suppressMessages(library(RSiena))
rd <- function(f) as.matrix(read.table(file.path("data", f)))
wave_files <- paste0("klas12p-friends-wave", c("A", "B", "C", "D"), ".dat")
raw <- lapply(wave_files, rd)
c(n_actors = nrow(raw[[1]]), n_waves = length(raw))
#> n_actors n_waves
#> 33 4
table(unlist(raw))
#>
#> 0 1 9 10
#> 3346 499 125 386Composition change in SAOMs
Ancillary self-study · ICPSR Network Analysis: Advanced Topics
ImportantOptional: not covered in the 2026 course
This document is not part of any taught session. Nobody is going to lecture it at you, nobody is going to grade you on it, and you can ignore it completely without falling behind.
It exists because it is a thing you will plausibly need next, and because it is easier to hand you something that works than to hand you a citation and wish you luck. Everything here runs end to end on the same machine setup you used in class. Every number and every figure on this page was produced by a chunk in this file: there are no screenshots of R output anywhere in the ancillary package.
How to work through it alone. Get the source (click the </> Code button at the top right, then View Source, and copy it into a .qmd file: or open the .qmd you were given directly), run the chunks in order, and read the prose between them: the prose is where the argument lives. Slow fits are identified in the prose, and precomputed fits load a shipped result while still showing you the code that produced it. Folded Depth boxes are optional extras; folded Stuck? boxes are hints. Open whichever you need and ignore the other. Exercises have a Solution tab: you are working alone, so use it.
NoteWhat this extends, and why it is here
Extends: the SAOM session (day 12, W3 Tue). We fitted s50, which is a tidy dataset: 50 girls, all present at all three waves. Your data will not be like that.
The problem it solves: actors who join or leave between waves. Students transfer schools, firms are founded and go bankrupt, states enter and exit the international system, patients are discharged. If you have panel network data of any real duration, you have this problem, and the default thing people do about it: drop everyone who was not there the whole time: throws away data and can bias what is left.
What you need: RSiena, plus the four klas12p-*.dat files shipped alongside this document in data/. Nothing to download.
1. Why this is not just a missing-data problem
There is a distinction here that is easy to blur and expensive to get wrong.
Missing data means the tie exists as a question but you do not know the answer. Pupil 7 was off sick the day the survey ran, so you do not know whether 7 nominated 12 as a friend. The tie variable \(y_{7,12}\) is well defined; you just did not observe it. RSiena handles this by imputing during simulation and excluding the cell from the target statistics.
Composition change means the tie does not exist as a question at all. Pupil 7 had not yet joined the class. There is no fact of the matter about whether 7 nominated 12, because 7 was not there to nominate anybody. \(y_{7,12}\) is not unknown, it is undefined.
Treating the second as if it were the first inflates your sample with cells that were never real, and: more insidiously: it tells the model that a bunch of actors spent a wave making the deliberate choice to have zero friends. The rate function will then work hard to explain why those actors were so inactive. They were not inactive. They were absent.
NoteDepth: why the actor-oriented formulation can do this at all
This is one of the genuinely nice consequences of writing the model at the level of actors rather than graphs.
A SAOM says: time runs continuously; every so often an actor gets an opportunity to change one tie; when they do, they pick the option that maximises their objective function plus noise. The model is a description of what individual actors do. If an actor is not present during some stretch of time, that is not a hole in the data: it simply means the actor had no opportunities during that stretch, which the model expresses directly by not giving them any.
An ERGM or a TERGM has no comparable move available, because it is defined as a probability distribution over graphs on a fixed node set. A graph on 26 nodes and a graph on 22 nodes are elements of different sample spaces, and there is no natural way to write a single ERGM over both. This is why the TERGM companion document has to drop four pupils and take the loss, and it is a real, if narrow, advantage of the actor-oriented framing. See Temporal ERGMs §6.1.
2. The data
Andrea Knecht’s Dutch classroom study, class 12p: 33 pupils, four waves of friendship nominations, with pupils entering and leaving. The files ship with this document.
