Duration Relational Event Models with remverse
A tutorial
A Duration Relational Event Model (DuREM) extends the standard relational event model (REM) to events that have both a start time and an end time. Instead of a single process governing when the next event fires, there are two linked sub-models:
- a start model, which describes which inactive dyad initiates a new event and when;
- an end model, which describes which currently active dyad terminates and when.
The two sub-models are estimated jointly. Statistics for each
sub-model can draw on (a) the accumulated event history —
duration-weighted versions of standard remstats effects such as
inertia() or reciprocity() — and (b) the
current active state of the network, i.e. the set of events
that have started but not yet ended. These active-state statistics can
only be used for relational events with duration.
The remverse DuREM pipeline follows the same three-step pattern as a standard REM:
remify(edgelist, duration = TRUE, ...) → remify_durem object
remstats(reh, start_effects = ..., end_effects = ...) → remstats_durem object
remstimate(reh, stats, ...) → remstimate_durem objectThis vignette walks through each step using the
randomREH3 dataset provided with remverse.
1 Data
1.1 The randomREH3 dataset
randomREH3 is a simulated sequence of 999 directed
duration events among 5 actors. Each row records one event with an
observed start time and end time:
| Column | Description |
|---|---|
time |
Start time of the event |
actor1 |
Initiating actor (integer ID) |
actor2 |
Receiving actor (integer ID) |
end |
End time of the event (NA for right-censored
events) |
setting |
Context of the interaction: "work" or
"social" |
duration |
Length of the event (end - time) |
library(remverse) # loads remify, remstats, remstimate; remdata is a dependency
#> Loading required package: remdata
data(randomREH3)
data(info3) # actor attributes (age, sex)
head(randomREH3)
#> time actor1 actor2 end setting duration
#> 2 18 5 1 24 social 6
#> 3 57 3 2 70 social 13
#> 4 64 1 5 85 social 21
#> 5 127 5 1 159 social 32
#> 6 228 1 4 239 work 11
#> 7 274 2 4 320 work 46Although the data contains both an end column and a
duration, only one of these columns (with these exact
names) is necessary for a DuREM analysis.
The data were generated from a known duration model: starting an event depended on inertia, reciprocity, sender out-degree, incoming shared partners, and sender age; ending an event depended on the dyad’s total active degree and the age difference of the two actors.
cat(sprintf(
"%d events: %d complete, %d right-censored\n",
nrow(randomREH3),
sum(!is.na(randomREH3$end)),
sum( is.na(randomREH3$end))
))
#> 999 events: 999 complete, 0 right-censoredThis particular dataset has no right-censored events (every event has
an observed end), but the pipeline fully supports censoring
(end = NA); see §5.1.
2 Step 1 — Processing with remify()
Pass duration = TRUE to tell remify that the edgelist
contains duration information. DuREM analysis are only possible under a
tie oriented model. The function returns an object of class
c("remify_durem", "remify").
reh <- remify(
edgelist = randomREH3,
duration = TRUE,
model = "tie",
directed = TRUE # actor1 initiates; the end process is undirected by default
)
#> Warning: 2 events start while another event for the same dyad is already
#> active. Check events: 320, 565.2.1 The remify_durem object
reh
#> Relational Event Network
#> (processed for tie-oriented modeling with duration):
#> > events = 999 (time points = 993)
#> > actors = 5
#> > (event) types = 1
#> > riskset = full
#> >> included dyads = 20
#> > directed = TRUE
#> > ordinal = FALSE
#> > weighted = FALSE
#> > time length ~ 50676
#> > interevent time
#> >> minimum ~ 1
#> >> maximum ~ 448
#> > duration
#> >> start = directed (actor1 initiates)
#> >> end = undirected (combined dyad-level rate)
#> >> event duration (complete events)
#> >>> minimum ~ 1
#> >>> median ~ 12
#> >>> maximum ~ 326summary(reh)
#> Relational Event Network
#> (processed for tie-oriented modeling with duration):
#> > events = 999 (time points = 993)
#> > actors = 5
#> > (event) types = 1
#> > riskset = full
#> >> included dyads = 20
#> > directed = TRUE
#> > ordinal = FALSE
#> > weighted = FALSE
#> > time length ~ 50676
#> > interevent time
#> >> minimum ~ 1
#> >> maximum ~ 448
#> > duration
#> >> start = directed (actor1 initiates)
#> >> end = undirected (combined dyad-level rate)
#> >> event duration (complete events)
#> >>> minimum ~ 1
#> >>> median ~ 12
#> >>> maximum ~ 326The plot() method for a remify_durem object
shows the duration-aware descriptives — including the distribution of
event durations and how many events are active over time — in addition
to the standard relational event descriptives of a remify
object.
plot(reh)
Alongside the standard remify slots ($M,
$N, $D, $edgelist,
$meta, …), a remify_durem object carries
DuREM-specific elements.
