is illustrated with an exemplary study on social interactions between freshmen students at the start of their new studies. We show how the framework can be used to study: (a) which predictors are important drivers of social interactions between freshmen students who start interacting at zero acquaintance; (b) how the effects of predictors change over time as acquaintance increases; and (c) the dynamics between the different settings in which students interact. Findings show that patterns of interaction developed early in the freshmen student network and remained relatively stable over time. Furthermore, clusters of interacting students formed quickly, and predominantly within a specific setting for interaction. Extraversion predicted rates of social interaction, and this effect was particularly pronounced on the weekends. These results illustrate how the relational event framework and its extensions can lead to new insights on social interactions and how they are affected both by the interacting individuals and the dynamic social environment.

Social Interaction Methods

A Bayesian actor-oriented multilevel relational event model with hypothesis testing procedures

Article Open access 17 July 2023

A Relational Event Approach to Modeling Behavioral Dynamics

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Introduction

Through social interactions, we build and maintain social relationships, express and adjust our personalities, exchange information, communicate feelings, and satisfy our fundamental needs for social belongingness and social achievements (Back, 2021; Bakan, 1966; Baumeister & Leary, 1995; Hogan, 1983). Social interactions are a key source of well-being (Kushlev et al., 2018; Lucas et al., 2008; Mueller et al., 2019; Sun et al., 2019), and this appears to hold quite universally. However, the way in which we engage in social interactions and the antecedents that drive us to engage in (specific) social interactions or not appear much less universal and highlight differences on both the individual and interpersonal level in social interaction behavior (see Back 2021; Echterhoff & Schmalbach 2018; Hopwood 2018; Sadler et al., 2011, for overviews). Conceptual models on the development of social relationships emphasize the key role of successive social interactions (Altman & Taylor, 1973; Back et al., 2011; Fehr, 2008; Knapp et al., 2014): People get to know each other and initiate and build social relationships through the flow of shared social interactions over time.

Longitudinal empirical approaches to understanding what drives us to engage in social interaction, to repeat (or not) previous social interactions over time, and the eagerness or speed by which we reach out to others for interaction (or by which we respond to invitations to interact) are, however, scarce (Geukes et al., 2019). Without such approaches it is difficult to develop a fine-grained understanding of how and why social interactions unfold over time. Specifically, there are three key domains of substantive research questions that are to date difficult to investigate given the lack of truly dynamic longitudinal approaches (see ; Back, 2021; Back & Vazire, 2015). First, we need to better understand social interaction processes by which interaction partners influence each other’s behavior and develop more or less intense forms of social relationships. Despite calls for a dynamic, process-oriented view on social interaction (Leenders et al., 2016; Back, 2021), the majority of research on social interaction is based on aggregated counts of social contacts, which provide a relatively static view of social interaction. This prevents us from understanding how important social interaction processes evolve and influence each other over time. Adopting a dynamic view on social interaction enables us to change focus from stable properties of social interaction (‘Are more extraverted individuals on average involved in more interactions?’) to discovering social interaction processes (‘Are, given their previous interactions with each other and other individuals until this time, more extraverted individuals more likely to interact together next?’).

Second, we need a more continuous understanding of social interaction processes across acquaintance levels. Most research examines either zero-acquaintance contexts (i.e., getting-to-know scenarios like first freshmen interactions, speed-dates) or short-term acquaintance contexts (e.g., interactions among students or within network groups) or long-term acquaintance contexts (e.g., interactions among friends or romantic partners). What is currently missing are continuous analyses across time, showing us when certain processes are particularly important and when exactly other processes start to kick-in. That is, we are required to examine questions of stability and change of the driving mechanisms underlying social interaction, including when, how, and why change occurs. These questions are, for example, especially interesting in the context of newly acquainted individuals and the role of personality differences for relationship development. Previous research suggests that how personality drives social interaction changes when individuals become acquainted with each other (Leckelt et al., 2015; Leckelt et al., 2020) but this has not yet been properly tested in a truly continuous fashion.

A third domain of key open questions pertains to the role of interaction settings for social interaction processes. Here, we refer with a ‘setting’ for social interaction to its environmental context, i.e., whether the same individuals interact at home, at work, at a party, etc. It is widely recognized that both characteristics of individuals (e.g., personality) and the environmental context (e.g., situational features; Rauthmann et al., 2014) have important effects on behavior. It is shown that while personality traits affect behaviors across many settings, an individual’s behavior in a specific setting is substantially dependent on the characteristics of the environmental context (Sherman et al., 2015). For example, extraverts behave more sociable in general, and people, and extraverts in particular, behave more sociable in leisure situations (Breil et al., 2019a). It has, however, not yet been investigated in how far and how interaction settings together with individual characteristics influence interaction dynamics, that is, interaction processes over time (e.g., ‘Is the effect of extraversion on the probability to interact next more or less emphasized in leisure settings compared to study-related settings?’) To develop a deeper understanding of how social interaction unfolds over time, we need to examine how various driving mechanisms affect social interactions across and within different settings.

Here, we argue that the challenges involved in tackling these three domains of open research questions can be met by making use of recent advances in both the collection and the analysis of dynamic interaction data. Recent technological advances have increased the possibilities to collect samples of naturally occurring social interactions (Kozlowski, 2015). For example, we may collect e-mail data to learn about patterns of digitally mediated communication between employees in an organization (Mulder & Leenders, 2019; Quintane & Carnabuci, 2016), or learn about real-life social interaction processes by recording naturally occurring social interactions by utilizing mobile phones (Geukes et al., 2019) or proximity sensors (Elmer & Stadtfeld, 2020). Rich data that contains detailed information on the flow of social interactions over time thus becomes increasing available. Pairing such data with data on traits and other characteristics of the individuals allows researchers to study what drives individuals to start, maintain, dissolve, and manage their social interactions over time and how others play a role in an individual’s interaction dynamic.