The coding scheme matters and it is exactly the distinction from §1:
| code | meaning | what to do with it |
|---|---|---|
0 |
no friendship | leave as 0 |
1 |
friendship | leave as 1 |
9 |
incidentally missing nominator (absent that day) | → NA, genuine missing data |
10 |
structurally missing (not in the class at that wave) | → composition change |
Nearly 400 cells coded 10. Those are the ones this document is about.
3. Building the composition-change object
3.1 First, the two missing codes go to NA
Both 9 and 10 become NA in the network array. That may look like it defeats the purpose: we just said they are different things. The point is that the distinction is carried by a separate object, not by the tie values. RSiena needs to be told who was present when, and once it knows that, it can tell which NAs are structural and which are incidental.
n <- nrow(raw[[1]])
arr <- array(NA_integer_, dim = c(n, n, 4))
for (i in 1:4) {
m <- raw[[i]]
m[m %in% c(9, 10)] <- NA
diag(m) <- NA # self-ties are never defined
arr[, , i] <- m
}
fr <- sienaDependent(arr)
fr
#> Type oneMode
#> Observations 4
#> Nodeset Actors (33 elements)3.2 Then, who was present when
klas12p-composition.dat has one row per actor and two columns: the wave at which they entered and the wave at which they left, on a continuous scale where wave 1 is time 1 and wave 4 is time 4. A value of 2.5 means the actor arrived halfway between waves 2 and 3.
comp <- read.table(file.path("data", "klas12p-composition.dat"))
names(comp) <- c("enters", "leaves")
table(comp$enters, comp$leaves)
#>
#> 1.5 3.5 4
#> 1 1 1 30
#> 2.5 0 0 1Thirty of the 33 pupils were present the whole time (1 to 4). Three were not: one left at 1.5 (partway through period 1), one left at 3.5 (partway through period 3), and one arrived at 2.5 (partway through period 2).
TipStuck? What the fractional times mean
The intervals are on the same continuous clock the SAOM uses internally. Because the model runs in continuous time between waves, it can accept “this actor joined partway through period 2” and simply give them opportunities to act from that moment onward.
If you do not know when someone joined, use the wave at which you first observed them. Being approximately right is much better than pretending they were there all along, and much better than deleting them.
sienaCompositionChange() wants a list, one element per actor, each a numeric vector of the intervals during which that actor was present.
cc_list <- Map(function(a, b) c(a, b), comp$enters, comp$leaves)
movers <- which(comp$enters != 1 | comp$leaves != 4)
str(cc_list[movers]) # the three who moved
#> List of 3
#> $ : num [1:2] 1 1.5
#> $ : num [1:2] 1 3.5
#> $ : num [1:2] 2.5 4
str(cc_list[1]) # a typical pupil, present throughout
#> List of 1
#> $ : num [1:2] 1 4
cc <- sienaCompositionChange(cc_list)3.3 Covariates and the data object
dem <- read.table(file.path("data", "klas12p-demographics.dat"))
names(dem) <- c("sex", "age", "ethnicity", "religion")
dem[dem == 0] <- NA # 0 is the missing code for all four
sex <- coCovar(dem$sex)
dat <- sienaDataCreate(fr, sex, cc)
dat
#> Dependent variables: fr
#> Number of observations: 4
#>
#> With composition change.
#> Nodeset Actors
#> Number of nodes 33
#>
#> Dependent variable fr
#> Type oneMode
#> Observations 4
#> Nodeset Actors
#> Densities 0.11 0.13 0.15 0.16
#>
#> Constant covariates: sexRead the print-out. The line that matters is With composition change. That is your confirmation that RSiena took the object and will use it. If it is absent, cc did not make it into sienaDataCreate() and everything below is wrong.
