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)?”

“13”

“…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…”

“…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.”

“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…”

“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,…”

“…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)).”

“19”

“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.”

“…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).”

“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…”

“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.”

“…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.”

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

“…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].”

“For instance, network studies of peer influence and social contagion suffer from a stubborn challenge of disambiguating such effects from homophily among peers and within communities (Christakis and Fowler, 2007; Lyons, 2011; Shalizi and Thomas, 2011).”

“The assumption of independent and identically distributed samples is ubiquitous in most causal inference methods, but this assumption cannot hold in many research areas, such as social media analytics [46] [123], herd immunity, and signal processing [140] [133].”

“Studies from social science have shown that data often exhibits correlation among the attributes of connected individuals [20, 29], and such insights are helpful in distilling actionable knowledge from such networks.”

“Separating social contagion and homophily is difficult [41, 42], and we interpret complex contagion broadly to include homophily; we focus on how both social reinforcement and homophily effects collectively boost the trapping of memes within dense communities, not on the distinctions between them.”

“Although it can be difficult to distinguish which mechanism has operated to cause homophily in purely observational studies (Shalizi and Thomas, 2011), experimental approaches have been used to demonstrate online peer influence affecting individual attitudes and behaviours, including musical preferences (Salganik et a…”

“…out others whose practices they wish to emulate, in which case the intent to adopt a practice produces rather than is caused by networks (Mouw 2002, Shalizi & Thomas 2011).3 Researchers have addressed 3Few studies have used longitudinal network data to compare the effects of influence and…”

“As a result, it is quite possible that some effects attributed to social capital are, in reality, due to selection (Mouw, 2003, 2006; Shalizi & Thomas, 2011).”

“Although in the latter case it is possible that apparent influence can be accounted for simply by homophily [Aral et al. 2009; Shalizi and Thomas 2011], our inferred diffusion trees nevertheless provide an effective upper bound on the actual diffusion taking place via the respective underlying networks.”

“We can, for example, divide participants into sub-populations and expose them to distinct stimuli, addressing the topic of causality as well as confounding factors both of which have proven problematic [64,121] for the current state-of-the-art [122,123].”

“It has been widely studied and received that there exhibits a strong correlation among the aŠributes of linked nodes [27, 29].”

“In part, this reflects fundamental methodological problems in distinguishing between homophily and social influence using standard data (Shalizi & Thomas 2011), and in part, genuine ambiguity in research results.”

“Moreover, homophily in unobserved attributes (latent homophily) that may be indicated by the very existence of a relationship of peers with a common friend (see Shalizi and Thomas 2011) will be equally represented in recipient and non-recipient peer groups.”

“It is also difficult to comprehend its nuanced refuta-tions by Lyons (2011) and by Shalizi and Thomas (2011).”

“However, in randomized clinical trials of social network interventions, the impact of interventions may be underestimated.(44,47) Social diffusion can also be viewed as contamination or interference if diffusion occurs from an experimental network into a control group network.”

“However, observational techniques struggle to overcome the confounding effects of unobservable factors 20 , while experimental studies, which provide more robust causal inference, are complex, difficult to implement and therefore more rare.”

“Aral et al. (2009) reviewed numerous statistical techniques that have been proposed to tease these processes apart using observational data and concluded that none are sufficient, a conclusion also reached by Shalizi & Thomas (2011).”

“Even discerning whether or not genuine social influence is occurring in a network is extremely challenging [211], and we find it helpful (for, e.”

“However, both methods cannot fully guarantee that we are able to capture contagion [65].”

“It has recently been suggested that certain, particular types of latent homophily, in which an unobservable trait influences both which friends one chooses and current and future behavior, may be impossible to distinguish from contagion in observational studies and hence may bias estimates of contagion and homophily […”

“…usual sorts of constraints affecting observational studies (e.g. the observed association not necessarily reflecting causal effects), plus other limitations that are distinctive to network data settings (Aral et al., 2009; Christakis and Fowler, 2007, 2013; Manski, 1993; Shalizi and Thomas, 2011).”

“This methodology does not pretend to yield causal conclusions by virtue of the statistical analysis; Shalizi and Thomas (2011) argued cogently that this is impossible in panel studies.”

“It is important to note that the study design we used precluded conclusions about what proportions of negative opinions expressed in the period were the consequence of exposure (contagion of opinions), the consequence of users creating connections to other users who already hold similar opinions (homophily), or if oth…”

“Limitations and Future Directions Shalizi and Thomas (2011) argued that network analyses of social influence are susceptible to bias due to selection of friends who are similar on unmeasured variables.”

“Allocating more spectrum and energy resources to users with strong ties can increase the peer discovery ratio, help avoid congestion, improve spectral efficiency, and eventually increase the overall throughput and coverage of the D2D underlaying cellular network.”

“For example, homophily occurs when unobserved tastes and preferences drive the formation of social ties; thus, the linked user dyads tend to be more similar in their uploaded photos than the average users (Aral et al. 2009, McPherson 2001, Shalizi and Thomas 2011).”

“For example, Shalizi and Thomas [35] show that social influence effects and assertive-mixing (self-selection) effects are typically confounded and that the estimation strategies Christakis and Fowler have adopted 4 might not suffice to separate between these effects.”

