Introduction to Dynamic Social Network Analysis with SIENA

1. Introduction to Dynamic Social Network Analysis with SIENA Richard Callahan, University of Washington rjcal@u.washington.edu http://students.washington.edu/rjcal/ Thanks to everyone in my research group from the 2007 SFI Complex Systems Summer School for their hard work and feedback, as well as Dan Hruschka and Raissa D’Souza for their guidance. Also many thanks to Joel Levine at Dartmouth College, Yanjie BIAN at the Hong Kong University of Science and Technology, and Mark Handcock and Kate Stovel at the University of Washington for teaching me everything I knew about network analysis prior to SFI.

2. Why Model Networks Over Time? • 1. We want to predict how contact networks for diseases change over time (epidemiology– 疾病流动预测) • 2. Predicting when a tie will become stronger or weaker may assist forecasts for information flow (marketing – 营销研究) • 3. CEOs may wish to know what kinds of people are emergent leaders (management– 经管研究，辨认有出现领导的特性的人) • 4. You want to know what makes a friendship tie more or less likely to influence someone to commit a deviant act (criminology– 偏差行为预测)

3. How can Networks Evolve? • Homophily （物以类聚）: Similar actors develop ties (McPherson, Smith-Lovin, and Cook 2001) • Reciprocity （互惠）: Ties that are mutual disappear less often • Balance theory （平衡理论）: The actor’s choice of ties does not conflict with those of his or her alters (Wasserman and Faust 1994) • Preferential attachment(特惠挑选）: Those who are popular become more popular (Barabasi et al. 1999)

4. Research Process for Exponential Random Graph (p*) Models • 1. Assume network ties are random variables（假设社会连带是随机变量） • 2. Make an assumption about tie dependence • 3. Infer the parameters to be estimated from the dependence assumption （根据有关连带的互相影响力的假设推断要估计的参数是什么） • 4. Simplify the number of parameters with constraints （用拘束来把参数的数量简单化） • 5. Estimate and interpret the parameters (Robbins, Pattison, Kalish and Lusher 2007) • 6. Tweak （微调） the analysis to get your algorithm to converge etc.

5. Examples of Parameters • Actor covariates （有关行动人的特性的变项）: • Gender • Chinese / non-Chinese • Age • Dyadic covariates （有关两个行动人的关系的特性的变项）: • Roommates • Same group • Network configurations（有关网络状态的变项）: • Density （密度） • Reciprocity • Transitive triangles （及物的三角） • Balance (for dynamic networks) • Popularity (in-degree of two)

6. Under the Hood: Exponential Random Graph Models (p*)–指数随即图表模型） Parameter to be estimated Adjacency matrix for the graph （图形的邻近矩阵） Normalizing constant（标准化性的常量） Network configuration (1 if present, 0 if not) Constraints often work by setting a number of ηA values equal to each other (e.g. reciprocity) (Source: Robbins, Pattison, Kalish and Lusher 2007)

7. How the P* Model Helps Us • Ties are conditionally independent given a vector of parameters η. This assumption is strong but seems more reasonable given a realistic parameter set. It’s also about the only kind of assumption we can reasonably make and still simulate the development of a graph (Snijders 2006). （以参数的向量η为条件，图形的连带出现的概率都是互相独立的） • The graph is therefore ergodic – as you change the graph you can always get back to where you came from with some probability. • Therefore, we have a Markov Graph and can simulate both the development of the Expontial Random Graph at one moment in time and the evolution of a network over time as a continuous-time stochastic process （网络的衍生是一个连续时间的随机过程）, using Markov Chain Monte Carlo (MCMC) estimation techniques.

8. Degeneracy in Parameter Estimation Sometimes you get stuck in a part of the parameter space… Source: Raissa D’Souza’s talk from SFI 2007 summer school

9. Simulation Estimation for Empirical Network Analysis (SIENA) （针对实证性的网分析的方针估计软件） Free Download! Read the Literature http://stat.gamma.rug.nl/stocnet/ http://stat.gamma.rug.nl/siena.html

10. Parameter Estimation for One Time Period • Most straightforward is Gibbs Sampler – but convergence is slow! Faster methods: 1. Metropolis-Hastings algorithm: like the Gibbs Sampler but stochastic 2. Change more than one edge （连带） at a time (e.g. triplets) 3. Inversion （倒化？）– with low probability, switch to the converse of the graph or something equally radical 4. Switch to an adaptive landscape (Lee Altenberg, Jon Wilkins) – but you have to know something about your data 5. Modify network configuration parameters such that you’re less likely to get stuck in degenerate solutions (example: alternating k-triangles)

11. Your Model is Misspecified when… • Actors are oriented according to a latent space (行动人依据潜在的空地所定向) • You pick the wrong parameters to estimate

12. Fit the data!

13. Advice and “Knowing Well” at Time of First Survey

15. Now on to networks over time… • Actors are now presented with choices to change their ties at a rate that can also be estimated from parameters • Given they have a choice, they then optimize their utility given an objective function and an endowment function • Objective function (效应函数）: How happy you are to change your ties in the long run • Endowment function（短时满意函数）: How happy you are to change your ties in the short run (Note that we are not suggesting that people are performing computations this complex, but are using this model to estimate and compare the effect of the parameters. In that sense this is no different from linear regression.)

16. Odds of Changing a Tie

17. Dynamic Modeling in SIENA!