Interpreting Window Effects

[non87]

Hello everyone, I am a new user of Goldfish. As a first thing, thank you very much for this wonderful package!

I am trying to use DyNAM model for my research, where I will have to estimate the effect of certain kind of dyadic events on the probability of other kinds of dyadic events. In particular, I have data about artists' group exhibitions and art auctions. I want to test if exhibiting together translate into selling together.

My best attempt at specifying such a model is the following (I am using the Social evolution data for reproducibility):

data("Social_Evolution")
set.seed(12345)

actors <- defineNodes(nodes = actors)
callNetwork <- defineNetwork(nodes = actors, directed = TRUE)
callNetwork <- linkEvents(x = callNetwork, changeEvent = calls,
                          nodes = actors)
callsDependent <- defineDependentEvents(events = calls, nodes = actors,
                                        defaultNetwork = callNetwork)
# Create a second network of calls to be used in the model specification
calls2 <- calls
# create a time differential between the two call networks
calls2$time <- calls2$time - 1500
# Subsample and re-order
calls2 <- calls2[sample.int(nrow(calls2), 100, replace = F), ]
calls2 <- calls2[order(calls2$time),]
callNetwork2 <- defineNetwork(nodes = actors, directed = TRUE)
callNetwork2 <- linkEvents(x = callNetwork2, changeEvent = calls2,
                          nodes = actors)

# Notice the last term of the formula
modNet <- estimate(callsDependent ~ inertia + recip(callNetwork) + trans + same(actors$floor) 
                  + same(actors$gradeType) + alter(actors$gradeType) + tie(callNetwork2, window=1500),
                  model = "DyNAM", subModel = "choice")

summary(modNet)

The key part of the code is the effect specification tie(callNetwork2, window=1500). I interpret it as the effect on the choice due to the event happening on the covariate network callNetwork2 in the 1500 seconds before the choice being modeled. This is exactly what I want, but I would really appreciate if a more expert user could vet the code (and perhaps correct it). Thanks again.

[auzaheta]

Hi @non87, thanks for posting your question and the good vibes about the package.

Short answer: Your interpretation is correct.
Long answer: Figure 2 on Stadfeld C. and Per B. has a nice representation of how the window effects look like in the timeline of events. goldfish does a quite straightforward representation of this creating a new events data frame that adds the dissolution (deletion) of the event happening on a plus window size time after the event.
You can look at the Global environment to a new object called something like calls2_1500. You will notice that every event on calls2 would have a corresponding event with an increment $-1$ at the time $time + 1500$. If a dependent event happens between the 1500 seconds after an event in calls2, then the corresponding change statistics would include the event in the covariate network as part of the explanatory effects during estimation.

> head(calls2_1500, 2)
        time   sender receiver increment
1 1220733470 Actor 72 Actor 50         1
2 1220734970 Actor 72 Actor 50        -1

As a remark of use of the window parameter: if the event time in your data is in seconds or an R date format, you can use shortcuts to define the windows using strings stating the preferred unit of time. In your example, window = "25 minutes" would give the same result.

It looks like it is worthed to improve the documentation regarding window effects and the effect interpretation. Thanks for pointing that out. Maybe a change in the title of this question might help other users to find this info. Something on the lines of "interpreting window effects" might do the trick.

I hope the answer is clear. Let me know if you would like to clarify something else.