$durem — a named list of DuREM
metadata:
reh$durem
#> $dur_directed_end
#> [1] FALSE
#>
#> $dur_type_exclusive
#> [1] FALSE
#>
#> $has_who_ended
#> [1] FALSE
#>
#> $has_censored
#> [1] FALSE
#>
#> $n_complete
#> [1] 999
#>
#> $n_censored
#> [1] 0| Field | Meaning |
|---|---|
n_complete |
Events with an observed end time |
n_censored |
Right-censored events (end = NA) |
has_censored |
Whether any events are censored |
dur_directed_end |
Whether the end process is directed |
has_who_ended |
Whether a who_ended column is present |
dur_type_exclusive |
Whether being active in one type blocks other types |
$edgelist_dual — the dual-event
expansion: one "start" row and one "end" row
per complete event (censored events contribute only a
"start" row), sorted by time. The status
column states whether the observation at that time point is either the
start of a new event or an end of an active
event. The DuREM models these observed outcomes jointly by specifying
separate sub-models for starting an event and for ending an event.
head(reh$edgelist_dual, 12)
#> time actor1 actor2 status duration .eidx
#> 1 18 5 1 start 6 1
#> 2 24 5 1 end 6 1
#> 3 57 3 2 start 13 2
#> 4 64 1 5 start 21 3
#> 5 70 3 2 end 13 2
#> 6 85 1 5 end 21 3
#> 7 127 5 1 start 32 4
#> 8 159 5 1 end 32 4
#> 9 228 1 4 start 11 5
#> 10 239 1 4 end 11 5
#> 11 274 2 4 start 46 6
#> 12 302 1 5 start 12 73 Step 2 — Statistics with remstats()
For duration models, remstats() accepts two formulas —
start_effects and end_effects — one per
sub-model. Each formula may mix two kinds of terms:
- History-weighted effects — the familiar
tie-oriented effects (
inertia(),reciprocity(),totaldegreeDyad(),send(),difference(), …), computed on the duration-weighted event history. An overview can be shown when running . - Active-state effects — effects that describe the
currently active network (events that have started but not yet
ended). These are the
active*()family and are unique to the duration model. An overview can be shown when running .
remstats() inspects each term, routes it to the
appropriate backend, and combines the results together
automatically.
3.1 Active-state effect functions
Which active-state effects are available depends on whether the
sub-model is directed. The start model
is directed whenever directed = TRUE; the end
model is undirected by default (set
dur_directed_end = TRUE in remify() to make it
directed).
Directed active-state effects (start model, or end
model when dur_directed_end = TRUE):
| Effect | Description |
|---|---|
activeTie() |
Is there currently an active event from actor \(i\) to actor \(j\)? |
activeOutdegreeSender() |
Number of active events actor \(i\) (sender) currently has as initiator |
activeIndegreeReceiver() |
Number of active events actor \(j\) (receiver) currently has as target |
activeTotaldegreeSender() |
Total active degree of actor \(i\) (as sender or receiver) |
activeTotaldegreeReceiver() |
Total active degree of actor \(j\) |
activeTotaldegreeDyad() |
Combined active degree of both actors |
activeReciprocalTie() |
Is the reverse dyad \(j \to i\) currently active? |
activeSharedPartners_otp() / _itp() /
_osp() / _isp() |
Active shared-partner effects (outgoing/incoming two-path, outgoing/incoming shared partner) |
Undirected active-state effects (end model, default):
| Effect | Description |
|---|---|
activeTie() |
Is the dyad currently active? |
activeDegreeMin() |
Minimum active degree of the two actors |
activeDegreeMax() |
Maximum active degree of the two actors |
activeDegreeDyad() |
Combined active degree of the two actors |
activeSharedPartners() |
Number of shared active partners |
All active-state effects share the optional arguments
scaling = c("none", "std") and
consider_type = c("ignore", "separate", "interact") (see
§3.3).
Note. A directed active-state effect such as
activeOutdegreeSender()cannot be used in the (undirected) end model — it would be rejected as an unknown effect for that sub-model. Put directed active-state effects in the directed start model, and use the undirected active-state effects (or history-weighted effects) in the default end model.
3.2 Computing statistics
Here we formulate a DuREM where the start model mixes history-weighted effects with a directed active-state effect, while the (undirected) end model uses history-weighted effects only.