Following previous suggestions for a micro-analytic approach in which social interactions are observed and studied on a fine-grained timescale (Butts, 2008; 2009; Geukes et al., 2019; Kitts & Quintane, 2019; Kozlowski, 2015; Leenders et al., 2016), the current study proposes and illustrates how such data can be potentially analyzed using a fairly new analytic technique, called “relational event models”. As will be illustrated in the current paper, relational event models are especially suited to study how continuous social interaction data unfolds over time. First, since social interaction processes operate beyond the individual (Back, 2021; Geukes et al., 2019), observations are mutually dependent and assumptions of standard data analytic methods are violated. Relational event models, however, can take into account complex network dependencies. The researcher can utilize this functionality of relational event models to study how individuals’ embeddedness in the overall dynamic network of interactions influences their interaction patterns (e.g., the more two individuals interact with the same others, the more likely it may be for them to interact with each other). Second, the order and timing of social interactions may contain important information on the dynamics of social interaction processes (Butts, 2008; Leenders et al., 2016; Quintane et al., 2014). When we have continuous-time interaction data, relational event models enable researchers to utilize this information in the data and study which factors influence the rhythm and speed of social interaction and how what happens next is influenced by what happened previously. Thus, in sum, relational event-modeling approaches provide psychology researchers with the analytical tools to overcome the previously described challenges and develop from continuous-time interaction data a detailed understanding of how social interaction unfolds over time.

In this article, we introduce relational event modeling and illustrate how this statistical framework can be employed to gain important insights from continuous-time social interaction data. First, a general introduction of relational event modeling is provided. We illustrate that relational event models enable us to study what drives social interaction processes by providing an example analysis of the data from the CONNECT study (Geukes et al., 2019). The data consist of observations of the real-life social interactions between university freshmen at the start of their curriculum. Specifically, we illustrate how relational event models can be used to study how students’ personality traits, demographic characteristics, the kind of situations they are in, their joint interaction history and their embeddedness in the overall dynamic network of interactions affect the way in which they develop and maintain social interactions with the other freshmen in a new community. Second, at the beginning of the observation period, the freshmen students are not yet acquainted with each other. As the students get to know each other, it is to be expected that what drives the social interactions between them changes (Leckelt et al., 2015; Leckelt et al., 2020). We illustrate how the basic relational event modeling analysis can be extended with a so-called “moving window” approach to study how the drivers of social interaction processes in the CONNECT data change over time. Third, we may distinguish between two settings for social interaction that the freshmen students move between: a leisure setting (e.g., an interaction in a restaurant or at a party) and a study-related setting (e.g., an interaction during class or as part of a learning activity). We further extend the analysis and model the setting (leisure versus study-related) as a dependent variable to study how the drives of social interaction processes in the CONNECT data behave across different settings for social interaction. Finally, we conclude with a discussion of the analyses in this paper and provide some outlook on future applications of relational event modeling in psychological research.

Modeling continuous-time social interaction data

Relational event models can analyze any type of continuous-time social interaction data that can be viewed as a so-called relational event history (Butts, 2008). The term “relational event history” refers to a sequence of successive social interactions between a set of individuals that contains information on who are involved in the interactions and the time (or order) when the interactions took place. See Table 1 for an example of an observed relational event history. Each row in Table 1 represents a so-called relational event, which is minimally defined as an interaction between two or more individuals at a specific point in time (Butts, 2008). Relational events can be, and often are, extended with more information on the social interaction, such as the “setting” for interaction or the “duration” of the interaction (see the rightmost two columns of Table 1).

Table 1 The first few social interactions observed between freshmen students at the beginning of their new studies in the CONNECT study (Geukes et al., 2019)

Full size table

Relational event models are especially suited to model relational event history data. They enable researchers to study how the complex interplay of individuals’ characteristics, their environment, and their history of interaction influences the probability for future social interaction, thereby continuously updating the past. In recent years, a number of relational event modeling approaches have been introduced (Butts, 2008; de Nooy, 2011; Perry & Wolfe, 2013; Stadtfeld & Block, 2017). The current paper focuses on Butts’ (2008) relational event model (REM), which provides an especially flexible framework for modeling relational event history data. Many of the concepts that we describe in the current paper, however, also apply to other relational event modeling approaches. For a comparison between different approaches, we refer the interested reader to Quintane et al.(2014, pp. 28-30).

In a REM, the probability of relational events to occur at a certain point in time or in the sequence is modeled. The core of the REM is the event rate λ. At a given time t, the event rate determines both (a) who will interact next, and (b) when the next interaction will take place. Therefore, a so-called “risk set” must be defined. This risk set $\mathcal {R}(t)$ contains all the events that can potentially occur at time t. Often, it makes sense to define the risk set as all possible directed or undirected pairs (s, r) of individuals. For example, given N individuals and undirected pairs, the risk set consists of $\frac {N(N-1)}{2}$ relational events. In principle, the events in the risk set can potentially occur at any point in time. It is possible, however, that the size of the risk set varies over time. For example, if an individual is not available for interaction for a certain time-interval during the study period, the events with that individual should be excluded from the risk set for the time points t that fall within that interval. Hence, we can flexibly account for individuals’ availability for social interaction to accurately model the social interaction processes among a set of individuals (see also ; Quintane et al., 2014).

While the event rate for a pair of individuals is assumed to change over the course of the study period, the event rate is assumed to remain constant from the time of the current event until the time of the next event. Given this piecewise constant hazard assumption, the waiting time from the current event at time t until the next event follows an exponential distribution, where the rate parameter is the sum of all the event rates for the pairs at time t:

$${\Delta} t \sim \text{Exponential} \Bigg( \sum\limits_{\mathcal{R}(t)} \lambda(s,r,t) \Bigg).$$

(1)

Thus, higher event rates at time t decrease the expected time until the next relational event (compared to lower event rates at time t).

Under the piecewise constant hazard assumption, the probability that the next observed relational event at time t is of the pair (i, j) is equal to

$$P((i,j)|t) = \frac{\lambda(i,j,t)}{{\sum}_{\mathcal{R}(t)}\lambda(s,r,t)},$$

(2)

i.e., the event rate of the pair (i, j) relative to the event rates of all the pairs (s, r) in the risk set $\mathcal {R}$ at time t, including (i, j) (Butts, 2008). Thus, pairs with a higher event rate at time t are more likely to be observed next than pairs with a lower event rate at time t.