checkpoint(actors = n,
waves = 4,
movers = sum(comp$enters != 1 | comp$leaves != 4))
#> ------------------------------------------------------------------
#> CHECKPOINT: actors = 33 | waves = 4 | movers = 3
#> ------------------------------------------------------------------4. Fitting, and what changes
eff <- getEffects(dat)
eff <- includeEffects(eff, transTrip, cycle3)
#> effectNumber effectName shortName include fix test initialValue
#> 1 23 transitive triplets transTrip TRUE FALSE FALSE 0
#> 2 43 3-cycles cycle3 TRUE FALSE FALSE 0
#> parm
#> 1 0
#> 2 0
eff <- includeEffects(eff, sameX, interaction1 = "sex")
#> effectNumber effectName shortName include fix test initialValue parm
#> 1 311 same sex sameX TRUE FALSE FALSE 0 0
alg <- sienaAlgorithmCreate(projname = NULL, seed = 6886, n3 = 1000)
#> If you use this algorithm object, siena07 will create/use an output file Siena.txt .
ans <- fit_or_load("saom_comp",
siena07(alg, data = dat, effects = eff, batch = TRUE, verbose = FALSE, silent = TRUE))
data.frame(effect = ans$effects$effectName,
est = round(ans$theta, 3),
se = round(sqrt(diag(ans$covtheta)), 3))
#> effect est se
#> 1 constant fr rate (period 1) 6.165 1.153
#> 2 constant fr rate (period 2) 5.956 0.950
#> 3 constant fr rate (period 3) 5.774 0.853
#> 4 outdegree (density) -2.569 0.148
#> 5 reciprocity 1.889 0.212
#> 6 transitive triplets 0.539 0.060
#> 7 3-cycles -0.599 0.116
#> 8 same sex 0.814 0.149Convergence first, as always:
round(as.numeric(ans$tconv.max), 4)
#> [1] 0.1152
max(abs(ans$tstat))
#> [1] 0.05297928tconv.max under 0.25 and all individual t-ratios under 0.1: this converged properly and you could report it.
Substantively: strong reciprocity, positive transitive triplets, negative 3-cycles (so closure is hierarchical rather than egalitarian: ties close into transitive triads but not into cycles), and same-sex friendship is clearly favoured. Standard adolescent-friendship findings, which is reassuring on a dataset this small.
NoteDepth: what the rate parameters are telling you
First, a note on why they are visible at all. By default siena07 uses conditional estimation, which conditions on the observed number of changes and does not report the rates as estimated parameters. Composition change makes conditional estimation impossible, so RSiena switches to unconditional estimation and the rate parameters appear in the output. You get them here as a side effect of the thing this document is about. (The Core exercise below turns this into the diagnostic it deserves to be.)
The three constant fr rate parameters are the estimated number of opportunities each actor gets to change a tie in each period. They are around 6, meaning the model thinks a typical pupil considered changing about six ties between consecutive waves.
Two things to notice.
First, these are opportunities, not changes. An actor who gets an opportunity is free to decide their current network is fine and change nothing: that is the “no change” option in the multinomial choice, and it is chosen often.
Second, this is precisely the parameter that composition change protects. Absent actors get zero opportunities in the periods when they are away, rather than being scored as actors who had six opportunities and used all of them to do nothing. Drop the composition-change object and the rate estimates absorb the absences, which distorts your reading of how fast the network is actually moving.
5. Structural zeros, the alternative approach
You will see a different technique in the literature and in older teaching material: code the absent actors’ ties as structural zeros (value 10 in the network array, with allowOnly = FALSE), which tells RSiena those cells are fixed and not to be modelled.
This is a supported approach for method-of-moments estimation, not a deprecated feature kept only for historical replication. The current RSiena manual presents structural-zero coding and composition-change directives as two ways to represent changing composition. It prefers a composition-change object when endowment or creation effects are needed, and it documents additional caveats for maximum-likelihood and Bayesian estimation. Those qualifications are more specific than a blanket rule against structural zeros.
Two reasons to prefer sienaCompositionChange():
- A structural zero says “this tie is fixed at zero.” That is a statement about a tie that exists as a question. Composition change says “this actor was not here.” Only the second one is true, and only the second one correctly removes the actor from the rate function.
- Composition directives can encode fractional entry and exit times directly. Structural zero coding records the constraint at observation waves. The directive therefore uses more timing information when those entry and exit times are known.
Structural-zero coding persists because it remains useful and because a large body of published work uses it. If you are replicating a paper that used structural zeros, preserve the coding and say so. For a new method-of-moments analysis with known entry and exit times, a composition-change object is usually the clearer representation, especially when creation or endowment effects are part of the specification.
