Concerns about Causality in the Network Influence Model

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Outcome behavior

Prior behavior

Behavior of network members

selection

influence

Answer: Control for Prior Behavior!

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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 1.2-1.4); 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 dependencies between 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, 329-392.Ord, Keith. "Estimation methods for models of spatial interaction."Journal of the American Statistical Association 70.349 (1975): 120-126.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), 192-215.

Verify with Simulation (student Ran Xu)

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Must Control for Prior

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Must Control for Prior

Concerns about Causality: Omitted Variables

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Response 2Shalizi and Thomas (2011) show that network influence is unidentifiable if there is a latent trait X(i) that causes both a tie in the network A(i,j) and the prior behavior or belief Y(I,t-1) (see their Figure 1 below, actually it is Figure 2 in the published article).

Shalizi, Cosma Rohilla, and Andrew C. Thomas. "Homophily and contagion are generically confounded in observational social network studies." Sociological Methods & Research 40, no. 2 (2011): 211-239.

Concerns about Causality: in Terms of Shalizi & Thomas

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Outcome behavior

Prior behavior

Behavior of network members

selection

influence

Unobserved Latent Trait X

Aij

Yt-1

Yt

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When Regression Doesn’t Work

Instrumental variables? Alternative assumptions, may be not better

Exclusion restriction Strong instrument Large n

Propensity scores? No better than the covariates that go into it

Heckman, 2005; Morgan & Harding, 2006, page 40; Rosenbaum, 2002, page 297; Shadish et al., 2002, page 164);

How could they be better than covariates? Propensity=f(covariates).

Shalizi & Thomas: Examine effects of non-neighbors Looks for bounds (or sensitivity) Examine clustering

PAUL ROSENBAUM

Possible Instrument for Network Influence: Third parties

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Outcome behavior

Prior behavior

Behavior of network members

selection

influence

Instrument:Friends of network members who are not friends of i

Aij

Yt-1

Yt

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Paul Holland says:

PAUL ROSENBAUM

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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. 2013.  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: 437-460.

spreadsheet for calculating indices [KonFound-it!©] powerpoint with examples and calculations (includes reference to STATA,

SAS and SPSS) https://www.msu.edu/~kenfrank/research.htm#causal

Effects of Social Capital on Implementation of Computers in the Classroom

14Coefficient was reduced by only 7% when controlling for prior.

Importance of Controlling for the Prior: Longitudinal Data

15Coefficient was reduced by only 7% when controlling for prior.

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They then argue that influence is identifiable if all of the information about the latent variable X on the prior behavior Y(I, t-1) is contained within the observed variable Z(i) (panel a), or all of the information about X on the network tie A(I,j) is conveyed by z. This is the familiar condition that X is not confounded with the exposure term either because it is unrelated to Y or unrelated to the network tie (Frank, 2000). Shalizi and Thomas (2011) then note that “whether we face the unidentifiable situation of Figure 2 or the identifiable case of Figure 3 currently depends upon subject matter knowledge rather than statistical techniques” (page 218). Correspondingly, we argue that the issue of identification cannot be fully resolved. Instead it can and should be debated in terms of the latent variable X. But the debate should not be in terms of whether such a variable X exists. Of course it does, except in rare circumstances where the selection of network members or the expression of attributes at t-1 is completely determined by observed characteristics. Instead we acknowledge that X exists, but ask how large must it be to invalidate the inference of network influence. In our particular case, X must be correlated with the outcome Y(t) and with the network exposure term (based on the sum of the Yj t-1) at ____ to invalidate our inference.

Modeling influence and selection simultaneously

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Shalizi and Thomas (2011) prove that network influence is unidentifiable if there is a latent trait X(i) that causes both a tie in the network A(i,j) and the prior behavior or belief Y(i,t-1) (see their Figure 2). They then argue that influence is identifiable if all of the information about the latent variable X on the prior behavior Y(I, t-1) is contained within the observed variable Z(i), or all of the information about X on the network tie A(I,j) is conveyed by z. This is the familiar condition that the latent variable X is not confounded with the network exposure term either because it is unrelated to Y or unrelated to the network tie, conditioning on other variables in the model. Shalizi and Thomas (2011) then note that “whether we face the unidentifiable situation [of Figure 2] or the identifiable case [of Figure 3] currently depends upon subject matter knowledge rather than statistical techniques” (page 218). They then go on to state on page 218 that “It is noteworthy that the most successful attempts at explicit modeling that handle both homophily and influence, as found in the work of Leenders (1995); Steglich et al. (2004) involves, all at once, strong parametric (exponential-family) assumptions, plus the assumption that observable covariates carry all of the dependence from X [latent variable] to Y [observable attribute of individual] and A [network relation].Thus the identification of the model depends on whether the observed covariates carry all of the dependencies. This is no different than the typical assumption of regression; the assumption applies whether or not one simultaneously models influence and selection.Shalizi and Thomas make a symmetric argument for the identification of the selection model. It depends on the quality of the covariates and not on simultaneously modeling influence.

Shalizi and Thomas 2011

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Christakis & Fowler: Contagion of Obesity

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C&F:Methods

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Lagged controls?

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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 friends1997 + γ own obesity it-1 +et :

Lyons: ρ 1 and ρ2 have opposite signs. Hmmmm. Collinearity problems?

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Christakis and Fowler Debate: Lyons

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Lyons, RussellThe spread of evidence-poor medicine via flawed social-network analysis, Stat., Politics, Policy 2, 1 (2011), Article 2. DOI: 10.2202/2151-7509.1024See Andrew Gelman: http://themonkeycage.org/blog/2011/06/10/1-lyonss-statistical-critiques-seem-reasonable-to-me-there-could-well-be-something-important-that-im-missing-but-until-i-hear-otherwise-for-example-in-a-convincing-reply-by-christakis-and-f/

Critique ofChristakis and Fowler“influence” model pages 5-6

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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 friends1997 + 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?

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homereflection

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 friends1997 + 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?

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homereflection

C&F:Methods

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directionality

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Christakis & Fowler: Directionality Results

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Are they statistically different from one another?No.

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Articles on Causality

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Articles on Causality

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