`nwrem`

Relational event model (ordinal partial likelihood, MLE)

Syntax

nwrem
[netname]
,
[nodsnd
nidrec
nidsnd
nodrec
ntdegsnd
ntdegrec
frpsndsnd
frrecsnd
covsnd(varname)
covrec(varname)
covint(varname)
covevent(netname)
rsndsnd
rrecsnd
seed(#)]

Degree effects


`nodsnd`	sender’s normalized out-degree affects the sending rate (share of all prior events in which this actor was the sender)
`nidrec`	receiver’s normalized in-degree affects the receiving rate (share of all prior events in which this actor was the receiver)
`nidsnd`	sender’s normalized in-degree affects the sending rate
`nodrec`	receiver’s normalized out-degree affects the receiving rate
`ntdegsnd`	sender’s normalized total degree (in+out, averaged) affects the sending rate
`ntdegrec`	receiver’s normalized total degree (in+out, averaged) affects the receiving rate

Inertia effects


`frpsndsnd`	“inertia”: the fraction of the sender’s own past sends that went specifically to this receiver affects the sending rate to that receiver
`frrecsnd`	“reciprocity of receipt”: the fraction of the sender’s own past receipts that came specifically from this receiver affects the sending rate to that receiver

Covariate effects


`covsnd(varname)`	a per-actor covariate affects the sending rate (an “ego” effect - varname is read from the CURRENT dataset, one row per actor, in netname’s own actor order - see nwload’s `xvars` option below)
`covrec(varname)`	a per-actor covariate affects the receiving rate (an “alter” effect)
`covint(varname)`	a per-actor covariate affects both the sending and the receiving rate together (the same variable, one shared coefficient)
`covevent(netname)`	a pairwise (dyad-level) covariate affects the rate of the event from sender to receiver directly - netname must already be a loaded network with the SAME actors as the event network, one value per ordered (sender,receiver) pair (read from its own tie values, exactly like nwergm’s `edgecov()`)

Recency effects


`rsndsnd`	“recency of sending”: how RECENTLY (not how often) the sender previously sent to this receiver affects the sending rate to that receiver again (1/rank among the sender’s own past receivers, most recent = rank 1; 0 if never sent to before)
`rrecsnd`	“recency of receipt”: how RECENTLY (not how often) the sender previously received from this receiver affects the sending rate back to that receiver (1/rank among the sender’s own past senders, most recent = rank 1; 0 if never received from before) - a recency-based reciprocity effect


`seed(#)`	set the random-number seed before estimation (affects only which of several internal optimizer restarts is tried first when the default starting point fails to converge - never affects the reported MLE once a fit succeeds)

Description

nwrem fits a relational event model (Butts 2008, “A Relational Event Framework for Social Action,” Sociological Methodology 38(1), 155-200) to a timestamped sequence of dyadic events, via the ordinal partial likelihood: at each event, the model asks “given that some event happened next, which of the n(n-1) possible ordered actor pairs was it,” and estimates which actor-level effects make the realized event more likely relative to every other pair that could have happened instead - the same conditional-likelihood logic Cox proportional-hazards models use.

Unlike nwergm (static structure) and nwsaom (discrete panel-wave evolution), nwrem works directly on a raw, continuous-time event stream - no snapshot or aggregation step. It requires netname to already be declared as an event-type temporal network via nwset’s eventtime(varname) option:

. nwset sender receiver, eventtime(t) name(mynet)
. nwrem mynet, nodsnd nidrec

Speed: on direct head-to-head wall-clock benchmarks against R’s own relevent::rem.dyad() 1.2-1 (identical data, identical effect set, ordinal=TRUE, fit.method="MLE" on the R side; nwrem’s own pure-Mata engine on this side - no native C backend yet): a 2-effect model (nodsnd+nidrec, 30 actors, 2000 events) runs consistently around 0.8s vs. R’s 1.54s - roughly 2x faster, with little run-to-run variation. The full 8-effect degree+inertia model on the identical data is faster than R on every repeated trial measured, but with real variation run to run - 9.2s to 48.6s across thirteen repeated fits (two independent benchmark sessions), median around 39s, against R’s own single measured 107.75s: roughly 2.5-3x faster typically, up to 12x when the optimizer’s first attempt happens to converge directly. The variation itself is a disclosed, understood property, not noise to average away: this particular 8-effect model sits on the degree-effect family’s own collinearity ridge (see the note on precision below), so nwrem’s own retry-based optimizer sometimes needs only one attempt and sometimes several before converging - R’s own single optim(BFGS) call has no equivalent retry strategy for the same ridge, which is why nwrem still wins on every trial despite its own variation. See dev/rem_benchmark.R/.do and dev/rem_benchmark_multi.R/.do in the package’s own source for the exact scripts.

nwrem fits any combination of the 14 effects above (at least one required). There is deliberately no intercept option - a term constant across every candidate pair at a given event cancels out exactly in the ordinal likelihood’s own normalization (the same reason Cox proportional-hazards models have no identifiable baseline intercept), so one is never estimable here regardless of what is requested. Effects not yet implemented (triadic/shared-partner effects, fixed effects, the full non-ordinal/waiting-time likelihood, Bayesian estimation) are tracked, not silently missing - see the package’s own development roadmap for what is planned next.

rsndsnd/rrecsnd are different from frpsndsnd/frrecsnd: the latter measure HOW OFTEN a sender has contacted a given partner relative to their total activity (a fraction); rsndsnd/rrecsnd measure HOW RECENTLY, via reciprocal RANK among that sender’s own past contacts, ignoring how many times contact happened before or since. A sender who contacted a partner once, very recently, scores as high on rsndsnd for that partner as one who contacted them constantly and most recently - only the ordering matters, not the count.

