Abstract

This visualization provides a dynamic representation of the microsteps involved in modeling network and behavior change with a stochastic actor-based model. This video illustrates how (1) observed time is broken up into a series of simulated microsteps and (2) these microsteps serve as the opportunity for actors to change their network ties or behavior. The example model comes from a widely used tutorial, and we provide code to allow for adapting the visualization to one’s own model.

Estimating the Stochastic Actor-Based Model (SABM)

SAB models provide a means for estimating the co-evolution of social network and individual attribute data (Snijders, Bunt, and Steglich 2010). The model requires panel data for both the network and attribute(s). However, the estimation does not merely model the differences between the observed panels.

An SABM assumes the observed data are snapshots of an unobserved process that is unfolding in continuous time between waves. The interval between observed waves is divided into a sequence of microsteps, each of which contains at most one change. In a given microstep, one randomly chosen actor has the opportunity to make one change, either to their outgoing ties (adding or dropping one), or to their behavior (increasing or decreasing one level). A chosen actor may also make no change. The model’s rate function determines which actor gets an opportunity, and which type of change they consider making. What choice they make is determined by effects in the model’s objective function(s), which account for the current network structure and behavior.

Because microsteps are unobserved, the model uses an agent-based model (ABM) to simulate how change may have unfolded across them. SABM estimation begins with an observed network (W1), then simulates change over microsteps up to the subsequent observed time point (W2). This process iterates by comparing the simulated W2 network to the observed W2 network, then updating parameter estimates and repeating the simulation until the model reaches convergence. Upon reaching convergence, parameter estimates are fixed and the same algorithm is then used to generate a large number of network/behavior change sequences (i.e., “chains”) for estimating standard errors.

The ABM algorithm and continuous time assumption are key to SABM estimation. Yet, the nature of these microsteps is often difficult to envision, especially for audiences unfamiliar with the model or its estimation. To illustrate how this process works, we fit a model to the “s50” data included in the RSiena package (Ripley et al. 2018), turning on the “returnChains” option to export each microstep chain created during the standard error estimation phase of the model-fitting algorithm.

Converting & Visualizing the Simulated Network Changes

Each simulation chain begins with the observed W1 network and smoking behavior as initial conditions. We then convert a sequence of simulated changes from one simulation chain into a networkDynamic object class (Butts et al. 2016), which we visualize using ndtv (Bender-deMoll 2016). Figure 1 shows the simulated change for one chain of microsteps from the s50 model example (we provide full code in the Appendices).

Figure 1. SABM Microstep Visualization. Use the (far-right) forward button to step through this visualization one microstep at a time. The node with an opportunity to make a decision is highlighted in red, and clicking it provides information about what choice they make. Node size is proportional to smoking level. Newly forming ties momentarily flash as green; dissolving ties as red. Pressing play allows the visualization to present the entire sequence of microsteps. The menu bar in the upper right allows adjustment of the video’s playback speed.


The current visualization comes from a chain with m=508 microsteps, which are interspersed between m+1 time points (i.e., network-behavior states). In stepping through the visualization one microstep at a time, you can observe which node has the opportunity to make a change, the type of change (behavior or network), and what choice they make (which may include no change). For instance, from time 10 to 11 (microstep 11) node V23 has the opportunity to make a network change, and chooses to add the tie to node V31 observed at time 11. The entire sequence of simulated changes from W1 to W2 is presented in the video.

This visualization illustrates the continuous time simulation procedure at the heart of SABM estimation. We hope this visualization will assist others in learning and teaching the estimation techniques behind the SABM. In addition, this visualization and accompanying code can be used by future researchers interested in presenting visualizations of network and behavior change from estimated SABMs in empirical studies.

References

Bender-deMoll, Skye. 2016. ndtv: Network Dynamic Temporal Visualizations. R Package Version 0.10. https://cran.r-project.org/web/packages/ndtv/.

Butts, Carter T., Ayn Leslie-Cook, Pavel N. Krivitsky, and Skye Bender-deMoll. 2016. NetworkDynamic: Dynamic Extensions for Network Objects. https://CRAN.R-project.org/package=networkDynamic.

Ripley, Ruth M, Tom AB Snijders, Zsofia Boda, Andras Voros, and Paulina Preciado. 2018. Manual for Rsiena. University of Oxford: Department of Statistics, Nuffield College. https://www.stats.ox.ac.uk/~snijders/siena/.

Snijders, Tom AB, Gerhard van de Bunt, and Christian EG Steglich. 2010. “Introduction to Stochastic Actor-Based Models for Network Dynamics.” Social Networks 32: 44–60.