Tutorial 17: Networks over Time

Many network data sets observe the same group more than once: a school class in autumn and again in spring, a firm every year. Before you fit a model of change you want to know how much changed. This tutorial shows the descriptive tools of the core: turnover between waves, correlation between waves, and how to turn a list of ties with time stamps into snapshots. The animated version, nwmovie, is in Tutorial 5; models of change are in Tutorial 19 and the nwsaom tutorials.

The data are the three waves of the Glasgow friendship study (glasgow1, glasgow2, glasgow3, 50 pupils). The script is example.do, the complete output example.log.

. nwwebuse glasgow, nwclear

. nwsummarize glasgow1

(Arcs: 113, Density: .0461; the second wave has 116 arcs. The full summaries are in the log.)

Turnover: stable, formed and dissolved ties

nwturnover compares two networks on the same nodes and counts the ties that were stable (present in both), formed (new in the second) and dissolved (gone in the second). Only presence is compared, not tie values.

. nwturnover glasgow1 glasgow2, generate(stab12)
----------------------------------------
  Networks: glasgow1 -> glasgow2
  Stable: 57  Formed: 59  Dissolved: 56
  Jaccard index: .331
  Persistence: .504

. nwturnover glasgow2 glasgow3, generate(stab23)
----------------------------------------
  Networks: glasgow2 -> glasgow3
  Stable: 66  Formed: 56  Dissolved: 50
  Jaccard index: .384
  Persistence: .569

Between the first two waves the pupils kept 57 friendships, dropped 56 and made 59 new ones: about half of the ties of the first wave were still there in the second (persistence .50 = 57 / (57 + 56)). The Jaccard index is the share of all ties of either wave that are stable: 57 / (57 + 59 + 56) = .33. It is the number that the longitudinal literature uses (Snijders’ SIENA documentation) to judge whether a network changes enough to be worth modelling, and whether it changes so much that the waves are hard to bridge: a common rule of thumb is that values below about .3 make estimation difficult. These networks, at .33 and .38, are in the usable range but with a lot of change.

The results are also stored (r(stable), r(formed), r(dissolved), r(jaccard), r(persistence)) for use in loops and tables. generate() saves for each pupil an own Jaccard index, restricted to that pupil’s ties, so you can see who is stable and who changes:

. summarize stab12 stab23

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
      stab12 |         48    .3944444    .3421413          0          1
      stab23 |         48    .3881944    .3075288          0          1

The average pupil has an own Jaccard index of about .39, and individuals range from 0 (no tie kept) to 1 (all ties kept). The variable has 48 values, not 50: for two pupils the own index is undefined (missing).

Correlation between waves

nwcorrelate (Tutorial 14) correlates the tie cells of two networks. It answers a related but different question from turnover: it compares the values of the cells, not only the counts of kept and new ties:

. nwcorrelate glasgow1 glasgow2
    Correlation: .473

. nwcorrelate glasgow2 glasgow3
    Correlation: .532

The second pair of waves is more alike in both measures. Both fit the same picture: friendships are fairly persistent, but a great deal changes in a year.

From time-stamped ties to snapshots

Panel data come as separate networks. Other data come as one list of ties with a time: an e-mail log, contacts with the day on which they happened. Declare the time variable with nwset and nwattime cuts out the ties active at a given time as an ordinary static network, to which every other command applies:

. input ego alter wave
. nwset ego alter, time(wave) name(mynet)

. nwattime mynet, at(2) name(t2)
----------------------------------------
  Static graph view: t2
  Source network: mynet (snapshot)
  At: 2
  Ties: 2

. nwturnover t1 t2, generate(stab_t12)
----------------------------------------
  Networks: t1 -> t2
  Stable: 0  Formed: 2  Dissolved: 1
  Jaccard index: 0
  Persistence: 0

In this toy example (the five ties are listed in the script) a tie is active in the wave in which it is recorded (snapshot). With interval() instead, a tie is active from its start time up to, but not including, its end time, and a tie without an end is open-ended; with eventtime() it is active at exactly the moment of the event. nwattime is deliberately simple: it gives you a static view, not a model of the process.

Which command when?

Question	Command
How many ties were kept, formed and dissolved between two waves?	`nwturnover`
How alike are two waves, corrected for density?	`nwcorrelate`
Show the waves as an animation	`nwmovie` (Tutorial 5)
A list of ties with times: the network at one time	`nwset ..., time()`, `nwattime`
A model of how the network changes	Tutorial 19, nwsaom