Tutorial 1: A first SAOM on the Glasgow friendship data

Goal. Fit a first stochastic actor-oriented model (SAOM) with nwsaom, understand every part of the output, and know when you can trust it.

Data. Three yearly waves of friendship among 50 pupils in a Scottish school, with the pupils’ smoking, drinking and sport at each wave. These are the data that RSiena ships as s50. They are available from the nwcommands website, so no file is needed. You need the core nwcommands and the nwsaom package (see Install); the commands below were run with nwsaom 1.1.1 and the core 3.10.0. The complete script and log are in example.do and example.log.

What a SAOM does, in three sentences

Between two observed waves a network changes through many small, unobserved steps. In each step one actor gets the chance to change one of its own outgoing ties (create one, drop one, or keep things as they are) and chooses the change that looks best from its own point of view. The model’s coefficients describe what “looks best” means (for example, “ties that are reciprocated are attractive”), and nwsaom finds the coefficients that reproduce the observed change.

Load and look at the data

. nwsaom version
nwsaom version 1.1.1, 27oct2026
  core package nwcommands : installed (development copy, no distribution date)
  native plugin           : .../saom_sim_macos.plugin (plugin build 140)
  compared with           : R RSiena 1.6.14
  license                 : GNU GPL-3

. nwwebuse glasgow, nwclear

nwwebuse loads the three friendship networks glasgow1, glasgow2 and glasgow3 and the actor variables smoke1-smoke3, alcohol1-alcohol3 and sport1-sport3 into the current dataset. Always look at the data before modeling. nwsaom describe prints what RSiena prints before an estimation:

. nwsaom describe, waves(glasgow1 glasgow2 glasgow3)

Network data: 3 waves, 50 actors, directed
----------------------------------------------------------
wave          ties     density   avg. degree
1              113      0.0461         2.260
2              116      0.0473         2.320
3              122      0.0498         2.440
----------------------------------------------------------
period      kept  created dissolved  Jaccard   Hamming
1->2          57       59        56    0.331       115
2->3          66       56        50    0.384       106
----------------------------------------------------------

The density barely moves, but the network is far from static: between the first two waves 57 ties were kept, 59 were created and 56 were dissolved. The Jaccard index (kept ties divided by all ties present at either wave) is about 0.33 to 0.38. A SAOM needs enough change to learn from, but also enough stability for the waves to be linked; The package help notes that a period with a Jaccard index below about 0.3 has few stable ties and carries little information about the change process. Here both periods are above that.

The first model

We start with the effects that almost every SAOM contains:

outdegree: the baseline tendency to have ties at all (it plays the role that the intercept or edges plays in other models);
reciprocity: a tendency to return ties;
transtrip: transitive triplets, “a friend of a friend becomes a friend”;
samex(smoke1): a preference for friends with the same smoking status.

. 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

seed(1) makes the run reproducible (the estimation is a stochastic simulation, so a different seed gives slightly different numbers). The header says that this is the default estimator: the method of moments, in its conditional form, which is RSiena’s default for one network.

The coefficient table

The coefficients are on the log-odds scale of an actor’s choice, so a positive number makes the corresponding change more attractive and a negative number less attractive, holding the other effects constant. The rest of the table (standard errors, z, p-value, interval) is read as in any other Stata estimation command.

outdegree is -2.77: with nothing else going on, creating a tie is unattractive. This is typical. Friendship networks are sparse, and the coefficient mostly tells you the density of the network. It is not interpreted substantively.
reciprocity is 2.46 (z = 12.4): pupils strongly prefer to return a friendship. Choosing someone who already named you is worth about 2.5 on the log scale, on top of the baseline.
transtrip is 0.62 (z = 8.1): the more friends in common via a path, the more attractive a tie is. Friendship clusters.
samex_smoke1 is 0.13 (z = 0.9): no evidence that pupils choose friends by smoking status, once reciprocity and clustering are in the model.

The rate parameters

The rate says how many opportunities for change an actor had on average during a period. Between the first two waves each pupil had about 6.5 opportunities to reconsider a friendship, and 5.3 between the second and third. The standard errors are 1.1 and 0.9. Rates are nuisance parameters: they are needed, but they are rarely the point of an analysis.

The convergence check

The last line is the most important one for deciding whether to believe the numbers. The estimation is an iterative simulation and its result is only valid if the simulated networks, averaged over many runs, reproduce the observed ones. For every parameter nwsaom computes a convergence t-ratio (the discrepancy between simulated and observed statistic, in standard-deviation units). RSiena’s rule, which nwsaom follows, is:

every t-ratio below 0.1 in absolute value and the overall maximum convergence ratio below 0.25: good;
overall maximum above 0.25: not converged; do not interpret the estimates, see Tutorial 2.

Here the overall ratio is 0.097, so the model converged. The option detail lists every t-ratio and the effect names RSiena would use for the same effects:

. nwsaom, waves(glasgow1 glasgow2 glasgow3) outdegree reciprocity transtrip samex(smoke1) seed(1) detail
...
RSiena effect names:
  samex_smoke1                  same smoke1
Convergence t-ratios (criterion: every |t| below 0.1; the overall maximum ratio below 0.25 is a separate criterion):
  outdegree                  0.072      reciprocity                0.072
  samex_smoke1               0.094      transtrip                  0.061
Overall maximum convergence ratio:  0.097

(The table and rates are repeated and are left out here.)

What the model stored

As other Stata estimation commands, nwsaom leaves its results in e(): e(b) and e(V) hold the coefficients and their covariance matrix, so test, lincom and estimates store work as usual (see Tutorial 2), and e(version) holds the release of the package that produced the results, which you should quote when you report an analysis.

Things to try

Replace samex(smoke1) with egox(smoke1) altx(smoke1): do smokers send or receive more friendship nominations?
Fit the model with only the two waves wave1(glasgow1) wave2(glasgow2).
Use a different seed() and see how much the coefficients move; this is the simulation noise.
Add indegpopularity and outactivity (a tendency for popular pupils to attract more ties, and for active pupils to send more).
Add detail, and compare the printed RSiena names with the effects table in nwsaom and RSiena.

Where next

Tutorial 2 shows what to do when the convergence line says “not converged”. The complete syntax is in Stata’s help nwsaom and on the nwsaom reference page.