“2009), but the issue of latent homophily is more challenging (Shalizi and Thomas 2011).”

“[ 22, 53]”

“Quantifying these social network effects is empirically challenging because it is difficult to distinguish social learning from common unobservable shocks faced by network members (Manski 1993, Bemmaor 1994, Aral et al. 2009, Shalizi and Thomas 2011).”

“These methods have come under considerable criticism from the statistical community (Cohen-Cole and Fletcher 2008; Lyons 2011; Shalizi and Thomas 2011), in part because these statistical models are not equipped to deal with dependence across individuals (Ogburn and VanderWeele 2014).”

“Yet our understanding of social influence is still incomplete (Sørensen and Fassiotto, 2011; Shalizi and Thomas, 2011).”

“1990), represent an important force affecting individuals’ adoption behaviors in a social network (Ibarra and Andrews 1993, Leenders 2002, Bruyn and Lilien 2008, Shalizi and Thomas 2011).”

“How different types of consumers are distributed over the network can have a dramatic impact on the diffusion process and the likely effects of seeding (Aral et al., 2009; McPherson et al., 2001; Noel & Nyhan, 2011; Shalizi & Thomas, 2011).”

“The authors’ additional assertion of contagion, however, has been criticized primarily on the basis of the difficulties to be found in distinguishing these phenomena from homophily [26–28].”

“Each of these methods is designed to solve problems of causality and identification that are caused by uncontrolled factors such as endogeneity, unobserved heterogeneity, and exogenous influence (Aral et al., 2009; Shalizi and Thomas, 2011).”

“581–590, and discussion (2013) 32(4):597–599.”

“…has considered the root cause of this correlation and distinguished between social influence , which is the tendency for linked individuals to adopt the characteristics of their neighbors, and homophily , where links are created based on the attribute similarities of the individuals [10, 15, 22].”

“Notable critiques of the social network ‘‘contagion’’ hypothesis have appeared in academic [23,24,25,26] and popular [27] literatures.”

“Related literature focuses on incentives, aiming at separating influence from selection effects, a task for which negative results exist in general (27, 28), using randomized experiments (29–32) and strategies tailored to specific applications (17, 33).”

“Compared with using observational data, running experiments such as peer encouragement designs can effectively avoid the presence of confounding due to homophily and common external causes (e.g., Manski 1993; Shalizi and Thomas 2011).”

“As Shalizi and Thomas (2011: 213) observed, “even when the true causal effect of the homophilous trait is zero, the trait can still act as a strong predictor of the outcome of interest.””

“Although it is difficult to separate contagion and homophily (see e.g., Shalizi & Thomas, 2011; also see Cohen-Cole & Fletcher, 2008; Fowler & Christakis, 2008b), it is well established by now that people with similar attributes tend to have a network tie.”

“social homophily and temporal influence are fundamentally confounded in observational studies [37].”

“As Shalizi and Thomas argue, contagion and selection processes are mutually influential, since our decisions about who we associate with are influenced by the ways in which these people shape our behaviour and vice versa [73].”

“Thus, affiliation would seem to be complementary to imitation, consistent with recent developments in social network research [64,65].”

“Unless panel data on social relationships and individual traits are available it is impossible to disentangle the above effects (Kossinets and Watts, 2009; Shalizi and Thomas, 2010), with the exception of”

“Indeed it is essentially impossible to identify the independent effects of structure in field work (Shalizi and Thomas, 2011), requiring experimental methods to untangle its consequences.”

“The lack of detailed information about the users prohibits us from assessing manifest homophily, and our analysis is thus subject to the problem of latent homophily which is generally confounded with contagion (8).”

“This lagged model is specifically recommended by Shalizi and Thomas (2010) and Vanderweele (2011) as an alternative to previous models that focused on contemporaneous effects because it helps to better control for homophily (the tendency of people to form social ties with others who have similar…”

“Finally, teasing apart the effect of peer influence from friend selection is difficult, and since we cannot account for the selection of friends on a variety of latent variables, we do not argue that our results imply causation (Shalizi and Thomas, 2011).”

“A third important consideration is homophily , the phenomenon that people are typically surrounded by similar others [192] because of self-selection, mutual influence and/or common circumstances [193].”

“Given the difficulty in distinguishing between potential explanations of observed behavior at the individual level (6), it is useful to examine population-level models and attempt to reproduce empirically observed popularity distributions using the simplest possible assumptions about individual behavior.”

“There may be some forms of latent homophily [26] for which we did not control—for example, a user’s technical proficiency—that might explain some of the variance in our data.”

“Although these choices are personal, they are not independent but potentially driven by several processes such as social influence [1], homophily [2], and information arriving from external sources like news or mass media [3].”

“Shalizi and Thomas (2011) show that in the presence of latent homophily, even if there is no unmeasured environmental confounding, the associations comparing ego-perceived friends and alter-perceived friends may differ in magnitude even when there is no social influence.”

“For example, homophily may constrain the spread of beliefs and behaviours such as smoking, obesity and even divorce [63–65], and the resulting beliefs can influence processes such as network updating that in turn influence homophily [66].”