WarningWhat structural zeros are legitimately for
Do not conclude that structural zeros are obsolete generally. They are the right tool whenever a tie is genuinely impossible rather than merely absent: a directed network where some actors cannot by construction send ties, two departments that are forbidden to collaborate, a bipartite structure encoded in a one-mode array.
The objection here is narrow and specific: using them to represent actors who were not there is a workaround for a problem that now has a purpose-built solution.
6. Exercises
Refit the §4 model without the composition-change object: that is, using only sienaDataCreate(fr, sex), and compare the rate parameters with the ones you got in §4.
dat_nocc <- sienaDataCreate(fr, sex) # note: no `cc`
eff2 <- getEffects(dat_nocc)
eff2 <- includeEffects(eff2, ________, ________)
eff2 <- includeEffects(eff2, sameX, interaction1 = "sex")
ans2 <- siena07(alg, data = dat_nocc, effects = eff2,
batch = TRUE, verbose = FALSE, silent = TRUE)In two sentences: which parameters move most, and does the direction of the change match what §4’s Depth box predicted?
Only three of 33 pupils move in and out here, which is why the §4 vs Core comparison is undramatic. Construct a harsher test: build a second composition-change object that additionally treats the pupils with the most incidentally missing data (code 9) as if they had been absent for the wave in which they are missing, refit, and see how much further the estimates shift.
Then argue: this is the real exercise: whether that second object is a better description of the data than the first, or a worse one. There is a defensible answer in each direction and what matters is that you can say which distinction from §1 you are relying on.
dat_nocc <- sienaDataCreate(fr, sex)
eff2 <- getEffects(dat_nocc)
eff2 <- includeEffects(eff2, transTrip, cycle3)
#> effectNumber effectName shortName include fix test initialValue
#> 1 23 transitive triplets transTrip TRUE FALSE FALSE 0
#> 2 43 3-cycles cycle3 TRUE FALSE FALSE 0
#> parm
#> 1 0
#> 2 0
eff2 <- includeEffects(eff2, sameX, interaction1 = "sex")
#> effectNumber effectName shortName include fix test initialValue parm
#> 1 311 same sex sameX TRUE FALSE FALSE 0 0
ans2 <- fit_or_load("saom_nocomp",
siena07(alg, data = dat_nocc, effects = eff2,
batch = TRUE, verbose = FALSE, silent = TRUE))
c(with_comp = length(ans$theta), without_comp = length(ans2$theta))
#> with_comp without_comp
#> 8 5The two fits do not have the same number of parameters, so you cannot line them up in a data frame. That is the first finding, not an obstacle. Here is why:
c(with_comp = ans$cconditional, without_comp = ans2$cconditional)
#> with_comp without_comp
#> FALSE TRUEWithout composition change, RSiena used conditional estimation: it conditions on the observed number of tie changes in each period and does not estimate the rate parameters as free parameters at all: they are recovered afterwards and stored in $rate. With composition change, conditional estimation is not available, so RSiena silently switched to unconditional estimation and the rates became ordinary parameters in $theta.
Nothing warned you about this. It is a good habit to check length(theta) and $cconditional whenever two SAOM fits refuse to line up.
Now the actual comparison. Rates first, pulling them from wherever each fit put them:
rate_with <- ans$theta[grep("rate", ans$effects$effectName)]
rate_without <- ans2$rate
data.frame(period = 1:3,
with_comp = round(rate_with, 3),
without = round(rate_without, 3),
pct_diff = round(100 * (rate_with - rate_without) / rate_without, 1))
#> period with_comp without pct_diff
#> 1 1 6.165 6.151 0.2
#> 2 2 5.956 4.916 21.2
#> 3 3 5.774 5.754 0.3And the structural effects, matched by name:
nm <- c("outdegree (density)", "reciprocity", "transitive triplets", "3-cycles", "same sex")
data.frame(
effect = nm,
with_comp = round(ans$theta[match(nm, ans$effects$effectName)], 3),
without = round(ans2$theta[match(nm, ans2$effects$effectName)], 3),
row.names = NULL)
#> effect with_comp without
#> 1 outdegree (density) -2.569 -2.691
#> 2 reciprocity 1.889 1.885
#> 3 transitive triplets 0.539 0.568
#> 4 3-cycles -0.599 -0.612
#> 5 same sex 0.814 0.861c(with_comp = as.numeric(ans$tconv.max), without_comp = as.numeric(ans2$tconv.max))
#> with_comp without_comp
#> 0.1151797 0.1087032Core. The rate parameters move and the structural effects barely do, which is what §4’s Depth box predicted, and the pattern of movement is sharper than you might expect.