The REM enables researchers to study the predictors that explain how an observed relational event history evolves over time by modeling the event rate. The event rate is modeled as the outcome variable on which predictors are regressed through a log-linear function:

$$\log \lambda(s,r,t) = \sum\limits_{p}{{\upbeta}_{p} x_{p}(s,r,t)}.$$

(3)

Here, β_p refers to the model parameter that denotes the magnitude of the effect of predictor x_p on the event rate. In this article, we follow Butts (2008) and refer to these predictors as statistics, but they are also sometimes referred to as “sequential structural signatures (SSS)” in the literature (Leenders et al., 2016; Pilny et al., 2016). Statistics can encode both exogenous and endogenous predictors of the event rate. First, exogenous predictors refer to any kind of variable that is external to the relational event history itself, such as individuals’ personality traits, age, or gender, or the environmental context (e.g., whether interaction occurs in a leisure or study-related setting). By including exogenous predictors of the event rate in the model we can study research questions like ‘Are more extraverted pairs more likely to interact next?’ or ‘Are pairs more likely to interact next if they are similar in age or gender?’. Second, it is assumed that each event in the observed sequence depends on the history of events. This assumption allows us to model the events independently, conditional on the history of events. How an event depends on the past is summarized by the endogenous predictors that are included in the model to explain the event rate. Endogenous predictors summarize characteristics of past interactions (Leenders et al., 2016), e.g., the volume of past interactions for a given student pair or the number of interaction partners with whom both students in a given student pair have interacted in the past. By including endogenous predictors of the event rate in the model we can study potential important research questions related to social interaction processes, like ’Does the time between subsequent interactions decrease if individuals have interacted more together in the past?’, or, interacting an endogenous predictor with an exogenous predictor, ’Are less extraverted pairs more likely to interact together next if they have interacted more together in the past compared to more extravert pairs?’. Estimation of the model parameters β_p associated with the predictors allows us to make inferences about the effects that drive how the sequence of social interactions evolves over time. For example, a positive parameter estimate for the exogenous predictor ‘extraversion’ indicates a tendency for more extraverted pairs to start interactions at a higher rate than less extraverted pairs.

A REM can be fitted both when the exact time points for the relational events are considered (e.g., $t_{1} = 1,\ t_{2} = 61,\ t_{3} = 121,\ \dots$) and when only the order of the relational events in the sequence is known (e.g., $t_{1} < t_{2} < t_{3} < \dots$). In the first case, the full likelihood is used, while in the second case the full likelihood reduces to an ordinal likelihood (pp. 163-165 ; Butts, 2008). In case the exact time points are available, it is recommended to use the full likelihood because using the ordinal likelihood instead would result in a loss of information (Quintane et al., 2014). When the ordinal likelihood would be used in such cases, nothing can be inferred about time-related concepts such as the speeding up or slowing down of social interaction. An advantage of using the ordinal likelihood, however, is that a REM can still be fitted when the timing of relational events is only known up to the order of the events in the sequence and the exact time points are unavailable.

Analysis I: The basic relational event model

Data

We show how to use the REM by providing some exemplary analyses of the CONNECT data (Geukes et al., 2019). The CONNECT study is an extensive research project into the joint development of personality and social relationships among freshmen students. Participants were 126 freshmen students who enrolled for the bachelor study in psychology at a university in Germany. Part of this study is an experience-sampling observation of the social interactions between these freshmen students. Our aim is not to fully analyze this dataset, but to show how the statistical approach of the REM can be used to study topics of psychological interest. The CONNECT data used in the following analyses as well as the code for all analyses can be found at https://osf.io/xjbm7/.

Over the course of the first 23 days of their new studies, the participating freshmen students used an app on a smartphone to report every face-to-face interaction longer than 5 min as well as every digitally mediated interaction. See Table 1 for the first four observed relational events and Fig. 1 for the frequency of the observed events over the days. The specific time points for the relational events are defined in minutes relative to the onset of the observation period. The exact time points are available; thus we will use the full likelihood in our analysis. The relational events in the CONNECT study are undirected: we do not distinguish between sending and receiving students in a relational event. This means that, at any point in time, $\frac {126 \cdot 125}{2} = 7875$ potential relational events can occur among the 126 students.

Theoretical background

Previous research indicates that extraverted individuals are more likely to select friends (Feiler and Kleinbaum, 2015; Selden & Goodie, 2018; Selfhout et al., 2010) and to have larger social networks (Wagner et al., 2014). Furthermore, extraversion is linked to a stronger motivation for affiliation in peer groups (Neel et al., 2016), and to more sociable behavior particularly in social interaction (e.g., ; Breil et al., 2019b). Extraverts also report to spend more time in social interactions (Asendorpf & Wilpers, 1998; Wilson et al., 2015). In general, extraversion most strongly relates to quantitative indicators of “getting ahead” in social groups such as the amount of social contact and social status (e.g., see Back 2021; Back & Vazire 2015; Grosz et al., 2020, for overviews). Agreeableness is shown to be related to being selected more as friend (Selden & Goodie, 2018; Selfhout et al., 2010). Similar to extraversion, agreeableness is linked to a stronger motivation for affiliation in peer groups (Neel et al., 2016). Agreeableness tends to be particularly related to qualitative indicators of “getting along” such as fewer social conflict (Asendorpf & Wilpers, 1998), particularly in long-term relationships, and less to the amount of social contact in newly emerging social relationships (e.g., see ; Back, 2021; Back & Vazire, 2015, for overviews). In the current analyses, we extend our understandings of the effects of the personality traits extraversion and agreeableness on social interaction behavior by studying their effects on the rate of continuously occurring social interactions. Specifically, we include personality traits (extraversion and agreeableness) to our model to understand how the personalities of two students affect the extent to which they choose each other as interaction partners.

Besides people’s personality traits (such as extraversion and agreeableness), another important human trait that affects behavior over time is habituation or routine–the tendency of humans to repeat past behavior (Leenders et al., 2016). Within the context of relational event models, this is often termed inertia. Inertia captures the tendency to repeat past interaction, and to repeat more those interactions that were more frequent in the past. In essence, inertia captures the routinization of social interaction choices (Leenders et al., 2016). Pilny et al., (2016) suggest that, following general theories of social networks, an inertia effect may be essential to include in any REM. A tendency for inertia is found in previous REM analyses of directed social interactions between students (Pilny et al., 2017; Stadtfeld and Block, 2017). Therefore, we add inertia to our model to study the tendency of the students in the CONNECT study to develop interaction routines and keep interaction with past partners.

