Tutorial 19: Longitudinal Models: An Overview

The first ERGM tutorial modeled a single, static network. Three model packages for network change build on the core, each for a different kind of longitudinal data:

Package	Model	Data
nwsaom	stochastic actor-oriented model (SAOM)	two or more observed panel waves
nwrem	relational event model (REM)	a timestamped stream of events
nwdynam	dynamic network actor model (DyNAM)	a timestamped stream of events

Installing the packages

Each is a separate GPL-3 package that needs the core nwcommands (see Installation & Setup):

nwinstall, models

for all four model packages at once (nwinstall, everything installs the core as well; a single package: nwinstall, modelpkg(nwsaom)). Each package reports its own release (and stores it in r(version)):

. nwsaom version
nwsaom version 1.1.0, 26oct2026

. nwrem version
nwrem version 1.0.8, 26oct2026

. nwdynam version
nwdynam version 1.1.3, 26oct2026

The examples below were run with release 1.0.1 of each package and the core nwcommands 3.0.0.

Stochastic actor-oriented models (SAOM)

Full nwsaom tutorials. This page is an overview. nwsaom has its own section with thirteen worked tutorials, each with real output:

1. A first SAOM
2. Convergence
3. Goodness of fit
4. Selection and influence
5. Testing and comparing
6. Beyond the basic model
7. Changing actor sets and missing data
8. Time-varying and dyadic covariates
9. Undirected and two-mode networks
10. Endowment, creation, interactions and rate effects
11. Simulation and what-if analysis
12. Conditional and unconditional estimation, threads and speed
13. Combining several groups with a meta-analysis
14. Several groups at once

See also nwsaom and RSiena and the installation page.

An SAOM (nwsaom) models change between two or more observed panel waves of the same network as a sequence of unobserved, actor-driven “ministeps”: one at a time, an actor is activated and may create or drop exactly one of its own outgoing ties, choosing among the alternatives via a model weighted by the same kind of effect coefficients an ERGM uses — but evaluated myopically, from that one actor’s own perspective only. That actor-level, myopic framing is what actually distinguishes an SAOM from an ERGM, not just “two waves instead of one”: an ERGM has no actors or ministeps at all, only a single probability distribution over entire graphs.

Here are three yearly waves of friendship among 50 pupils in a Scottish school (the Glasgow data, RSiena’s s50 data), with outdegree, reciprocity, transitive closure, and homophily on smoking:

. nwwebuse glasgow, nwclear

. nwsaom, waves(glasgow1 glasgow2 glasgow3) outdegree reciprocity transtrip samex(smoke1) seed(1)
-------------------------------------------------------------------------------------------------------------------------
SAOM (Method of Moments, conditional), waves: glasgow1 glasgow2 glasgow3
Actors: 50                             Periods: 2
-------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
glasgow1_t~3 | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   outdegree |    -2.7657   .1525954   -18.12   0.000    -3.064781   -2.466618
 reciprocity |   2.455705   .1983861    12.38   0.000     2.066875    2.844534
samex_smoke1 |   .1333049   .1456629     0.92   0.360    -.1521891     .418799
   transtrip |   .6194921   .0767219     8.07   0.000       .46912    .7698642
------------------------------------------------------------------------------
Rate parameters (estimated, one per inter-wave period):

             |   period1    period2 
-------------+---------------------
        rate |    6.4783     5.2605 
          se |    1.1113     0.8674 
Overall maximum convergence ratio: 0.097 (criterion: below 0.25; met)
Convergence t-ratios (criterion: all below 0.1 in absolute value): met

outdegree plays the same baseline-density role edges plays in an ERGM. reciprocity and transtrip (transitive triplets: a friend of a friend becomes a friend) are both strongly positive; once they are in the model, pupils show no significant tendency to befriend others with the same smoking status (samex_smoke1). The rate table says how often, on average, a pupil had the opportunity to change a friendship in each period. The last line checks convergence: an overall maximum convergence ratio below 0.25 (with every t-ratio below 0.1 it is reported as good) means the estimates can be used; otherwise, run the model again starting from them with theta0().

