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Inferential Network Analysis

Course Dates and Times

Monday 25 February – Friday 1 March, 09:00–12:30
15 hours over 5 days

Philip Leifeld

University of Glasgow

See under 'Prerequisite Knowledge'

Tasks for ECTS Credits

2 credits (pass/fail grade) Attend at least 90% of course hours, participate fully in in-class activities, and carry out the necessary reading and/or other work prior to, and after, classes.

3 credits (to be graded) As above, plus complete daily assignments.

4 credits (to be graded) As above, plus complete a seminar paper with a grade higher than F.

Instructor Bio

Until March 2019, Philip Leifeld is Professor of Research Methods at the University of Glasgow in the School of Social and Political Sciences. From April 2019, he takes up a post as Professor of Comparative Politics in the Department of Government at the University of Essex.

Philip's research interests are social and political networks, quantitative methods, policy debates, and the study of policy processes.

His work has appeared in a number of journals, such as the American Journal of Political Science and the Journal of Statistical Software.

Twitter  @PhilipLeifeld

This course revolves around the idea of creating probabilistic statistical models of networks. This is a big departure from the descriptive analysis of networks (e.g., measuring the centrality of a node) and also a fairly big departure from the statistical modelling of non-network data with the regression framework.

Our goal is to develop statistical models that can accomplish the same general objectives as regression models (fitting parameters to data with probabilistic models), while accounting for the substantial endogenous complexity inherent to network data.

To accomplish this, we will consider two basic approaches to modelling networks.

The approach on which we will spend the most time involves explicitly modelling the network dependencies present in the data. Starting cross-sectionally, we will introduce the exponential random graph model (ERGM) and consider it in some detail – including specification, estimation, fit checking, diagnosing problems, limitations, and post-estimation analysis and interpretation. We will then extend our knowledge of this approach to longitudinal, repeatedly observed networks by considering the Temporal ERGM and the stochastic actor-oriented model (SAOM, more commonly known as SIENA), which are closely related.

We close by considering alternative approaches to modelling networks, including the latent space network model and the quadratic assignment procedure, in which network dependencies are projected into the error term rather than explicitly modelled.

We will also discuss two additional models for temporal data: the temporal network autocorrelation model (TNAM), which is a model for the behaviour of nodes in a network, and the relational event model (REM), which can model a temporally more fine-grained series of network ties.

For each topic we cover, we will also consider how to perform such analyses in R using several example datasets.

If you want, you can present your own problems in class, and benefit from constructive feedback from the group.

What you will learn

This course will enable you to think about your own network data from a statistical and theoretical point of view. You will learn how to translate their theoretical questions into statistical models and how to answer these questions using empirical data and estimation.

This is an advanced course, which assumes existing knowledge of basic social science research methods, at least through generalised linear models (logit, the linear model, etc...) as well as basic knowledge of network analysis.

You should know the basic anatomy of networks as well as the descriptive tools of network analysis (e.g., measures of centrality, plotting and visualisation, etc...).

All techniques will be demonstrated using the R statistical language.

While this is not a course *about* software, basic familiarity with R is helpful, because I will not go into detail about how to load/manage data or use R's more basic functions. That said, a high level of R (e.g., programming competency) is not necessary.

Please install R and the packages statnet and xergm before the course.

Each course includes pre-course assignments, including readings and pre-recorded videos, as well as daily live lectures totalling at least three hours. The instructor will conduct live Q&A sessions and offer designated office hours for one-to-one consultations.

Please check your course format before registering.

Online courses

Live classes will be held daily for three hours on a video meeting platform, allowing you to interact with both the instructor and other participants in real-time. To avoid online fatigue, the course employs a pedagogy that includes small-group work, short and focused tasks, as well as troubleshooting exercises that utilise a variety of online applications to facilitate collaboration and engagement with the course content.

In-person courses

In-person courses will consist of daily three-hour classroom sessions, featuring a range of interactive in-class activities including short lectures, peer feedback, group exercises, and presentations.


