Homophily and Contagion Are Generically Confounded in Observational Social Network Studies

“Or rather are they close in the network because of these similarities, through the processes known assortative mixing on traits, or more simply as homophily (McPherson et al., 2001)?”

“…inter-connected clusters of nodes, with minimal connection between clusters — has been thoroughly explored in the recent literature (explicitly in Girvan and Newman (2002); Newman and Girvan (2003); Bickel and Chen (2009); Porter et al. (2009); Fortunato (2010), implicitly in much smaller…”

“…of nodes, with minimal connection between clusters — has been thoroughly explored in the recent literature (explicitly in Girvan and Newman (2002); Newman and Girvan (2003); Bickel and Chen (2009); Porter et al. (2009); Fortunato (2010), implicitly in much smaller clusters in Elwert and…”

“The “easy” solution is to use expert knowledge of the system to identify all causally relevant variables, measure a sufficient set of them, and adjust for them appropriately (Morgan and Winship, 2007; Pearl, 2000; Spirtes et al., 2001).”

“…with minimal connection between clusters — has been thoroughly explored in the recent literature (explicitly in Girvan and Newman (2002); Newman and Girvan (2003); Bickel and Chen (2009); Porter et al. (2009); Fortunato (2010), implicitly in much smaller clusters in Elwert and Christakis (2008)).”

“…of actual processes of transmission and influence, which have been extensively studied in social psychology and allied fields since the 1920s (Bartlett, 1932; Sperber, 1996; Huckfeldt et al., 2004; Friedkin, 1998).13 However, not only is it adequate to demonstrate the existence of the…”

“19”

“The example of biology suggests that a powerful way of doing such tests is to use “neutral models” (Harvey and Pagel, 1991; Gillespie, 1998), which biologists use to test claims that features of organisms are evolutionary adaptations; we note the similarity with the “null hypothesis” in general…”

“The topic of community discovery — essentially, dividing graphs into homogeneous, densely inter-connected clusters of nodes, with minimal connection between clusters — has been thoroughly explored in the recent literature (explicitly in Girvan and Newman (2002); Newman and Girvan (2003); Bickel and Chen (2009); Porter…”

“Probabilistically, the vector Y (t) is a Markov chain, specifically a variant of the “voter model” of statistical mechanics on a graph (Liggett, 1985; Sood and Redner, 2005); the minor addition of low-frequency noise (doing the opposite of the selected neighbor) keeps the homogeneous configurations…”

“…processes of transmission and influence, which have been extensively studied in social psychology and allied fields since the 1920s (Bartlett, 1932; Sperber, 1996; Huckfeldt et al., 2004; Friedkin, 1998).13 However, not only is it adequate to demonstrate the existence of the phenomenon we are…”

“…of the block structure may make the problem worse — consider the cases where the generating mechanism may be a mixed-membership block model (Airoldi et al., 2008) or “role” model (Reichardt and White, 2007) but communities are “discovered” assuming a simple modular network structure.”

“This idea has considerable plausibility and has been picked up by a number of other authors (Anagnostopoulos et al., 2008; Bramoullé et al., 2009), who have shown that it works as a test for direct influence in some models.”

“(2004) involves, all at once, strong parametric (exponential-family) assumptions, plus the assumption that observable covariates carry all of the dependence from X to Y and A; the latter is also implicitly assumed by the matching methods of Aral et al. (2009). Whether we face the unidentifiable situation of Figure 1,…”

“19”

“…with minimal connection between clusters — has been thoroughly explored in the recent literature (explicitly in Girvan and Newman (2002); Newman and Girvan (2003); Bickel and Chen (2009); Porter et al. (2009); Fortunato (2010), implicitly in much smaller clusters in Elwert and Christakis (2008)).”

“…the system, but this still places the burden on the investigator to pursue as many possible latent factors as may be present — an extremely onerous task in a multi-decade observational study — or to work exclusively with experimental data, such as in the recent work of Fowler and Christakis (2010).”

“This idea has considerable plausibility and has been picked up by a number of other authors (Anagnostopoulos et al., 2008; Bramoullé et al., 2009), who have shown that it works as a test for direct influence in some models.”

“Probabilistically, the vector Y (t) is a Markov chain, specifically a variant of the “voter model” of statistical mechanics on a graph (Liggett, 1985; Sood and Redner, 2005); the minor addition of low-frequency noise (doing the opposite of the selected neighbor) keeps the homogeneous configurations…”

“At the level of expectations, then, this process belongs to the family of linear social influence models used in, e.g., Friedkin (1998).”