Covariate effects require the current Stata dataset, at the time nwrem is called, to have exactly one row per actor in netname’s own actor order - NOT the event-level dataset netname itself was declared from. Use nwload’s xvars option first to load that per-node dataset:

. nwload mynet, xvars
. gen seniority = ...
. nwrem mynet, nodsnd covsnd(seniority)

This mirrors nwsaom’s own nodecov() convention exactly, not a new mechanism specific to nwrem.

covevent() is different: it is a per-pair (not per-actor) covariate, so it is read from ANOTHER already-loaded network’s own tie values rather than from a Stata variable - the same convention nwergm’s edgecov() already uses for dyadic covariates. Declare the pairwise covariate as its own network first, then reference it by name - nwset’s edgelist option is required here (nwset otherwise reads three bare variables as a wide affiliation matrix, not an edgelist):

. nwset i j value, name(seatdist) edgelist
. nwrem mynet, nodsnd covevent(seatdist)

covevent(seatdist) must have the same actors as mynet; its tie value for the ordered pair (sender,receiver) enters the sending rate directly for that pair (no ego/alter broadcasting, unlike covsnd()/covrec()/covint()). Because the effect reads (sender,receiver) values directly, nwset does not auto-symmetrize an edgelist declaration: an ordered pair with no explicit row gets value 0, even if its reverse pair was given a value. For a covariate that is genuinely symmetric (e.g. physical distance), supply BOTH ordered pairs (i,j) and (j,i) explicitly; for one that is genuinely directional (e.g. “i reports to j”), that asymmetry is exactly what covevent() is for.

A note on precision: nodsnd/nidrec/nidsnd/nodrec/ntdegsnd/ ntdegrec are each a running average - the fraction of all prior events in which an actor sent/received - and that fraction’s cross-actor spread narrows as the event sequence grows (it converges toward 1/n for every actor). This means, unlike an ordinary regression covariate, point estimates from these effects can remain noisy even with several thousand events, a genuine property of the effects themselves (verified against a real reference relational-event-model implementation on identical data, not a limitation of this command). Combining several of these degree-type effects in the same model (e.g. nodsnd with nidsnd and ntdegsnd together) can also produce a nearly flat ridge in the likelihood surface along some combination of their coefficients - different starting values can then converge to visibly different individual coefficients while fitting the data almost equally well; check whether the overall model fit (log likelihood) is what actually matters for your question before over-interpreting any single coefficient in that situation. The fitted model reliably improves on the no-effect baseline even when a single point estimate is imprecise; interpret standard errors accordingly and prefer larger event counts where possible.

Examples

Fit a relational event model on a small event log:

. clear
. input sender receiver t
. 1 2 1
. 1 3 2
. 2 1 3
. 1 2 4
. 3 2 5
. 2 3 6
. 1 3 7
. 3 1 8
. 2 1 9
. 1 3 10
. end
. nwset sender receiver, eventtime(t) name(chat)
. nwrem chat, nodsnd nidrec

(a handful of events on very few actors, as above, has too little information to pin down either coefficient precisely - the wide confidence intervals in this toy example are expected, not a sign of a problem; see this help file’s own note on precision above)

Add an inertia effect (does a sender tend to keep sending to the same recent partner) alongside a degree effect:

. nwrem chat, nidrec frpsndsnd

Add an actor-attribute covariate effect - does a per-actor variable affect the sending rate:

. nwload chat, xvars
. gen seniority = _n
. nwrem chat, nodsnd covsnd(seniority)

Add a pairwise covariate effect - does a variable specific to the (sender,receiver) pair
itself, not to either actor alone, affect the sending rate (seat distance is symmetric, so both
ordered pairs are given explicitly - see the note on symmetry above):

. clear
. input i j value
. 1 2 5
. 2 1 5
. 1 3 2
. 3 1 2
. 2 3 8
. 3 2 8
. end
. nwset i j value, name(seatdist) edgelist
. nwrem chat, nodsnd covevent(seatdist)

Add a recency effect - does a sender tend to return to whoever they contacted most recently,
regardless of how often (contrast with frpsndsnd above, which is about frequency):

. nwrem chat, nodsnd rsndsnd

Stored results

Scalars

e(N) number of events
e(nodes) number of actors
e(ll) log likelihood at the MLE

Macros

e(cmd) nwrem
e(title) “Relational event model (ordinal partial likelihood, MLE)”
e(depvar) name of the event network fit

Matrices

e(b) coefficient vector
e(V) variance-covariance matrix (observed information)