This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc.). Registered participants will be informed at the time of change.

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, please contact us before registering.

Day Topic Details
1 Introduction and why we need network-specific models (and not regressions).

75% lecture on network modelling;
25% R lab on data preparation for network analysis.

2 Introduction to the ERGM, form, specification, estimation, and interpretation.

75% lecture on ERGM;
25% R lab on ERGM specification, estimation, and interpretation.

3 The ERGM, form, specification, estimation, and interpretation (continued).

75% lecture on ERGM;
25% R lab on ERGM specification, estimation, and interpretation.

4 Longitudinal network models: TERGM, TNAM, and SAOM.

75% lecture on TERGM, TNAM, and SAOM;
25% R lab on implementation in R.

5 Latent Space Models, QAP, temporal network autocorrelation models, and relational event models.

75% lecture on LSM, QAP, and REM;
25% R lab on implementation in R.

Day Readings
  • Lusher, Dean, Johan Koskinen and Garry Robins. 2013. Exponential Random Graph Models for Social Networks. New York, NY: Cambridge University Press. Chapters 2-5.
  • Cranmer, Skyler J., Philip Leifeld, Scott D. McClurg and Meredith Rolfe. 2017. Navigating the Range of Statistical Tools for Inferential Network Analysis. American Journal of Political Science. 61(1): 237-251.
  • Butts, C. T. (2008). network: A Package for Managing Relational Data in R. Journal of Statistical Software, 24(2):1–36.
  • Handcock, M. S., Hunter, D. R., Butts, C. T., Goodreau, S. M., and Morris, M. (2008). statnet: Software Tools for the Representation, Visualization, Analysis and Simulation of Network Data. Journal of Statistical Software 24(1):1–11.
  • Hunter, David R., Mark S. Handcock, Carter T. Butts, Steven M. Goodreau and Martina Morris. 2008. ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of Statistical Software 24(3):1-29.
  • Cranmer, Skyler J. 2011. Inferential Network Analysis with Exponential Random Graph Models. Political Analysis 19: 66-86.
  • Goodreau, Steven M., Mark S. Handcock, David R. Hunter, Carter T. Butts and Martina Morris. 2008. A statnet tutorial. Journal of Statistical Software 24(9): 1-26.
  • Morris, Martina, Handcock, Mark S. and Hunter, David R. 2008. Specification of Exponential-family Random Graph Models: Terms and Computational Aspects. Journal of Statistical Software 24(4):1-24.
  • Leifeld, Philip and Volker Schneider. 2012. Information Exchange in Policy Networks. American Journal of Political Science 53(3): 731-744.
  • Leifeld, Philip and Dana R. Fisher. 2017. Membership Nominations in International Scientific Assessments. Nature Climate Change.
  • Heaney, Michael T. and Philip Leifeld. 2018. Contributions by Interest Groups to Lobbying Coalitions. The Journal of Politics.
  • Ingold, Karin and Philip Leifeld. 2016. Structural and Institutional Determinants of Influence Reputation: A Comparison of Collaborative and Adversarial Policy Networks in Decision Making and Implementation. Journal of Public Administration Research and Theory 26(1): 1-18.
  • Leifeld, Philip, Skyler J. Cranmer and Bruce A. Desmarais. 2018. Temporal Exponential Random Graph Models with btergm: Estimation and Bootstrap Confidence Intervals. Journal of Statistical Software.
  • Czarna, Anna Z., Philip Leifeld, Magdalena Śmieja, Michael Dufner and Peter Salovey. 2016. Do Narcissism and Emotional Intelligence Win Us Friends? Modeling Dynamics of Peer Popularity Using Inferential Network Analysis. Personality and Social Psychology Bulletin 42(11): 1588-1599.
  • Snijders, Tom A.B., Gerhard G. van de Bunt and Christian E.G. Steglich. 2010. Introduction to Stochastic Actor-based Models for Network Dynamics. Social Networks 32(1):44 – 60.
  • Leifeld, Philip and Skyler J. Cranmer. 2015. The Temporal Network Autocorrelation Model. Working Paper.
  • Butts, C. T. (2008). A Relational Event Framework for Social Action. Sociological Methodology, 38(1):155–200.
  • Malang, Thomas, Laurence Brandenberger and Philip Leifeld. 2017. Networks and Social Influence in European Legislative Politics. British Journal of Political Science.
  • Krackhardt, David. 1988. Predicting with networks: Nonparametric multiple regression analysis of dyadic data. Social Networks 10(4):359-381.
  • Hoff, Peter D., Adrian E. Raftery and Mark S. Handcock. 2002. Latent Space Approaches to Social Network Analysis. Journal of the American Statistical Association 97(460):1090-1098.

