Inferential Network Analysis

Inferential Network Analysis, by Cranmer, Desmarais, and Morgan, is a new entry in the Cambridge University Press Analytical Methods for Social Research series. The text is an extension of the authors’ materials for teaching network analysis to graduate students in the social sciences. This book would serve as an excellent text for a course targeted at graduate students in statistics, in non-statistical disciplines with substantial statistical understanding, or even advanced undergraduate statistics majors. It is also well set up for self-study by anyone with appropriate background knowledge.

The focus of the book is on exponential random graph models (ERGMs) and latent space models. Note that the tools presented focus on inference about network structure. Coverage does not extend to processes operating over networks, such as contagion, social influence, or social support. The material covered does assume that readers are familiar with descriptive methods and visualization for network data, so it would serve best as a text for a second course in a sequence, or with a supplementary opening unit incorporating additional materials.

The introductory chapters open with a nice description of why inference with networks is far more challenging that inference with independent or clustered data (long-range dependence) and gives intuitive examples of network processes. This is followed by a brief presentation of the Conditional Uniform Graph Test (a form of hypothesis testing with a bootstrap null distribution from a generative model for the network), and an equally brief presentation of the Quadratic Assignment Procedure (a form of permutation test on adjacency matrices).

The majority of the book (Chapters 3 through 7) focuses on the preeminent statistical model for network data, the ERGM. It begins with an introduction to the mathematics of ERGMs, the required assumptions, and evaluation of model fit. Essential network statistics commonly used in ERGMs are also presented. A particularly useful section delineates the multiple levels of interpretation that can be made from ERGM results (network, edge, and subgraph).

Later chapters on ERGMs give an in-depth discussion of how to translate a theory about the generative process of a network to statistics that can be included in an ERGM and of the process of model building. There is a very nice discussion of degeneracy, the major complication that arises in the estimation of many ERGMs. Finally, they present a few alternatives to cross-sectional, binary edge network—including bipartite, longitudinally-observed, and weighted (valued-edge) networks.

The final section (Chapters 8 through 10) presents an alternative statistical framework for modeling network data: the latent space model (LSM). This follows a similar structure to the presentation of ERGMs, opening with the mathematical and theoretical underpinnings of the model, followed by an exploration of model building and evaluation of model fit. The authors then present an introduction to the complexities of interpreting LSM results, and then proceed to a summary of the assumptions, strengths, and weaknesses of the approach. Issues of estimation and interpretation are explored in-depth in their own chapter. The section wraps up with the presentation of alternatives to the basic LSM: weighted networks, agent-level random e ects, spatial clustering, and the latent factor model.

Each section of the book includes brief descriptions of and references to applied examples using the techniques presented. These are followed by a demonstration on one of a handful of recurring examples. Each demonstration includes a clear description of the problem, thoroughly-commented R code, and a complete interpretation of the results. Finally, each chapter wraps up with a set of problems guiding the reader through writing a report using the tools presented. All code and data used in the recurring examples are provided in an R package.

Overall, this book fills a needed gap in resources for people learning to model network data. While several texts cover descriptive methods and competing generative models, we have to date been missing an in-depth coverage of how to use inferential methods with network data, especially one so well-grounded in practice.