2R

Course Content

This module covers advanced statistical methods for analyzing social network data, focusing on testing hypotheses about network structure (e.g. reciprocity, transitivity, and closure), and the formation of ties based on attributes (e.g. homophily). The first three days provide an in depth discussion of exponential random graph models (also known as ERGM or p* models). We then introduce longitudinal models such as RSiena models (SAOMs) and relational event models.
Software used includes: MPNet and R packages RSiena.

Course Objectives

The module aims to familiarize participants with the formal statistical analysis of network data for selection mechanisms, as well as selection and influence in longitudinal models. Participants will become familiar with specific programmes designed for these analyses and with the mathematical basis for the modelling approaches, and they will learn how to conduct statistical analyses of their own network data. Participants are encouraged to bring with them their own network data to be analyzed using the techniques covered. The course provides a thorough, yet intuitive introduction to these models and does not require advanced statistical knowledge. It does require basic knowledge of logistic regression and the principle of significance tests in classic (survey) research.

In general the module focuses on how do the characteristics of a network of interest differ from chance? At the end of the module, participants should be able to answer questions, such as:
– Is there more reciprocity in an advice network than could be expected by chance?
– Is there a tendency towards homophily? (do smokers tend to be friends with other smokers? and do non- smokers tend to be friends with other non-smokers)?
– Is there more transitivity (are friends of friends also friends) or closure or cyclicality in a network than expected by chance, controlling for the degree distribution?
– Do advice and friendship ties tend to overlap (multiplexity)?
– Considering the friendship network for different classes at the same time, is there an overall tendency towards clustering? Are there differences in tendency between classes?

Course Prerequisites

Participants should have taken an introductory course in social network analysis, so be familiar with such terms as reciprocity, density, indegree and outdegree. Participants should also have taken a basic module in (logistic) regression analysis

Remedial Reading

Scott, J. 1992. Social Network Analysis. Sage.

Representative Background Reading

Wasserman, S., and Faust, K. 1996. Social Network Analysis. Cambridge University Press.

Required Reading – (this book will be provided by ESS):

Lusher, D., Koskinen, J., and G. Robins. Editors. 2013. Exponential Random Graph Models for Social Networks. Cambridge University Press

Background knowledge required

Statistics

OLS – elementary

Maximum Likelihood – elementary

Computer Background

R – elementary

Maths

Calculus – moderate

Linear Regression – elementary

POTENTIAL ESS APPLICANTS ARE TO BE ADVISED THAT RECORDINGS WILL NOT BE MADE AVAILABLE FOR THIS COURSE.

For in person study, please note: For participation in this course, students are required to bring with them their own laptops.

1. Exponential Random Graph Models: general intro, MLE, MCMC and undirected networks

This first session focuses on a class of statistical models, known as exponential random graph models (ERGMs or p* models). ERG models (Lusher et al., 2013; Wasserman and Robins, 2005; Robins et al., 2007) enable one to test for the presence of different local processes simultaneously (e.g., homophily, reciprocity, transitivity, cyclicality or multiplexity). The focus is on providing a thorough, yet intuitive introduction to the general principles of ERG models. This includes the difference between pseudo-likelihood and maximum likelihood estimation (MLE), and an introduction into MCMC. This introduction does not require advanced statistical knowledge. It does require basic knowledge of logistic regression and the principle of significance tests in classic (survey) research. Lusher, D., Koskinen, J., Robins, G. 2013. Exponential Random Graph Models for Social Networks. Cambridge University Press. Wasserman, S., Robins, G. 2005. An introduction to random graphs, dependence graphs, and p*. In Carrington, P.J., Scott, J., and Wasserman, S. (eds.), Models and Methods in Social Network Analysis. New York: Cambridge University Press. Robins, G., Pattison, P., Kalish, Y., Lusher, D. 2007. An introduction to exponential random graph (p*) models for social networks. Social Networks 29: 173-191.

2. Exponential Random Graph Models: convergence, directed networks and attributes

In this session we focus on running ERG models, getting convergence and interpreting the results using MPNet (Robins et al., 2007; Hunter 2007). We consider structural effects for both undirected and directed networks to test for reciprocity, transitivity and cyclicality (Robins et al., 2009). We also deal with ERG models with actor attributes to test for homophily and differential expansiveness and popularity. In addition, examples of recently published papers are discussed to better understand the interpretation of ERG models (e.g. de Klepper et al., 2017). Robins, G., Snijders, T.A.B., Wang, P., Handcock, M., Pattison, P. 2007. Recent developments in exponential random graph (p*) models for social networks. Social Networks 29: 192-215. Hunter, D. 2007. Curved exponential family models for social networks. Social Networks 29: 216-230. Robins, G., Pattison, P., Wang, P. 2009. Closure, connectivity, degree distributions: Exponential random graph (p*) models for directed social networks. Social Networks 31: 105-117. de Klepper, M.C., Labianca, G.J., Sleebos, E., Agneessens, F. 2017. Sociometric status and peer control attempts: A multiple status hierarchies approach. Journal of Management Studies 54: 1-31.