Closure is the tendency of individuals to interact with others with whom they share past interaction partners, i.e., the friends of my friends become my friends (Leenders et al., 2016). The tendency for closure is often found to be an important feature in forming social networks (Robins, 2013). A tendency for closure goes beyond the pair and describes the social embedding of individuals in the larger network. Evidence for a tendency for closure is found in previous REM analysis of directed social interactions (phone calls) between students (Pilny et al., 2017; Stadtfeld & Block, 2017). There are several reasons why this might be expected (see also ; Leenders et al., 2016). Having communication partners in common can be the consequence of having similar preferences and behavior, which might make the students more attractive to each other (similarity attracts). Another driver can be that having joint communication partners increases the opportunity to meet or to learn about each other. Either way, we would expect that the closure or shared partner effect may be an important predictor of social interaction in the CONNECT study. We add a shared partner effect to our model to study whether students who interact with the same others are also quicker to interact among each other. A further question to explore is whether the effects of inertia and shared partners on the event rate act the same across students’ personality trait levels. In order to study this question, we add interactions between the endogenous mechanisms (‘inertia’ and ‘shared partners’) and students’ personality trait effects (‘extraversion’) and (‘agreeableness’) to our model.

Homophily, or the tendency to interact or form relationships with others who are similar on one or more features, such as sex or age, has found to be an important mechanism in forming social networks (McPherson et al., 2001; Snijders & Lomi, 2019). Previous research showed that demographic similarity, including having the same gender and age, positively predicts friendship formation among adolescents (Rivera et al., 2010; van Zalk & Denissen, 2015). It is therefore important to account for effects of gender and age similarity on the probability for students to interact in our analyses of the CONNECT data.

The students in the CONNECT study recorded their interactions with fellow students both during weekdays and weekends. However, from Fig. 1 we can see that the number of events between students is considerably and consistently higher on weekdays (when they have classes and other obligations) than the number of events on weekend days (when they are entirely free to do as they wish). Previous research among university students has found evidence for differences in communication patterns during weekdays compared to weekends (Masuda & Holme, 2019). Therefore, we introduce a weekend effect in our model to control for this difference in event rate and investigate if students interact differently during weekdays compared to weekend days. Finally, these freshmen regularly interact in groups, rather than in pairs. We will show a way to deal with that within the confines of the REM and analyze whether group interaction differs from dyadic interaction.

Model specification

A typical relational event model includes characteristics of the individuals, of the pairs of individuals, and of the way they are embedded in the network at large. In our example below, we will include a selection of effects to study the research questions that we described above. Of course, many more kinds of variables are possible to analyze social interaction dynamics. For an overview, see, for example, Butts (2008), Leenders et al., (2016) and Vu et al., (2017).

In this first model, we assume that effects are constant over time. We will relax this assumption later.

Baseline

We include a baseline (intercept) effect to capture the baseline rate for starting social interactions. The baseline simply is a statistic that is always equal to 1 for every dyad. It plays the same role in the REM as an intercept in a linear regression model: it captures the average tendency of student pairs to start interactions when all other statistics are zero.

Gender similarity

Two statistics are used to summarize similarity in gender. First, the statistic x_both.male(s, r) is equal to 1 if both students in the pair (s, r) are male and equal to 0 if not. Second, the statistic x_mixed.gender(s, r) is equal to 1 if one student in the pair (s, r) is male and the other is female and equal to 0 if not. The student pair (s, r) in which both students are female acts as the reference category. In the CONNECT sample, the majority of the students is female (80%) and thus the majority of the potential student pairs (64%) consists of students who are both female. Student pairs of mixed gender make up 32% of the potential student pairs and the remaining 4% are student pairs where both students are male. A positive model parameter β_both.male would indicate that male student pairs (s, r) interact at a higher rate than student pairs with another gender composition. Similarly, a positive model parameter β_mixed.gender would indicate that mixed-gender student pairs (s, r) tend to interact at a higher rate than other student pairs. Comparing these effects helps analyze gender preferences in the developing of social interaction.

Age similarity

Based on previous research, we include similarity in age in our example model to test if it positively affects social interaction for freshmen students. One approach is to calculate the difference in age between students and use that difference as an explanatory variable in our model. In this specific dataset, age differences are, however, limited. When a population is quite homogeneous with respect to a personal characteristic like age, students who are older than the common age can be seen as “outsiders” and be interacted with differently—a phenomenon connected to surface-level diversity (Thatcher and Patel, 2012). Therefore, in this analysis we dichotomize the age of students in a “young” category (age 24 or younger) and a “comparatively old” category (age 25 or older). Two statistics are used to summarize similarity in age. The statistic x_both.older(s, r) is equal to 1 if both students are aged 25 years or older and equal to 0 otherwise. The statistic x_mixed.age(s, r) is equal to 1 if one student in the pair is “young” and the other is “older”. The student pair (s, r) in which both students are aged younger than 25 years acts as a reference category. The majority of the students in the CONNECT sample is classified as “young” (82%) and thus the majority of the potential student pairs (67%) consists of students that are both “young”. Student pairs of mixed age make up 30% of the potential student pairs and the remaining 3% are student pairs in which both students are “older”. A positive model parameter β_both.older would indicate that “older” student pairs are likely to interact at an event rate than student pairs with a different age composition. Similarly, a positive model parameter β_mixed.age would indicate that mixed age student pairs are likely to interact at a higher rate than student pairs with another age composition. This allows the researcher to discover any possible age-related faultlines and the tendency of older students to interact in a different manner from younger students (or mixed-age pairs).

Extraversion

Students in the CONNECT study provided self-report measures on personality traits by completing the GSOEP Big-Five Inventory (BFI-S; ; Hahn et al., 2012) that was part of an online survey. To obtain a measure of extraversion, the three BFI-S items that measure extraversion were averaged (α = .85). Responses to these items were allowed to range on a scale from 1 (does not apply at all) to 7 (applies perfectly). Almost all of the 126 students filled out these items. The responses for two students were missing and we replaced those by the group mean. The other 124 participants scored an average of 5.1 and a standard deviation of 1.1. Finally, the extraversion scores were standardized.

