remstats_prefattachment: Compute Butts' (2008) Preferential Attachment Network...

In dream: Dynamic Relational Event Analysis and Modeling

Compute Butts' (2008) Preferential Attachment Network Statistic for Event Dyads in a Relational Event Sequence

Description

The function computes the preferential attachment network sufficient statistic for a relational event sequence (see Butts 2008). Preferential attachment measures the tendency towards a positive feedback loop in which actors involved in more past events are more likely to be involved in future events (see Butts 2008 for an empirical example and discussion).This measure allows for preferential attachment scores to be only computed for the sampled events, while creating the statistics based on the full event sequence. Moreover, the function allows users to specify relational relevancy for the resulting statistics.

Usage

remstats_prefattachment(
  time,
  sampled,
  observed,
  sender,
  receiver,
  dependency = FALSE,
  relationalTimeSpan = 0
)

Arguments

time	The vector of event times from the post-processing event sequence.
sampled	A vector for the post-processing event sequence where i is equal to 1 if the observed dyadic event is sampled and 0 if not.
observed	A vector for the post-processing event sequence where i is equal to 1 if the dyadic event is observed and 0 if not.
sender	The vector of event senders from the post-processing event sequence.
receiver	The vector of event receivers from the post-processing event sequence
dependency	TRUE/FALSE. TRUE indicates that temporal relevancy will be modeled (see the details section). FALSE indicates that temporal relevancy will not be modeled, that is, all past events are relevant (see the details section). Set to FALSE by default.
relationalTimeSpan	If dependency = TRUE, a numerical value that corresponds to the temporal span for relational relevancy, which must be the same measurement unit as the observed_time and processed_time objects. When dependency = TRUE, the relevant events are events that have occurred between current event time, t, and t - relationalTimeSpan. For example, if the time measurement is the number of days since the first event and the value for relationalTimeSpan is set to 10, then only those events which occurred in the past 10 days are included in the computation of the statistic.

Details

The function calculates preferential attachment for a relational event sequence based on Butts (2008).

Following Butts (2008), the formula for preferential attachment for event e_i is:

PA_{e_{i}} = \frac{d^{+}(r(e_{i}), A_t)+d^{-}(r(e_{i}), A_t)}{\sum_{i=1}^{|S|} (d^{+}(i, A_t)+d^{-}(i, A_t))}

where d^{+}(r(e_{i}), A_t) is the past outdegree of the receiver for e_i, d^{-}(r(e_{i}), A_t) is the past indegree of the receiver for e_i, \sum_{i=1}^{|S|} (d^{+}(i, A_t)+d^{-}(i, A_t)) is the sum of the past outdegree and indegree for all past event senders in the relational history.

Moreover, researchers interested in modeling temporal relevancy (see Quintane, Mood, Dunn, and Falzone 2022) can specify the relational time span, that is, length of time for which events are considered relationally relevant. This should be specified via the option relationalTimeSpan with dependency set to TRUE.

Value

The vector of event preferential attachment statistics for the relational event sequence.

Author(s)

Kevin A. Carson [e-mail], Diego F. Leal [e-mail]

References

Butts, Carter T. 2008. "A relational event framework for social action." Sociological Methodology 38(1): 155-200.

Quintane, Eric, Martin Wood, John Dunn, and Lucia Falzon. 2022. “Temporal Brokering: A Measure of Brokerage as a Behavioral Process.” Organizational Research Methods 25(3): 459-489.

Examples

# A Dummy One-Mode Event Dataset
events <- data.frame(time = 1:18,
                                eventID = 1:18,
                                sender = c("A", "B", "C",
                                           "A", "D", "E",
                                           "F", "B", "A",
                                           "F", "D", "B",
                                           "G", "B", "D",
                                           "H", "A", "D"),
                                target = c("B", "C", "D",
                                           "E", "A", "F",
                                           "D", "A", "C",
                                           "G", "B", "C",
                                           "H", "J", "A",
                                           "F", "C", "B"))

# Creating the Post-Processing Event Dataset with Null Events
eventSet <- create_riskset( type = "one-mode",
                          time = events$time,
                          eventID = events$eventID,
                          sender = events$sender,
                          receiver = events$target,
                          p_samplingobserved = 1.00,
                          n_controls = 6,
                          seed = 9999)

#Computing the preferential attachment statistic for the relational event sequence
eventSet$pref <- remstats_prefattachment(
   time = as.numeric(eventSet$time),
   observed = eventSet$observed,
   sampled = rep(1,nrow(eventSet)),
   sender = eventSet$sender,
   receiver = eventSet$receiver)

dream documentation built on Jan. 21, 2026, 1:06 a.m.