1. Concerns about Causality
Prior Behavior of network members
influence
Outcome behavior
selection
Prior behavior

2. Answer: Control for Prior Behavior!
There  are heightened concerns about potential dependencies in estimating any social network model (e.g., Robins et al., 2007; Steglich, Snijders and Pearson, 2010 ). Regarding model 91) estimated influence is biased if the errors are not independent of the network exposure term (see Ord, 1975, equations ); the estimate of influence will be positively biased if there is some unexplained aspect of enforcement behavior that is related to the network exposure. The most compelling source of such dependencies would be if people choose to interact with others whose behaviors are similar to their own, known as selection in the network literature. Those who tended to engage in enforcement at time 1 might have chosen to interact with similar others between time 1 and time 2, and also would have been inclined to engage in enforcement behaviors at time 2. Because the network exposure term is likely confounded with prior enforcement behavior, model 1 includes a control for prior enforcement behavior.
A second concern in the influence model would arise if the model of a fisherman’s behaviors was a function of the contemporaneous behaviors of his/her network members. This would essentially put the outcome on both sides of the model in which case the errors would be directly related to the exposure term. It is for this reason that we model enforcement behavior as a function of the previous behaviors of others in one’s network. This avoids creating dependenices beteween the errors and predictors by putting the same variables on both sides of the model. Even given our approach there may still be concerns about omitted variables that create dependencies between the errors and the exposure term. Therefore we quantify the robustness of our inferences to potential omitted variables (Frank, 2000 ).
 Steglich, Christian E.G. Tom A.B. Snijders, and Michael Pearson (2010). Dynamic Networks and Behavior: Separating Selection from Influence. Sociological Methodology, 40,
Ord, Keith. "Estimation methods for models of spatial interaction."Journal of the American Statistical Association  (1975):
Robins, Garry L., Tom A.B. Snijders, Peng Wang, Mark Handcock, and Philippa Pattison. Recent developments in exponential random graph (p*) models for social networks. Social Networks 29 (2007),
Frank, K.A. and Xu, Ran Causal Inference for Social Network Analysis. James Moody and Ryan Light edits. Oxford Handbook of Social Network Analysis. Oxford, UK.

3. Verify with Simulation (student Ran Xu)
Frank, K.A. and Xu, Ran Causal Inference for Social Network Analysis. James Moody and Ryan Light editors. Oxford Handbook of Social Network Analysis. Oxford, UK.

5. Must Control for Prior

7. Must Control for Prior

8. Identification for Cross-sectional Data
From: Causal Inference for Social Network Analysis
Kenneth A. Frank* and Ran Xu*. Forthcoming in Handbook for Social Network Analysis. James Moody and Ryan Light. Oxford press.
*Equal co-authors.

9. Errors correlated with Predictors for Cross-sectional Data
Behavior of person 1 at time 1=f(behavior of person 2 at time 1)
+ error for person 1 at time 1
Behavior of person 2 at time 1=g(behavior of person 1 at time 1)
+ error for person 2 at time 1
Behavior of person 1 at time 1=f(behavior of person 2 at time 1)
+ error for person 1 at time 1
Predictor correlated with error term
Behavior of person 1 at time 1=f(g[behavior of person 1 at time 1
+error for person 2 at time 1]
+error for person 1 at time 1

10. Errors not correlated with predictors for longitudinal data
Behavior of person 1 at time 1=f(baseline behavior person 1) + error person 1 at time 1
Behavior of person 2 at time 1=f(baseline behavior person 2) + error person 2 at time 1
Behavior of person 1 at time 2=g(behavior of person 2 at time 1,
behavior of person 1 at time 1)
+ error for person 1 at time 2
Behavior of person 2 at time 2=g(behavior of person 1 at time 1,
behavior of person 2 at time 1)
+ error for person 2 at time 2
Behavior of person 1 at time 2=g(behavior of person 2 at time 1)
+behavior of person 1 at time 1
+ error for person 1 at time 2
Terms not inherently correlated
Behavior of person 1 at time 2=g[f(baseline behavior of person 2 at time 1)
+ error for person 2 at time 1])
+behavior of person 1 at time 1
+ error for person 1 at time 2
Terms not inherently correlated

11. Identification for Longitudinal Data
From: Causal Inference for Social Network Analysis
Kenneth A. Frank* and Ran Xu*. Forthcoming in Handbook for Social Network Analysis. James Moody and Ryan Light. Oxford press.
*Equal co-authors.