“15It should be clarified here that the problem is not the ecological fallacy, or a red-state/bluestate issue, (Gelman et al., 2008) since the simulation is not aggregating any data. have also shown that the combination of homophily and contagion can imitate a causal effect of the homophilous trait.”

“(See Blume et al. 2010 for a recent review of the group-effects literature.) However, this does not quite answer our questions, since Manski (1993) considered influence from the group average, rather than from individual members of the network neighborhood, and one could hope this would provide enough extra informatio…”

“…common to all the classical sociologists (even, in his own way, to Max Weber), and going back through them to Montesquieu if not beyond (Aron, 1989), is that social structure explains culture, or that the latter reflects the former; in many versions, culture is an adaptation to social…”

“13”

“This is easiest to see when all other causes of adoption of a trait aside from the network itself are eliminated, such as person-to-person infectious diseases (Bartlett, 1960; Ellner and Guckenheimer, 2006; Newman, 2002), though other examples include the spread of innovations (Rogers, 2003).”

“This random copying model is, of course, a drastic oversimplification of actual processes of transmission and influence, which have been extensively studied in social psychology and allied fields since the 1920s (Bartlett, 1932; Sperber, 1996; Huckfeldt et al., 2004; Friedkin, 1998).(13) However, not only is it adequa…”

“…We are not aware of any studies in the sociology of culture or related fields employing formal neutral models; however, something similar to this is implicit in the arguments of Lieberson (2000),20 and some other strands of recent work on “endogenous explanations of culture” (Kaufman, 2004).”

“…in 4010 of these 5000 trials is Effect of Phantom ‘Influencer' on ‘Influenced' in Time Series Effect of Phantom ‘Influenced' on ‘Influencer' in Time Series the estimate less than zero despite the lack of a direct connection, in line with the empirical results of Cohen-Cole and Fletcher (2008).”

“…We are not aware of any studies in the sociology of culture or related fields employing formal neutral models; however, something similar to this is implicit in the arguments of Lieberson (2000),20 and some other strands of recent work on “endogenous explanations of culture” (Kaufman, 2004).”

“Treated at face value, this can produce an incoherent probability distribution for the evolution of the system (Lyons, 2010), as well as implying a scarcely-comprehensible notion of simultaneous causation (rather than coupled behavior or feedback); this can be somewhat salvaged by considering it as…”

“(The following remarks apply, with suitable changes, to many other high-quality studies, e.g., Bakshy et al. (2009); Anagnostopoulos et al. (2008); Yang et al. (2007); Bramoullé et al. (2009).)”

“…of the block structure may make the problem worse — consider the cases where the generating mechanism may be a mixed-membership block model (Airoldi et al., 2008) or “role” model (Reichardt and White, 2007) but communities are “discovered” assuming a simple modular network structure.”

“As Ernest Gellner (1973) put it, “Social structure is who you can marry, culture is what you wear at the wedding.””

“…long been concerned with this issue, under the label of “selection versus influence” or “homophily versus contagion” (Leenders, 3There are however claims in the medical literature (Atkinson, 2007) that certain viruses induce obesity in rodents and may contribute to the condition in human beings.”

“…with minimal connection between clusters — has been thoroughly explored in the recent literature (explicitly in Girvan and Newman (2002); Newman and Girvan (2003); Bickel and Chen (2009); Porter et al. (2009); Fortunato (2010), implicitly in much smaller clusters in Elwert and Christakis (2008)).”

“This parallels the other great project of social science, which is to explain differences in cultural choices by location within the social structure, or, at a broader scale, by differences between social structures (Boudon, 1986/1989; Berger, 1995; Lieberson, 2000).”

“Indeed, this has been shown to cause difficulties in other social situation where this sort of phantom influence can be observed: among others, Calvó-Armengol and Jackson (2009) note that estimating the apparent effect of parental influence on their child’s educational outcomes is confounded by…”

“(The following remarks apply, with suitable changes, to many other high-quality studies, e.g., Bakshy et al. (2009); Anagnostopoulos et al. (2008); Yang et al. (2007); Bramoullé et al. (2009).)”

“12Preliminary versions of these results appeared in Shalizi (2007), and as long ago as 2005 at http://bactra.org/notebooks/neutral-cultural-networks.html.”

“Obesity, smoking habits and even happiness (Christakis and Fowler, 2007, 2008; Fowler and Christakis, 2008) have been claimed to spread as epidemics in social networks (see however Shalizi and Thomas (2011) for a criticism of these results).”

“Statistical techniques such as permutation tests and matched sampling [5] help control for confounds, but ultimately cannot resolve this fundamental problem [39].”

“One paper in particular identifies two further, important assumptions that may be necessary or implicit in the directional test [77].”