There are two ways in which a trait like extraversion can be included in an analysis. One approach is to include it as a fixed sender effect, where it can be assessed whether extraverted students start more interactions. However, since the dataset only includes undirected interactions (so we cannot distinguish whether the more extraverted person was the sender or receiver of specific interactions), we cannot show this here.

An alternative approach in the case of undirected pairs is to study whether interaction is driven by higher extraversion levels for the most extraverted student or least extraverted student in the pair. In particular, we want to study whether it takes a minimum level of extraversion to interact with others and whether overly extraverted students are attractive interaction partners or not. We do this by computing two extraversion scores for each student pair. The first measure is the minimum level of extraversion of the two students in a pair. The statistic x_{extraversion.min}(s, r) is equal to the standardized extraversion score for the student with the lowest extraversion score in the pair (s, r). This statistic tells us that both students have at least a level of x_{extraversion.min}(s, r) on extraversion. The higher this value, the extraverted the student pair can be considered to be. A positive model parameter β_{extraversion.min} would indicate that the higher the extraversion of the least extraverted student in the pair, the higher their interaction rate. So, if interacting with a (largely) unknown individual requires to have at least some minimum level of extraversion, this would follow from this analysis. This is a relevant question, considering that most students in the dataset were unfamiliar to each other at the beginning of the study.

Our second measure, x_{extraversion.max}(s, r), is equal to the highest standardized extraversion score for the students in the pair (s, r). This captures an upper bound for extraversion: both students are not more extraverted than x_{extraversion.max}(s, r). The lower this statistic, the less extraverted the students in the pair are. If we observe a positive model parameter β_{extraversion.max}, this would indicate that student pairs with at least one highly extraverted member interact at a higher rate than pairs where both students are less extraverted.

Agreeableness

Students’ personality trait agreeableness is measured in the online survey with three BFI-S and two additional BFI statements (Rammstedt & John, 2007). Responds to these statements ranged from 1 (does not apply at all) to 7 (applies perfectly). To obtain a measure of agreeableness, the three BFI-S items and the two additional BFI items were averaged (α = .56). Again, two students did not fill out these items and their scores were replaced by the overall mean. Agreeableness had a mean of 5.0 and a standard deviation of 0.8. Finally, the agreeableness scores were standardized.

Similar to the extraversion measures we computed above, we define two agreeableness statistics. The statistic x_{agreeableness.min}(s, r) is equal to the lowest standardized agreeableness score of the two students in the pair (s, r). This measure captures the minimal level of agreeableness of both students in a pair. A positive model parameter β_{agreeableness.min} would indicate that the higher the agreeableness of both students, the higher their interaction rate. Second, x_{agreeableness.max}(s, r) is equal to the highest standardized agreeableness score for the students in the pair (s, r). This value shows that none of the students in the pair score higher on agreeableness than x_{agreeableness.max}. A positive model parameter β_{agreeableness.max} would indicate that student pairs with higher levels of agreeableness interact at a higher rate than student pairs who both have lower agreeableness.

Inertia

It is common to add an inertia effect to a REM model by defining x_inertia(s, r, t) as the (relative) number of previous (s, r) interactions at time t. The more past interactions between a pair of students, the more likely it is that this pair will interact soon again. The CONNECT data enable us to refine this measure and describe the intensity of past interactions between a student pair with greater detail. Because the CONNECT data include information on the exact starting and ending times of the interactions, we can also include the duration of past events into the measure. It is reasonable to expect that past events that lasted longer will be more likely to be repeated than brief past events. Therefore, we account for the duration of past interactions in the inertia effect. Moreover, the CONNECT dataset has information on a second feature that is likely to affect repetition: group interactions. A fair amount (36%) of interaction among the students occurs in groups of more than two students. It is reasonable to expect that being together with person A in a ten-person group will be a less strong trigger for repeated interaction with A than when the interaction with A occurred in a small group or with A directly. Hence, we let the number of students involved in a past group interaction affect the weight with which past relational events are added to the inertia count. Let e = {t_e,s_e,r_e} refer to an observed relational event e at time t_e between students s_e and r_e, let A_e refer to the set of students involved in the social interaction that relational event e was part of and let d_e refer to the duration of this interaction. We define the inertia statistic for the student pair (s, r) at time t as follows:

$$x_{\text{inertia}}(s,r,t) = \sum\limits_{t_{e} < t, s_{e} = s, r_{e} = r} \frac{1}{\vert A_{e} \vert - 1} \cdot \ln(d_{e}),$$

(4)

The measure x_inertia(s, r, t) captures the sum of the past interactions between two students, weighted to the duration of the interactions and the number of students involved in each past interaction episode. To get an intuition of how this statistic weights the intensity of different kinds of past events between a student pair, Fig. 2 shows the weight of an event for increasing duration of interactions with two individuals (as in 64% of observed interactions), three individuals (as in 17% of observed interaction), or eight individuals (97.5% of the observed interactions is with eight students or less). The duration of the interactions ranges from 5 to 1805 min, the median duration is 30 min, and 97.5% of the interactions lasted 240 min or less.

In the case of endogenous statistics that are counts of past events, it is advisable to perform some kind of scaling method to make the statistic comparable over time and obtain well-behaved model parameters (Butts, 2008; DuBois et al., 2013; Schecter & Quintane, 2020). Here, we follow the recommendations of Schecter and Quintane (2020) and scale the weighted count by standardizing it per time point t as follows:

$$X_{\text{inertia}}(s,r,t) = \frac{X_{\text{inertia}}(s,r,t) - \bar{X}_{\text{inertia}}(t)}{SD(X_{\text{inertia}}(t))},$$

(5)

where $\bar {X}_{\text {inertia}}(t)$ and SD(X_inertia(t)) refer to, respectively, the mean and standard deviation of the inertia statistic at time t over all pairs (s, r). A positive model parameter β_inertia indicates that student pairs (s, r) who interacted more intensively in the past are likely to interact at a higher rate in the future than student pairs who interacted less intensively in the past. Of course, a researcher does not have to include event duration or group size and can use the common unweighted measure if preferred.