12. Must Control for the Prior

13. Christakis & Fowler: Contagion of Obesity

15. C&F: Methods
Lagged controls?

16. Christakis & Fowler Model
Should we use simultaneous or staggered behavior?
They use both:
yit = ρ1∑i’wii’tyi’t/∑i’wii’t + ρ2∑i’wii’tyi’t-1/∑i’wii’t + γ yit-1 +eit
Obesity2000=ρ1obesity of friends2000 +ρ2obesity of friends γ own obesity it-1 +et :
Lyons: ρ 1 and ρ2 have opposite signs. Hmmmm.
Collinearity problems?

17. Christakis and Fowler Debate: Lyons

18. “influence” model pages 5-6
Critique of
Christakis and Fowler
“influence” model pages 5-6
Lyons, Russell
The spread of evidence-poor medicine via flawed social-network analysis, Stat., Politics, Policy 2, 1 (2011), Article 2. DOI: /
See Andrew Gelman:

19. Christakis & Fowler Model
Should we use simultaneous or staggered behavior?
They use both:
yit = ρ1∑i’wii’tyi’t/∑i’wii’t + ρ2∑i’wii’tyi’t-1/∑i’wii’t + γ yit-1 +eit
Obesity2000=ρ1obesity of friends2000 +ρ2obesity of friends γ own obesity it-1 +et
Same data on right and left hand sides of model
Lyons: ρ1 and ρ2 have opposite signs: hmmm
Collinearity problems?

20. C&F: Methods
directionality

21. Christakis & Fowler: Directionality Results
Are they statistically
different from
one another?
No.

22. Articles on Causality

25. Articles on Causality

27. It’s all in how you talk about it!
Do best method you can
Include relevant controls!
But science is as much in the nature of the discourse as the method
Virtue epistemology
Greco, 2009; Kvanig, 2003; Sosa, 2007
What would it take to invalidate the inference?
How much bias must be present to invalidate an inference?
Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B   What would it take to Change an Inference?: Using Rubin’s Causal Model to Interpret the Robustness of Causal Inferences.   Education, Evaluation and Policy Analysis.  Vol 35: 
Greco, J. (2009). ‘The Value Problem’. In Haddock, A., Millar, A., & Pritchard, D. H. (Eds.), Epistemic Value. Oxford: Oxford University Press.
Kvanvig, J. L. (2003). The Value of Knowledge and the Pursuit of Understanding. Oxford: Oxford University Press.
Sosa, E. (2007). A Virtue Epistemology. Oxford: Oxford University Press.

28. Frank, K. A. , Maroulis, S. , Duong, M. , and Kelcey, B. 2013
Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B   What would it take to Change an Inference?: Using Rubin’s Causal Model to Interpret the Robustness of Causal Inferences.   Education, Evaluation and Policy Analysis.  Vol 35: 
Abstract We contribute to debate about causal inferences in educational research in two ways. First, we quantify how much bias there must be in an estimate to invalidate an inference. Second, we utilize Rubin’s causal model (RCM) to interpret the bias necessary to invalidate an inference in terms of sample replacement. We apply our analysis to an inference of a positive effect of Open Court Curriculum on reading achievement from a randomized experiment, and an inference of a negative effect of kindergarten retention on reading achievement from an observational study. We consider details of our framework, and then discuss how our approach informs judgment of inference relative to study design. We conclude with implications for scientific discourse. Keywords: causal inference; Rubin’s causal model; sensitivity analysis; observational studies