Look at which period moves. Periods 1 and 3 agree to within a fraction of a percent. Period 2 is off by more than twenty percent, and period 2 is the one containing the arrival, the pupil who joins at time 2.5.
The general mechanism is the one described earlier: without the composition-change object, an actor who was not in the class is scored as an actor who was there, was handed a full allocation of opportunities, and used every one of them to change nothing. The model has only one dial for that, the rate, so it concludes the network was moving more slowly than it really was. That is the direction we see.
I will not pretend to a complete account of why the arrival distorts period 2 so much more than the two departures distort periods 1 and 3. Plausibly an arriving actor is the harder case: their ties all become visible at once, and how the estimator reads that burst depends on whether it knows the actor is new. If you want to settle it, the experiment is right there: vary the composition list one mover at a time and refit. That is a genuinely good afternoon’s work and I would rather flag the open question than paper over it.
The structural parameters: reciprocity, transitivity, homophily: hardly shift, because they are estimated from the actors who actually acted, and those are the same actors in both fits.
The honest summary of this comparison is that with three movers out of 33 the substantive conclusions do not change. Do not generalise from that. The distortion scales with the fraction of your panel that turns over, and it lands hardest on the periods where the turnover happens. With a third of the panel moving in and out: completely ordinary in organisational or clinical data: you get rate estimates that are badly wrong in specific periods, and if the timing of the turnover correlates with anything substantive, the structural estimates follow.
So the reason to use composition change here is not that it rescues this analysis. It is that it is the correct model of what happened, it costs three lines, and you will not remember to add it later when the stakes are higher.
Stretch. The argument against the harsher object: a pupil who was absent on survey day is a genuine missing-data problem, and RSiena’s missing-data machinery is designed for it: it imputes during simulation and excludes those cells from the target statistics, which is the statistically correct treatment. Recoding them as composition change tells the model something false (they were not in the class) in order to avoid a problem the model already handles well.
The argument for it: if a pupil is missing at a wave, you have no information about their choices at that wave either way, and the rate function is arguably better off not attributing opportunities to them. This is more defensible when the missingness is heavy and long: a pupil missing three of four waves is functionally absent whatever the coding says.
The distinction from §1 that decides it: was the tie well defined and unobserved, or undefined? For a pupil who was enrolled but off sick, the tie was well defined. That points to missing data, not composition change. The line genuinely blurs when absences get long enough that “enrolled” stops describing anything real, and at that point you should say in your write-up which choice you made and why, because a reader cannot tell from the coefficients.
7. Readings
- Ripley, Snijders, Boda & Vörös, Manual for RSiena (current edition: check stats.ox.ac.uk/~snijders/siena for the latest). The composition-change section is short and worth reading in full. Note the syllabus cites a 2012 edition with Preciado as an author, which is roughly fourteen years stale, and the author line has changed. Use the current one.
- Huisman & Snijders (2003), “Statistical analysis of longitudinal network data with changing composition,” Sociological Methods & Research 32(2):253–287. The method underneath
sienaCompositionChange(). - Huisman & Steglich (2008), “Treatment of non-response in longitudinal network studies,” Social Networks 30(4):297–308. On the §1 distinction, done carefully, with simulations showing when it matters.
Versions: expand if your numbers differ from mine
data.frame(package = "RSiena",
version = as.character(packageVersion("RSiena")))
#> package version
#> 1 RSiena 1.5.0
cat("R", as.character(getRversion()), "\n")
#> R 4.3.3