Shared partners

The statistic x_{shared.partners}(s, r, t) is the number students h that s and r both interacted with before time t. We standardize the variable per time point in the same way as for the inertia statistic (see Eq. 5). A positive model parameter β_{shared.partners} indicates that student pairs (s, r) who have more past shared partners are likely to interact at a higher rate in the future than student pairs who have fewer past communication partners in common. This statistic helps us understand whether having third parties involved (i.e., statistical significance of the coefficient) matters for the building up of relationships among freshmen and how strong the effect is (i.e., size of the coefficient). Finding a non-significant effect is informative as well, as that signals that interaction does not depend on shared others but is driven purely by individual or dyadic traits (depending, provided, of course, on the other variables and coefficients in the model as well).

Weekdays versus weekend

The statistic x_weekend(t) is equal to 1 for all student pairs at time t if time t is in the weekend and equal to 0 if not. A negative model parameter β_weekend indicates that relational events in the weekend occur with at a lower rate in the weekend than interactions during the week.

Group interaction

None of the relational event models deal with group interaction in a fully natural way. Within the REM, there are two ways of dealing with group interactions. The first is to add potential groups as separate “actors” in the model (e.g., see ; Lerner et al., 2019), such that the individual actors can engage in interaction with these groups in addition to the interactions they can have with the other individuals (and even interactions between groups can be accommodated in this way). This is a useful method for relational events with a small set of actors, but can become computationally cumbersome for a large number of actors (and, hence, a larger set of potential groups). A possible refinement is to allow groups to come into existence (and dissolve) over the course of the observation period and include them as potential receivers during their existence (and exclude them when they are not active). This latter approach forms the basis of the recent DyNAM-i model of Hoffman et al., (2020). Although elegant, this latter approach focuses on the choice of individuals to join and leave a group and does not naturally address the situation when a group gets together (and dissolves itself) as a group. In the context of the freshmen, groups get together for study or for social activities and are more naturally seen as group action, rather than as interactions between a group and an individual.

In this paper, we show a simple alternative that appears somewhat artificial, but appears to work quite well nonetheless. The approach considers a group interaction as a set of interactions between all individuals in the group, occurring jointly and during the same time period. Mathematically, we divide group interactions (i.e., interactions with more than two students) into the set of dyadic interactions between every pair of students in the group happening in random order.^{Footnote 1} Since relational events that are part of a group interaction have the same timestamp, which is not possible in a REM, a time difference between such relational events is induced before estimation (but after computation of the statistics, so the statistics are not affected by it). The time difference is such that these events are evenly spaced between the current time point minute t and the next minute t + 1. Since we induced a small time difference between relational events that were originally part of a group interaction, the rate of social interaction is artificially increased. We include a group effect in our REM to control for this artificial increase in the rate. The statistic x_group(t) is equal to 1 for all student pairs in the risk set at time t if the relational event that we observe at time t is part of a group interaction and equal to 0 if not. Although somewhat artificial at first sight, this approach seems to work well in practice. It does make the underlying assumption that all students are aware of each other’s presence in the group and consider all other participants in the group as potential communication partners while in the group. This may not be realistic for very large groups or for groups that are externally regulated in their communication. However, the fast majority (81%) of the interactions in the CONNECT study occurs in small groups with only two or three students.

The inclusion of the “group” variable not only takes care of the inflated interaction rates during times of group interaction, but it also allows the researcher to study the behavior of individuals vis-a-vis a group context. For example, a researcher can study whether extraverted student pairs are more likely to interact within a group context. Or one can analyze whether social similarity (such as having similar age, similar gender, or similar shared partners) affects the tendency to interact within a group. Just by itself, a positive model parameter β_group indicates that relational events tend to occur more in a group setting than outside of groups.

Interaction effects

Similar to the inclusion of interaction effects between predictors in linear regression or loglinear regression, we can also include interaction terms between variables in a relational event model. Interacting the “inertia” and “shared partners” with the four personality trait effects results in eight interaction effects. A positive model parameter β_{inertia.×.extraversion.min}, for example, would indicate that the effect of inertia on the rate of social interaction increases for student pairs with a higher minimum level of extraversion. As in standard regression models, the interpretation of interaction effects requires a researcher to also include the main effects into the model.

Estimation

Appendix A provides the reader with the script for the preparation and estimation of the REM analysis. First, the statistics are computed using the novel R software package remstats.^{Footnote 2} This software package has been developed to assist in the computation of commonly used REM statistics in an accessible manner. Second, estimation of the model parameters is realized using the R software package relevent (Butts, 2008). We build the models in a stepwise fashion, expanding the set of variables in consecutive steps. In total, we estimate five nested models (see Table 2).

Table 2 Relational event model parameter estimates with standard errors, BIC and goodness-of-fit (gof) results

Full size table

Results

Model selection and goodness-of-fit

The five models we fitted vary in their fit to the data and in the complexity of the models. A straightforward measure that balances fit and complexity is the Bayesian Information Criterion (BIC). This value can be computed directly from the maximum likelihood. Better models have lower BIC values. As can be seen from Table 2, Model 4 is the model with the lowest BIC, i.e., according to the BIC, the model with the best balance of fit and complexity among the five models.

To assess how well the models explain the observed relational event sequence, we perform a goodness-of-fit analysis. For each event, we calculate the predicted rates for each dyad (by plugging the coefficient estimates into Eq. 3). The probability of a specific dyad to host the next event is relative to its rate (see Eq. 2). This means that the model expects that it is most likely that the next event is going to occur among the dyads that have the highest predicted rates. If the model captures the empirical reality well, we would expect that in a fair proportion of the events, the actual event would occur for a dyad that was among the dyads with the highest predicted rates. Hence, we define goodness-of-fit (gof) as the proportion of instances in which the next observed event was in the top 5% of dyads with the highest predicted rates. Recall that at any point in time, 7875 events can potentially occur, but only one actually does. The model aims to predict which of these 7875 events occur at every point in time, which is an extremely ambitious objective. Hence, any model that somewhat consistently ranks the actual event among the top 5% of 7875 possibilities can be interpreted as performing really well. A similar approach to evaluate goodness-of-fit is performed by Pilny et al., (2016) and DuBois et al., (2013). For an in-depth goodness-of-fit analysis, we refer the interested reader to the approach proposed by Brandenberger (2019).