# Start model (directed): history-weighted effects + active out-degree of sender
start_fx <- ~ inertia(scaling = "std") +
reciprocity(scaling = "std") +
activeOutdegreeSender(scaling = "std")
# End model (undirected): history-weighted effects
end_fx <- ~ totaldegreeDyad(scaling = "std") +
difference("age", attr_actors = info3, scaling = "std")
dstats <- remstats(
reh = reh,
start_effects = start_fx,
end_effects = end_fx,
memory = "decay",
memory_value = 2000,
display_progress = FALSE
)dstats
#> Relational Event Network Statistics
#> > Model: tie-oriented (duration)
#> > Computation method: per time point
#> > Start dimensions: 1957 time points x 20 dyads x 4 statistics
#> > Start statistics:
#> >> 1: baseline.start
#> >> 2: activeOutdegreeSender.start
#> >> 3: inertia.start
#> >> 4: reciprocity.start
#> > End dimensions: 1957 time points x 10 dyads x 3 statistics
#> > End statistics:
#> >> 1: baseline.end
#> >> 2: totaldegreeDyad.end
#> >> 3: difference_age.endThe returned object is of class "remstats_durem". The
statistics element can be viewed as a stacked remstats object:
head(dstats$stacked$remstats_stack)
#> obs log_interevent baseline.start activeOutdegreeSender.start inertia.start
#> 1 1 1.791759 0 0.0000000 0
#> 2 0 1.791759 1 -0.4873397 0
#> 3 0 1.791759 1 -0.4873397 0
#> 4 0 1.791759 1 -0.4873397 0
#> 5 0 1.791759 1 -0.4873397 0
#> 6 0 1.791759 1 -0.4873397 0
#> reciprocity.start baseline.end totaldegreeDyad.end difference_age.end
#> 1 0 1 0 -0.3721042
#> 2 0 0 0 0.0000000
#> 3 0 0 0 0.0000000
#> 4 0 0 0 0.0000000
#> 5 0 0 0 0.0000000
#> 6 0 0 0 0.0000000
#> time_index dyad process actor1 actor2
#> 1 2 4 end 1 5
#> 2 2 1 start 1 2
#> 3 2 2 start 1 3
#> 4 2 3 start 1 4
#> 5 2 4 start 1 5
#> 6 2 5 start 2 13.3 Event types and consider_type
Similar as history-based statistics, the active-state statistics
accept a consider_type argument that controls how the
setting event type is handled when the model is built on a
typed risk set:
| Value | Behaviour |
|---|---|
"ignore" (default) |
Counts active events of any type |
"separate" |
One statistic per type; only type-\(c\) events contribute to the type-\(c\) stat |
"interact" |
One statistic for every combination of past event types and the
event type in the riskset (only possible when setting in of the
remify object). In case of C event types, this
results in C^2 distinct statistics. |
# Rename `setting` to `type` and build a typed duration history
history_typed <- randomREH3
names(history_typed)[names(history_typed) == "setting"] <- "type"
reh_typed <- remify(history_typed, duration = TRUE, model = "tie", directed = TRUE)
# "separate": one activeTie statistic per setting
dstats_sep <- remstats(
reh_typed,
start_effects = ~ activeTie(consider_type = "separate")
)
dimnames(dstats_sep$start_stats)[[3]]4 Step 3 — Estimation with remstimate()
remstimate() dispatches on the
"remstats_durem" class and fits the joint start/end model.
The start and end sub-models are stacked into a single long-format
design matrix; start statistics are zero for end rows and vice
versa.
4.1 Fitting the model
fit <- remstimate(reh = reh, stats = dstats)fit
#> Relational Event Model (tie oriented, duration)
#> Estimation: MLE [ glm ]
#>
#> Coefficients:
#>
#> baseline.start activeOutdegreeSender.start
#> -7.2005633 0.0461310
#> inertia.start reciprocity.start
#> 0.3852725 0.4169325
#> baseline.end totaldegreeDyad.end
#> -2.9004091 0.0501352
#> difference_age.end
#> 0.3787515
#>
#> Null deviance: 28873.87
#> Residual deviance: 23182.67
#> AIC: 23196.67 AICC: 23196.73 BIC: 23235.734.2 Coefficients and summary
coef(fit)
#> baseline.start activeOutdegreeSender.start
#> -7.2005633 0.0461310
#> inertia.start reciprocity.start
#> 0.3852725 0.4169325
#> baseline.end totaldegreeDyad.end
#> -2.9004091 0.0501352
#> difference_age.end
#> 0.3787515summary(fit)
#> Relational Event Model (tie oriented, duration)
#> Estimation: MLE [ glm ]
#> --------------------------------------------------
#>
#> Coefficients:
#> Estimate Std. Err z value Pr(>|z|)
#> baseline.start -7.200563 0.039916 -180.3928 < 2e-16 ***
#> activeOutdegreeSender.start 0.046131 0.064670 0.7133 0.47564
#> inertia.start 0.385273 0.036346 10.6001 < 2e-16 ***
#> reciprocity.start 0.416932 0.036146 11.5348 < 2e-16 ***
#> baseline.end -2.900409 0.035847 -80.9113 < 2e-16 ***
#> totaldegreeDyad.end 0.050135 0.030040 1.6689 0.09513 .