3. Exponential Random Graph Models: multiple networks and two-mode networks

In this session we go on to present a series of multiple networks (such as advice and friendship – Skvoretz and Agneessens, 2007) using ERG models (Lazega and Pattison 1999). We then proceed to models for two-mode networks (also known as affiliation or bipartite networks) using ERG models (Skvoretz and Faust, 1999; Agneessens and Roose, 2008; Wang et al., 2009; 2013). Skvoretz, J., Agneessens, F. 2007. Reciprocity, multiplexity, and exchange: Measures. Quality and Quantity 41: 341-357. Lazega, E., Pattison, P. 1999. Multiplexity, generalized exchange and cooperation in organizations: a case study. Social Networks 21: 67-90. Skvoretz, J., Faust, K. 1999. Logit models for affiliation networks. Pp. 253 280 in Sociological Methodology 1999, volume 29 edited by M.E. Sobel and M.P. Becker. Cambridge, MA: Basil Blackwell. Agneessens, F., Roose, H. 2008. Local structural properties and attribute characteristics in 2-mode networks: p* models to map choices of theater events. Journal of Mathematical Sociology 32: 204-237. Wang, P., Sharpe, K., Robins, G., Pattison, P. 2009. Exponential random graph (p*) models for affiliation networks. Social Networks 31: 12-25. Wang, P., Pattison, P., Robins, G. 2013. Exponential random graph (p*) model specifications for bipartite networks. Social Networks 35: 211-222.

4. Longitudinal analysis for selection and influence using an actor-oriented approach (RSIENA)

The last two session offer an overview of longitudinal network models. On day four we focus in detail on actor-oriented approach (RSiena/SAOMs; Snijders et al., 2010; Steglich et al, 2010), and compare this to longitudinal approaches that use an ERGM approach (Krivitsky and Goudreau, 2016; Block et al., 2016). To understand the interpretation of ERG models we discuss examples of recently published papers focusing on selection to understand, for example, how advice seeking comes about (Agneessens and Wittek, 2012), as well as selection and influence models to test for example whether job satisfaction impacts trust or trust impacts job satisfaction (Agneessens and Wittek, 2010). Snijders, T.A.B., van de Bunt, G.G., Steglich, C.E.G. 2010. Introduction to actor-based models for network dynamics. Social Networks 32: 44-60. Steglich, C., Snijders, T.A.B., Pearson, M. 2010. Dynamic networks and behavior: Separating selection from influence. Sociological Methodology 40: 329-393. Block, P., Stadtfeld, C., Snijders, T.A.B. 2016. Forms of dependence: Comparing SAOMs and ERGMs from basic principles. Sociological Methods Research, in press Krivitsky, P.N., Goodreau, S.M. 2016. STERGM – Separable Temporal ERGMs for modeling discrete relational dynamics with statnet. The Statnet Development Team. Agneessens, F., Wittek, R. 2012. Where do intra-organizational advice relations come from? The role of informal status and social capital in social exchange. Social Networks 34: 333-345. Agneessens, F., Wittek, R. 2010. Social capital and employee well-being: disentangling intrapersonal and interpersonal selection and influence mechanisms. Revue Francaise de Sociology.

5. Comparing networks and longitudinal analysis with relational event models

In this last session we touch upon longitudinal models for events (e.g., email communication, rather than states such as friendship), called relational event models (Butts, 2008; Stadtfeld and Geyer-Schulz, 2011). We also discuss recent developments for analysing networks for different groups at the same time (such as different classes in schools or different teams within companies) and multilevel networks (Snijders and Baerveldt, 2003; Lubbers and Snijders, 2007; Weihua, 2015; Lazega and Snijders, 2016). Butts, C.T. 2008. A relational event framework for social action. Sociological Methodology 38: 155-200. Stadtfeld, C., Geyer-Schulz, A. 2011. Analyzing event stream dynamics in two mode networks: An exploratory analysis of private communication in a question and answer community. Social Networks 33: 258-272. Snijders, T.A.B., Baerveldt, C. 2003. A multilevel network study of the effects of delinquent behavior on friendship evolution. Journal of Mathematical Sociology 27: 123-151. Lubbers, M.J., Snijders, T.A.B. 2007. A comparison of various approaches to the exponential random graph model: A reanalysis of 102 student networks in school classes. Social Networks 29: 489-507. Weihua, An. 2015. Multilevel meta-network analysis with application to studying network dynamics of network interventions. Social Networks 43: 48-56. Lazega, E., Snijders, T.A.B. (eds.) 2016. Multilevel social network analysis. Springer.