For relational events that were originally part of group interactions, we determine whether the highest ranked relational event within that group is in the top 5%. This gof metric thus refers to the ability of the models to predict the most plausible student pair who takes part in the next interaction. For the baseline-only, Model 0, this means that goodness-of-fit is calculated as 14.2%, i.e., we expect that if interaction occurs completely random, that in 14.2% of the interactions at least one student pair is correctly predicted (as being in the top 5%).

Goodness-of-fit results in Table 2 shows that introducing the personality traits in Model 1 only slightly increases the gof compared to the baseline-only Model 0. Note that the personality trait variables do not vary over time and thus predict the same student pairs in the top 5% for all time points. Apparently, these student pairs do interact slightly more often on average in the sequence than would be expected on random. Subsequently, there is a large increase in goodness-of-fit when the endogenous effects (inertia and shared partners) are introduced in Model 2. Model 2 is able to correctly predict (as being in the top 5%) at least one dyad in over half of all of the 2886 interactions over the course of the 3-week period. This large increase in goodness-of-fit for Model 2 indicates that these endogenous effects are very important in predicting the social interactions among freshmen students. Introducing the demography (gender and age) and event effects (group interactions, weekdays-versus-weekends) in Model 3 further increases the goodness-of-fit metric slightly. Introducing the interaction effects in Model 4 leads to a slight decrease in the goodness-of-fit metric. This indicates that interacting the endogenous effects (inertia and shared partners) with the personality traits extraversion and agreeableness has little value and even harms the predictive performance of our model. The best performing model (Model 3) correctly predicts (as being in the top 5 %) at least one student pair in almost 55 % of all interactions, which is remarkable and lends credence to the idea that these variables capture the most important drivers of the social interaction choices these freshmen made in the process of getting to know each other and new study mates.

Interpretation

Table 2 shows the estimated relational event model parameters and their standard errors for the five different models. Below, we interpret the parameters for the model with the best goodness-of-fit results, Model 3.

Because the relational event model is a loglinear model (see Eq. 3), we can take the log-inverse of the estimated model parameters to obtain a more meaningful metric for interpretation. For the baseline parameter the log-inverse refers to the average number of relational events per minute for a student pair with zeroes on all other statistics. After multiplication by the size of the risk set, we obtain the average predicted number of relational events per minute, $\exp ({\upbeta }_{\text {baseline}}) \times 7875 \approx 0.14$. The inverse of this number is the average expected number of minutes between two relational events: 7.08 min.

For all other effects, the log-inverses of the model parameters refer to baseline rate multipliers. For example, $\exp$ (β_inertia) ≈ 1.15 indicates that for student pairs who interacted with one standard deviation more intensively in the past compared to student pairs who interacted with average intensity, the baseline rate of starting a social interaction is multiplied by 1.15. Thus, for these student pairs, the predicted waiting time between the start of two social interactions is on average $\frac {1}{\exp ({\upbeta }_{\text {baseline}}) \times 7875 \times \exp ({\upbeta }_{\text {inertia}})} \approx 6.17$ min.

Figure 3 summarizes how the personality traits affect the time between interactions for a student pair. Results in Table 2 show that, after controlling for all the other effects, higher extraversion levels for both the least and most extraverted student in the pair positively affect the event rate. Higher extraversion levels for the students in the pair are related to higher event rates. The expected time between subsequent interactions is most strongly determined by the least extraverted student in the pair, as visualized in Panel 1 of Fig. 3. The left column depicts student pairs where at least one member has an extraversion score of 1 standard deviation below the average. The cells in the table show the expected time until their next interaction. As can be seen, the extraversion of the most extraverted student in the pair has a small positive effect on the waiting time; the pairs with both students below the mean in extraversion tend to wait 0.41 min (5%) longer before they interact again than pairs with only one student below the mean and the other above the mean. The top row depicts student pairs where at least one member has an extraversion score of 1 standard deviation above the average. Here, we see that the extraversion of the least extraverted student in the pair has a larger positive effect on the waiting time; the pairs with one student above the mean in extraversion and the other below the mean tend to wait 1.92 min (32%) longer before they interact again that pairs with both students above the mean in extraversion. The results are subtle, but consistent: whereas the most extraverted communication partner has a small positive effect, the lowest extraverted partner most strongly determines the rhythm of social interaction.

Furthermore, results in Table 2 show a negative effect of agreeableness maximum and no effect of agreeableness minimum on the rate of interaction. As Panel 2 in Fig. 3 shows, after controlling for all of the other effects, when at least one partner scores 1 standard deviation above the mean in agreeableness (top row), the student pair takes longer to activate than student pairs where both students are low in agreeableness. Agreeableness is often considered to be a superordinate trait that includes compliance, modesty, and tender-mindedness (p. 217 ; Matsumoto and Juang, 2012). Considering that the participants do not know each other at the beginning of the study period and find themselves in new territory (new university environment, new city to live, new people to get to know, new tasks), highly agreeable individuals may be more conscientious and particular in their interactions, whereas low agreeable individuals might be more progressive and impulsive in their interaction choices.

The results in Table 2 further show that both endogenous variables (inertia and shared partners) have a positive effect on the rate of interaction. The students show clear signs of habituation and the development of “preferred” communication partners to continue interaction with repeatedly. The inertia parameter is 0.14, showing that, after controlling for all of the other effects, student pairs who interacted more intensively in the past are likely to interact at an even higher rate in the future. Similarly, student pairs with more past communication partners in common tend to interact at a higher event rate than student pairs who had fewer shared partners.