#> difference_age.end 0.378751 0.034933 10.8422 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Null deviance: 28873.87 on 1957 degrees of freedom
#> Residual deviance: 23182.67 on 1950 degrees of freedom
#> Chi-square: 5691.2 on 7 degrees of freedom, p-value 0
#> AIC: 23196.67 AICC: 23196.73 BIC: 23235.73Each coefficient quantifies the effect of the corresponding statistic
on the start or end event rate. For example,
activeOutdegreeSender.start captures engagement: a sender
who is already in many active events may be less (or more) likely to
initiate another, corresponding to a negative (or positive) coefficient,
while totaldegreeDyad.end describes how a dyad’s
accumulated activity in past events relates to how quickly its events
terminate.
4.3 Diagnostics
diag <- diagnostics(fit, reh, dstats)
plot(diag)
4.4 Model comparison
Because remstimate_durem returns a standard
logLik object, information criteria compare nested models
in the usual way:
# A simpler model: baseline dynamics only
dstats_simple <- remstats(
reh,
start_effects = ~ inertia(scaling = "std"),
end_effects = ~ totaldegreeDyad(scaling = "std"),
memory = "decay",
memory_value = 2000
)
fit_simple <- remstimate(reh = reh, stats = dstats_simple)
logLik(fit)
#> 'log Lik.' -11591.34 (df=7)
logLik(fit_simple)
#> 'log Lik.' -11708.23 (df=4)
AIC(fit)
#> [1] 23196.67
AIC(fit_simple)
#> [1] 23424.455 Additional topics
5.1 Duration based event weights
When computing the history-weighted (endogenous) effects,
inertia(), reciprocity(), etc., the duration
of past events are used as event weights according to the formulas:
(duration + 1)^psi_startfor thestart_effects(duration + 1)^psi_endfor theend_effects.
Thus, the psi_start and psi_end arguments
of remstats control the duration-weighting exponent applied
to the history-weighted terms (and are ignored for active-state terms).
Defaults are psi_start = 1 and psi_end = 1,
implying that events with longer duration result in a larger weight in
the endogenous statistics. On the other hand, if these arguments would
be set to a negative value, then events with a longer duration have a
smaller weight in the endogenous statistics. Thus, the
psi_start and psi_end have a comparable role
as the memory_value argument which affects the weight of
events as function of the transpired time. Moreover, if events also have
a weight by its (e.g., for quantifying the intensity of an event),
specified via event_weight, the weight of the past event is
computed by multiplying its weight with the duration-based
weight.
5.2 Right-censored events
Right-censored events (end = NA in the edgelist) are
fully supported. They contribute a start row to the dual edgelist and
appear in the active-state counts until the end of the observation
window, but never produce an observed end event. The $durem
slot records how many events are censored:
reh$durem$n_censored
#> [1] 0
reh$durem$n_complete
#> [1] 9995.3 Simultaneous events and boundary coincidences
The dual edgelist may contain multiple rows at the same time point —
two events starting simultaneously, or one event ending exactly when
another begins. remify_durem handles these automatically,
computing the active state consistently just before each time point.
# Time points in the dual edgelist shared by more than one row
tab <- table(reh$edgelist_dual$time)
head(tab[tab > 1], 6)
#>
#> 523 945 1240 1954 4329 4944
#> 2 2 2 2 2 25.3 Directed end process
By default the end process is undirected — either actor can terminate
an event. To model a directed end process (e.g. when a specific actor
ends the event), set dur_directed_end = TRUE. This makes
the directed active-state effects available in
end_effects as well:
reh_de <- remify(randomREH3, duration = TRUE, model = "tie",
directed = TRUE, dur_directed_end = TRUE)
dstats_de <- remstats(
reh_de,
start_effects = ~ inertia(scaling = "std") + activeOutdegreeSender(scaling = "std"),
end_effects = ~ activeOutdegreeSender(scaling = "std")
)
fit_de <- remstimate(reh = reh_de, stats = dstats_de)
coef(fit_de)References
Butts, C. T. (2008). A relational event framework for social action. Sociological Methodology, 38(1), 155–200. https://doi.org/10.1111/j.1467-9531.2008.00203.x
Hoffman, M., Block, P., Elmer, T., & Stadtfeld, C. (2020). A model for the dynamics of face-to-face interactions in social groups. Network Science, 8(S1), S4–S25. https://doi.org/10.1017/nws.2020.3
Lakdawala, R., Leenders, R., Ejbye-Ernst, P., & Mulder, J. (2026). Modelling interaction duration in relational event models. arXiv preprint. https://doi.org/10.48550/arXiv.2602.21000