Software Requirements

All software we use is free: R and several of its packages (e.g. ergm, statnet, xergm).

Hardware Requirements

Bring your own laptop (Windows, Linux, MacOS).


Berardo, Ramiro and John T. Scholz. 2010
Self-Organizing Policy Networks: Risk, Partner Selection, and Cooperation in Estuaries
American Journal of Political Science 54(3):632-649

Cranmer, Skyler J., Bruce A. Desmarais and Elizabeth Menninga. 2012
Complex Dependencies in the Alliance Network
Conflict Management and Peace Science 29(3): 279–313

Dekker, D., Krackhardt, D., and Snijders, T. A. B. 2007
Sensitivity of MRQAP tests to collinearity and autocorrelation conditions
Psychometrika, 72(4):563– 581

Desmarais, Bruce A. and Skyler J. Cranmer. 2012
Micro-Level Interpretation of Exponential Random Graph Models with Application to Estuary Networks
Policy Studies Journal 40(3): 402– 434

Desmarais, Bruce A. and Skyler J. Cranmer. 2012
Statistical Mechanics of Networks: Estimation and Uncertainty
Physica A 391(4):1865– 1876

Desmarais, Bruce A. and Skyler J. Cranmer. 2017
Statistical Inference in Political Networks Research
In: Oxford Handbook of Political Networks, edited by Jennifer N. Victor, Alexander H. Montgomery and Mark Lubell

Goodreau, Steven M., James A. Kitts and Martina Morris. 2009
Birds of a feather, or friend of a friend? Using exponential random graph models to investigate adolescent social networks
Demography 46(1):103– 125

Hanneke, Steve, Wenjie Fu and Eric P. Xing. 2010
Discrete Temporal Models of Social Networks
Electronic Journal of Statistics 4:585– 605

Krivitsky, Pavel N. and Mark S. Handcock. 2008
Fitting Latent Cluster Models for Networks with latentnet
Journal of Statistical Software 24(5):1-23

Leifeld, Philip and Skyler J. Cranmer. 2015
A Theoretical and Empirical Comparison of the Temporal Exponential Random Graph Model and the Stochastic Actor-Oriented Model

Leenders, R. T. A. J. 2002
Modeling social influence through network autocorrelation: Constructing the weight matrix
Social Networks, 24(1):21–47

Lerner, J., Bussmann, M., Snijders, T. A. B., and Brandes, U. 2013
Modeling frequency and type of interaction in event networks
Corvinus Journal of Sociology and Social Policy, 4:3–32

Lusher, Dean, Johan Koskinen and Garry Robins. 2013
Exponential Random Graph Models for Social Networks
New York, NY: Cambridge University Press

Robins, G., Pattison, P., Kalish, Y., and Lusher, D. 2007
An introduction to exponential random graph (p*) models for social networks
Social Networks, 29(2):173–191

Schaefer, David R. and Christopher Steven Marcum. 2018
Modeling Network Dynamics
In: Oxford Handbook of Social Network Analysis, edited by James Moody and Ryan Light

Recommended Courses to Cover Before this One

Winter School

Introduction to Applied Social Network Analysis

Introduction to R

Linear Regression with R/Stata: Estimation, Interpretation and Presentation

Interpreting Binary Logistic Regression Models

Summer School

R Basics