The positive parameter estimate for both-male indicates that, after controlling for all of the other effects, pairs of male students tend to have a higher rate of interaction than other student pairs. Conversely, the negative parameter for mixed-gender implies that male-female student pairs tend to have lower interaction rates than other student pairs. However, the majority of the CONNECT sample is female, such that 2525 pairs of students have mixed gender, 300 are all-male, and 5050 are all-female. Therefore, mixed-gender pairs have a higher a priori opportunity for interaction than all-male pairs. Indeed, the predicted time between interactions is on average $\frac {1}{300 \times \exp ({\upbeta }_{\text {baseline}}) \times \exp ({\upbeta }_{\text {both.male}})} \approx 102.01$ min for male-male pairs, $\frac {1}{2525 \times \exp ({\upbeta }_{\text {baseline}}) \times \exp ({\upbeta }_{\text {mixed.gender}})} \approx 24.00$ min for mixed-gender interactions, and $\frac {1}{5050 \times \exp ({\upbeta }_{\text {baseline}})} \approx 11.04$ min between female-female interactions. This shows that, despite the strong preference for same-gender interaction (and especially male-male interaction), interactions that involve one or two female students strongly outnumber interactions that are all-male.

In terms of the effect of age, Table 2 shows that, after controlling for all of the other effects, student pairs in whom both students are aged 25 years or older (“old”) display a higher expected rate of interaction than student pairs of another age composition. Student pairs of mixed age tend to interact at a lower rate than pairs of another age composition. This shows that there is a strong preference for same-age-group interaction (and especially for comparatively “old” student pairs). Like for gender, age is quite skewed, with 253 “old” dyads, 5253 “young” dyads, and 2369 dyads of mixed age. Hence, the expected time between interactions is, on average, $\frac {1}{253 \times \exp ({\upbeta }_{\text {baseline}}) \times \exp ({\upbeta }_{\text {both.older}})} \approx 186.85$ min for two older students, $\frac {1}{2369 \times \exp ({\upbeta }_{\text {baseline}}) \times \exp ({\upbeta }_{\text {mixed.age}})} \approx 56.66$ min for mixed-age students, and $\frac {1}{5253 \times \exp ({\upbeta }_{\text {baseline}})} \approx 10.62$ min for a pair of younger students.

The positive model parameter estimate for the “group” effect accommodates the increase in the event rate that was induced by dividing observed group interactions into dyadic relational events that follow each other rapidly. Considering that originally 2886 relational events were observed but 11,690 relational events after the division of group interactions into dyadic relational events, the event rate was increased by a factor $\log (\frac {11690}{2886}) \approx 1.40$. Subtracting this number from the estimated group effect, 2.15 − 1.40 = 0.75, gives us a “net” estimate of the tendency of freshmen to interact in pairs versus in groups. This positive effect indicates that, after controlling for all of the other effects, the freshmen engage in group interactions with a higher rate than in pairwise interactions.

The negative model parameter estimate for the “weekend” effect indicates a lower rate for engaging in social interactions during the weekend than during working days, after controlling for all of the other effects. On working days the predicted time between events is on average $\frac {1}{7875 \times \exp ({\upbeta }_{\text {baseline}})} = 7.08$ min and on weekend days the predicted time between events is on average $\frac {1}{7875 \times \exp ({\upbeta }_{\text {baseline}} + {\upbeta }_{\text {weekend}})} = 15.07$ min. This is in concert with Fig. 1 where the number of events on weekend days is considerably and consistently lower than the number of events on working days.

From this first example analysis, we can see that the relational event model can highlight the effect of personality and personal and interpersonal characteristics on how these adolescents interact in a natural experiment: a situation where the students are unfamiliar to each other and are stimulated to find attractive interaction partners. In itself, this is a very straightforward model—essentially just a loglinear model—but it not only allows us to uncover the drivers of how these youngsters learn to interact with each other, but the REM allows a researcher to quantify the effects in terms of time and timing as well: how much longer does it take between two individuals in condition A versus individuals in condition B?

Analysis II: Relational event modeling with dynamic effects

In the analysis above, we made the underlying assumption that the effects are constant over the study period. However, the data concern freshmen who are starting a new life, with new people to get to know, a new place to live, and a new environment. As a result, we would expect to see some development of the way in which the freshmen develop their new persona as a student and learn whom to (not) interact with. Therefore, we now refine our model by dropping the assumption of constant parameter values and allow the parameters to vary over time. This allows us to study the second domain of key open questions outlined in the introduction, i.e., perform a continuous analysis of social interaction processes across acquaintance levels. Some of the interesting questions in this context are whether the effect of personality increases or decreases over time, how long it takes for inertia to kick in, or whether same-gender interaction may be considered a safe bet at the beginning of the period, while mixed-gender interaction gains attractiveness over time.

Our approach is to not put any constraints on the development of these effects (although that can certainly be done) and allow the parameter values to vary freely over the observation period. We do this by following Mulder and Leenders (2019) who extended the REM with a moving window approach. In this approach, a window of a pre-specified length slides over the entire observed relational event sequence. In each slice, the relational event model is fitted to the subset of relational events that falls within the window. Together, these slides create a picture of how the predictors of social interaction change over time. Following Mulder and Leenders (2019), a moving window REM can be fitted in the following steps:

1.
Determine a window length.
2.
Fit the specified REM to the subset of relational events that fall within the first window. Save the parameter estimates.
3.
Move the window such that it partly overlaps with the previous window but also contains a new subset of relational events.
4.
Fit the specified REM to the new subset of relational events. Save the parameter estimates.
5.
Repeat Steps 3 and 4 until all relational events in the sequence are analyzed.

The choice of window length should depend on theoretical and statistical reasons. Ideally, the window length is chosen such that it corresponds to the empirically established or assumed temporal nature of the effects of interest (Mulder & Leenders, 2019). The smaller the window length, the more sensitive the results will be to each point in time (and the more estimates will reflect what happens on a given day or brief period of time). The wider the intervals, the smoother the development over time. Furthermore, the window length should be large enough such that it contains enough relational events to reliably estimate model parameters. The overlap between subsequent windows determines the smoothness of the results, where a higher number of events that overlap results in greater smoothness.

Since the interactions between the freshmen students in the CONNECT study are observed during the first three weeks of their acquaintance, we are interested to study how effects change over relatively short time intervals as the network develops during the getting-to-know-you processes. Therefore, we choose a window length of three days with two days overlap. This combination of window length and overlap between the windows allows us to study daily variation while also maintaining enough events in each window to reliably estimate model parameters. The number of events per window varies between 455 and 2937.