"Identifying causal effects attributable to network membership is a key challenge in empirical studies of social networks. In this article, we examine the consequences of endogeneity for inferences about the effects of networks on network members’ behavior. Using the House office lottery (in which newly elected members select their office spaces in a randomly chosen order) as an instrumental variable to estimate the causal impact of legislative networks on roll call behavior and cosponsorship decisions in the 105th–112th Houses, we find no evidence that office proximity affects patterns of legislative behavior. These results contrast with decades of congressional scholarship and recent empirical studies. Our analysis demonstrates the importance of accounting for selection processes and omitted variables in estimating the causal impact of networks."

"While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general approach for establishing identifiability utilizing algebraic arguments. A theorem of J. Kruskal for a simple latent-class model with finite state space lies at the core of our results, though we apply it to a diverse set of models. These include mixtures of both finite and nonparametric product distributions, hidden Markov models and random graph mixture models, and lead to a number of new results and improvements to old ones. In the parametric setting, this approach indicates that for such models, the classical definition of identifiability is typically too strong. Instead generic identifiability holds, which implies that the set of nonidentifiable parameters has measure zero, so that parameter inference is still meaningful. In particular, this sheds light on the properties of finite mixtures of Bernoulli products, which have been used for decades despite being known to have nonidentifiable parameters. In the nonparametric setting, we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed, but we explicitly describe the conditions."

"In this paper we address the general question of how social influence determines collective outcomes for large populations of individuals faced with binary decisions. First, we define conditions under which the behavior of individuals making binary decisions can be described in terms of what we call an influence-response function: a one-dimensional function of the (weighted) number of individuals choosing each of the alternatives. And second, we demonstrate that, under the assumptions of global and anonymous interactions, general knowledge of the influence-response functions is sufficient to compute equilibrium, and even non-equilibrium, properties of the collective dynamics. By enabling us to treat in a consistent manner classes of decisions that have previously been analyzed separately, our framework allows us to find similarities between apparently quite different kinds of decision situations, and conversely to identify important differences between decisions that would otherwise appear very similar."

"Disentangling the effects of selection and influence is one of social science's greatest unsolved puzzles: Do people befriend others who are similar to them, or do they become more similar to their friends over time? Recent advances in stochastic actor-based modeling, combined with self-reported data on a popular online social network site, allow us to address this question with a greater degree of precision than has heretofore been possible. Using data on the Facebook activity of a cohort of college students over 4 years, we find that students who share certain tastes in music and in movies, but not in books, are significantly likely to befriend one another. Meanwhile, we find little evidence for the diffusion of tastes among Facebook friends—except for tastes in classical/jazz music. These findings shed light on the mechanisms responsible for observed network homogeneity; provide a statistically rigorous assessment of the coevolution of cultural tastes and social relationships; and suggest important qualifications to our understanding of both homophily and contagion as generic social processes."

It will be interested to see how they argue this isn't confounded six ways from Sunday.

"How does the composition of a population affect the adoption of health behaviors and innovations? Homophily—similarity of social contacts—can increase dyadic-level influence, but it can also force less healthy individuals to interact primarily with one another, thereby excluding them from interactions with healthier, more influential, early adopters. As a result, an important network-level effect of homophily is that the people who are most in need of a health innovation may be among the least likely to adopt it. Despite the importance of this thesis, confounding factors in observational data have made it difficult to test empirically. We report results from a controlled experimental study on the spread of a health innovation through fixed social networks in which the level of homophily was independently varied. We found that homophily significantly increased overall adoption of a new health behavior, especially among those most in need of it."

We study how a behavior (an idea, buying a product, having a disease, adopting a cultural fad or a technology) spreads among agents in an a social network that exhibits segregation or homophily (the tendency of agents to associate with others similar to themselves). Individuals are distinguished by their types (e.g., race, gender, age, wealth, religion, profession, etc.) which, together with biased interaction patterns, induce heterogeneous rates of adoption. We identify the conditions under which a behavior diffuses and becomes persistent in the population. These conditions relate to the level of homophily in a society, the underlying proclivities of various types for adoption or infection, as well as how each type interacts with its own type. In particular, we show that homophily can facilitate diffusion from a small initial seed of adopters.

Assumes all homophilous traits are measured, I believe.