Checking the model

With three waves, estat timetest asks whether an effect had the same size in both periods:

. estat timetest

Test of time heterogeneity (score-type test; RSiena's sienaTimeTest)
----------------------------------------------------------------------
Joint test of all period-specific deviations:  c =    5.3581   d.f. = 4   p-value = 0.2525

Test of each effect (is its parameter the same in all periods?)
effect                           c  d.f.   p-value
outdegree                    0.063     1    0.8013
reciprocity                  0.931     1    0.3346

(output shortened to the joint test and the test of each effect). No effect differs significantly between the periods. estat importance says how much each effect contributes to the actors’ choices, as RSiena’s sienaRI does:

. estat importance

Relative importance of effects (RSiena's sienaRI); expected over the actors at the start of each period
------------------------------------------------------------------------------
effect                  estimate     s.e.     sigma   semi-std.    RI p1    RI p2
outdegree                -2.7657   0.1526    0.4384     -1.2124   0.4253   0.4967
reciprocity               2.4557   0.1984    0.2140      0.5255   0.3749   0.3074
samex_smoke1              0.1333   0.1457    0.5043      0.0672   0.0376   0.0358
transtrip                 0.6195   0.0767    0.6514      0.4036   0.1622   0.1601
------------------------------------------------------------------------------
Certainty R_H of the actors' choices:   0.2677   0.3493
RI: expected relative importance of the effect (shares sum to 1 within a period); semi-std. = estimate x sigma.

Reciprocity and the outdegree term dominate the actors’ choices; smoking similarity hardly matters. Further postestimation includes estat gof (goodness of fit), estat score (a test of effects held fixed with fix()) and estat simulate. This is only an overview; the nwsaom section has thirteen worked tutorials, an installation page and a guide for RSiena users. Beyond this model, nwsaom also fits co-evolving behavior (behavior()), several dependent networks (nwsaom multinet), maximum likelihood instead of the method of moments (ml), and Bayesian estimation (nwsaom bayes); see Tutorial 6 and the nwsaom reference page.

Relational event models (REM)

An REM (nwrem) is built for the opposite kind of data: a raw, continuous-time stream of individual events (an email sent, a call placed, a message posted) rather than snapshots at a handful of waves. There’s no aggregation step at all — every single event is its own observation, compared against every other actor-pair that could have generated an event at that same moment but didn’t.

. input sender receiver t

        sender   receiver          t
  1. 1 2 1
  2. 1 3 2
  3. 2 1 3
  4. 1 2 4
  5. 3 2 5
  6. 2 3 6
  7. 1 3 7
  8. 3 1 8
  9. 2 1 9
 10. 1 3 10
 11. end

. nwset sender receiver, directed eventtime(t) name(chat)

. nwrem chat, nodsnd nidrec
------------------------------------------------------------
Relational event model (ordinal partial likelihood, MLE)
Network: chat                          Actors: 3
Events: 10                             Log likelihood:  -15.9033
------------------------------------------------------------
------------------------------------------------------------------------------
        chat | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      nodsnd |   1.268517   1.354189     0.94   0.349    -1.385644    3.922677
      nidrec |  -5.567583   3.511088    -1.59   0.113    -12.44919    1.314023
------------------------------------------------------------------------------

nodsnd asks whether a sender’s own total out-activity so far predicts sending the next event; nidrec asks the same for a receiver’s in-activity. Ten events among three actors is nowhere near enough data to estimate anything precisely — the point here is the workflow, not the substantive result.

Dynamic network actor models (DyNAM)

nwdynam works on the same kind of event stream, but splits an event into two decisions: who acts next (the rate sub-model) and whom that actor chooses (the choice sub-model). The event log above is directed, so we can fit the rate sub-model to it directly; here, does an actor’s in- or out-degree so far predict how soon it acts?

. nwdynam chat, submodel(rate)
------------------------------------------------------------
Dynamic Network Actor Model - rate sub-model, no intercept (MLE)
Network: chat                          Actors: 3
Events: 10                             Log likelihood:  -10.9009
------------------------------------------------------------
------------------------------------------------------------------------------
        chat | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       indeg |   .1728906   1.091221     0.16   0.874    -1.965863    2.311645
      outdeg |  -.1728888    .658234    -0.26   0.793    -1.463004    1.117226
------------------------------------------------------------------------------

The choice sub-model (the default, nwdynam chat, with effects such as inertia and recip) is fitted the same way; on ten events among three actors it gives degenerate estimates (huge standard errors), so it is not shown here — use a real event log. See the nwdynam and nwrem reference pages for the effects each package offers.

Which one fits your data?

If you observed the network at a handful of discrete points in time (a survey repeated every year, say), reach for nwsaom. If you have a genuine timestamped log of individual interactions, nwrem and nwdynam use that timing directly rather than throwing it away by collapsing into waves.