Longitudinal Network Models

Scott Duxbury’s Longitudinal Network Models is part of the Sage Quantitative Applications in the Social Sciences series, otherwise known as “little green books.” The book offers a practical guide to a wide range of statistical models for dynamic network data that have been developed in recent years. The methods covered in the book focus on how to model (1) change in a network across time and/or (2) network effects on change in individual covariates (e.g., behavior change due to peer influence). The book reviews the most commonly used models by social scientists and is restricted to methods for “complete” or “sociocentric” network data (as opposed to “egocentric” data). The book assumes only basic familiarity with network analysis and linear models and, in this way, meets its goal of being generally accessible. I will briefly summarize each of the chapters, then highlight the book’s contributions and limitations.

Chapter 1 sets the stage by overviewing what longitudinal network models are and why we need them. There is useful nuts and bolts guidance regarding data structures and ways of organizing network panel data (i.e., snapshots of a full network at multiple time points). A section on modeling capabilities offers entree to the multitude of research questions network models can address. This section also underscores why network analysis can be daunting—some researchers are interested in explaining change in a network; others are interested in network effects on behavior change; and still others are interested in both. Each of these calls for a different modeling approach. The chapter concludes by discussing how model choice should be driven by theoretical concerns regarding the nature of ties and their change.

The meat of the book is Chapters 2-5, which review a total of six models. Chapters 2 and 3 each cover one of the more widely used approaches to modeling network panel data. The Temporal Exponential Random Graph Model (TERGM) and Stochastic Actor-Oriented Model (SAOM) can answer similar questions about how networks change. Duxbury provides guidance to model selection by way of differences in their assumptions and how they model change, with implications for their interpretation and suitability for various types of relations. Whereas these models assume ties are persisting “states” (e.g., friendships), Chapter 4 focuses on networks of relational events, where ties are fleeting and dependence accumulates across time. The focus here is on modeling which relational event happens next across a long sequence of events. This chapter devotes the greatest attention to the Relational Event Model (REM), but gives a brief introduction to the Dynamic Network Actor Model (DyNAM).

Chapter 5 “flips” the research question by discussing methods for testing network influence, whereby actor covariates are the outcome of interest and network measures are predictors. Two models are described: the Temporal Network Autocorrelation Model (TNAM) and a variation of the SAOM from Chapter 3. A key distinction is that the TNAM treats the network as exogenous, while an SAOM models endogenous change in both individual covariates and networks (i.e., co-evolution). Duxbury discusses the assumptions and trade-offs of each approach and their implications for the types of questions the models can answer.

Chapter 6 concludes by reviewing some current issues in network modeling (e.g., missing data, measurement error, unobserved heterogeneity). Duxbury summarizes current understandings and best practices and points to where greater methodological development is needed.

The book excels at helping the reader wrap their head around these modeling approaches, facilitated by a general overview of each model’s assumptions, specification, and advanced considerations. There is also a helpful “intuition” section that describes each model using a simplified framework likely to be more familiar to the general reader (e.g., think of a TERGM as a logistic regression). I appreciated the start-to-finish examples for many of the models, which covered data format, model setup and estimation, goodness of fit, and interpretation. Duxbury deserves credit for showing how to use average marginal effects and predicted plots to assist with interpretation.

Perhaps the greatest value in this book is in helping to point the reader in the right direction. The book excels at conveying the capabilities of each modeling framework and providing direction on which model to choose based on one’s data and research question. There is enough detail to give the reader a rough outline of the data requirements and analysis steps.

Covering these sophisticated models in so few pages is a challenging task. Accompanying R scripts for the examples help fill in some of the blanks. Yet, lingering questions are unavoidable. I found the coverage of the REM model to be the most wanting, mainly due to the counterintuitive nature of the example data. Specifically, the REM was developed to take advantage of the exact timing or sequence of relational events. The example of online transactions between buyers and sellers is presented as such a case yet, without explanation, detailed information on event timing was discarded as transactions were aggregated into monthly snapshots (resulting in data that resembles the panel data used by a TERGM or SAOM). This made it difficult to align the example with the model description. I was also left wondering about the motivation for using an REM versus a TERGM with such data and trade-offs between these approaches. More conventional relational event data could have avoided this confusion. The example also implies that high rates of simultaneous events are tolerable, but without insight into how the model accommodates this.

Given this book has the potential to be an important resource on many researchers’ pathways into network modeling, I am obligated to note several issues with interpretation in hopes of curtailing their diffusion. I highlight three in particular, each of which is a common pitfall when interpreting these models.

First, Duxbury makes the important point that when modeling higher-order structures, models should test for lower-order structures nested within them (e.g., two-stars nested within triads, sender/receiver effects nested within homophily terms). In turn, lower-order effects cannot be interpreted in isolation from significant higher-order terms, which is something that could have been more consistently reinforced to the reader. For instance, in Chapters 2 and 3, the interpretation of sender/receiver effects for program year are misleading because of the significant effect for program year homophily. Significant sender, receiver, and homophily effects for a given covariate must be interpreted jointly. Doing so suggests a more nuanced pattern, whereby (1) more advanced students send more ties and (2) ties are more likely to be directed to peers in one’s program year or lower, relative to more advanced peers. This type of misinterpretation can be avoided by calculating predicted values based on all effects that share a nesting structure and across the full range of sender and receiver scores.

A second issue relates to how the standard implementations of TERGMs and SAOMs do not differentiate tie formation from tie dissolution. Duxbury notes this, but then the language used in describing effects occasionally slips into a “tie formation” explanation. Understandably this allows for simpler prose, but it risks mischaracterizing the model. Unless explicitly modeled as separate processes, effects in these models should be interpreted as affecting the creation or persistence of a tie, relative to tie dissolution or failure to form.

The third issue pertains to interpreting effects in the behavior function of a SAOM. While this function does take the form of a multinomial logistic regression predicting the adoption of different levels of a behavior, it does not acknowledge an actor’s current behavior state. Hence, the model is agnostic about whether adopting a particular behavior level represents an increase, decrease, or stability. Unless intentionally specified, SAOM behavior functions do not predict change per se, nor the direction of change. This isn’t intuitive and problems arise when people try to interpret it as predicting something like a change score. For example, the null estimate for the trend effect in the book’s example implies that actors are indifferent about their level of smoking (net of other effects). By contrast, a positive trend effect would signal that actors tend to have higher levels of the behavior, but would not indicate whether this was due to actors increasing their behavior or remaining at a higher level (and does not indicate that smoking prevalence changed across waves). The book is clearer in interpreting the peer influence effect, but spelling out a complementary scenario would help readers still grappling with this unfamiliar model interpretation. Namely, the positive estimate for smoking similarity also means that a smoking student with non-smoking friends is likely to change to become similar to their friends, which represents a decrease in their smoking level. It is possible to discern effects on the direction of behavior change, but that requires going beyond the standard model specification.

In sum, this book is a useful resource for researchers considering a dynamic network analysis and who want direction on which modeling approach to take, types of questions that can be answered, and what goes into an analysis.