"While there has been much work examining the affects of social network structure on innovation adoption, models to date have lacked important features such as meta-populations reflecting real geography or influence from mass media forces. In this article, we show these are features crucial to producing more accurate predictions of a social contagion and technology adoption at the city level. Using data from the adoption of the popular micro-blogging platform, Twitter, we present a model of adoption on a network that places friendships in real geographic space and exposes individuals to mass media influence. We show that homopholy both amongst individuals with similar propensities to adopt a technology and geographic location are critical to reproduce features of real spatiotemporal adoption. Furthermore, we estimate that mass media was responsible for increasing Twitter's user base two to four fold. To reflect this strength, we extend traditional contagion models to include an endogenous mass media agent that responds to those adopting an innovation as well as influencing agents to adopt themselves."

Christakis & Fowler respond to critics. Unsurprisingly, I am unconvinced.

We probably should've cited this, yes.

"We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position model. The embedded vectors are clustered through minimization of a mean square error/criteria. We prove that this method is consistent for assigning nodes to blocks, as only a negligible number of nodes will be mis-assigned. We prove consistency of the method for directed and undirected graphs. The consistent block assignment makes possible consistent parameter estimation for a stochastic blockmodel. We extend the result for when the number of blocks grows slowly with the number of nodes. Our method is also computationally feasible even for very large graphs."

I am deeply suspicious, from the abstract.

Did I really use "probably" twice in one sentence that way?  Sigh.

At last!

" These findings underscore the fundamental difference between information spread and other contagion processes: despite multiple opportunities for infection within a social group, people are less likely to become spreaders of information with repeated exposure."

"An increasing number of scholars are using longitudinal social network data to try to obtain estimates of peer or social influence effects. These data may provide additional statistical leverage, but they can introduce new inferential problems. In particular, while the confounding effects of homophily in friendship formation are widely appreciated, homophily in friendship retention may also confound causal estimates of social influence in longitudinal network data. We provide evidence for this claim in a Monte Carlo analysis of the statistical model used by Christakis, Fowler, and their colleagues in numerous articles estimating "contagion" effects in social networks. Our results indicate that homophily in friendship retention induces significant upward bias and decreased coverage levels in the Christakis and Fowler model if there is non-negligible friendship attrition over time."

Of course, saying "we assume that correlated effects are absent" is, in this context at least, very much a "we assume we have a can opener" move.

Social influence on diagnosis, not actually producing autism. Heard the talk at the MERSI conference in 2009; it sounded pretty convincing.

That is NOT how you bring a mathematical model to empirical data.

" focus on Flickr and Last.fm, two social media systems in which we can relate the tagging activity of the users with an explicit representation of their social network. We show that a substantial level of local lexical and topical alignment is observable among users who lie close to each other in the social network. We introduce a null model that preserves user activity while removing local correlations, allowing us to disentangle the actual local alignment between users from statistical effects due to the assortative mixing of user activity and centrality in the social network. ... suggests that users with similar topical interests are more likely to be friends, and therefore semantic similarity measures among users based solely on their annotation metadata should be predictive of social links. We test this ... on the Last.fm data set ... social network constructed from semantic similarity captures actual friendship [better] than Last.fm's suggestions based on listening patterns"

Why had I not heard of this book?!?

Clever! But what if wife-at-time-of-death is more similar to the husband than the ex-wife was? (Or had more important common environments.)

"Henrich and Boyd (2002) were the first to propose a formal model of the role of attraction in cultural evolution. They came to the surprising conclusion that, when both attraction and selection are at work, final outcomes are determined by selection alone. This result is based on a determistic view of cultural attraction, different from the probabilistic view introduced in Sperber (1996). We defend this probabilistic view, show how to model it, and argue that, when both attraction and selection are at work, both affect final outcomes."

"We consider the algorithmic problem of selecting a set of target nodes that cause the biggest activation cascade in a network. In case when the activation process obeys the diminishing return property, a simple hill-climbing selection mechanism has been shown to achieve a provably good performance. Here we study models of influence propagation that exhibit critical behavior and where the property of diminishing returns does not hold. We demonstrate that in such systems the structural properties of networks can play a significant role. We focus on networks with two loosely coupled communities and show that the double-critical behavior of activation spreading in such systems has significant implications for the targeting strategies. In particular, we show that simple strategies that work well for homogenous networks can be overly suboptimal and suggest simple modification for improving the performance by taking into account the community structure."

"network of political discussions on one of the most popular Polish Internet forums.... The comments of the participants are ... mostly disagreements, with strong percentage of invective and [provocation]... Binary exchanges (quarrels) play significant role in the network growth and topology. Statistical analysis shows that the growth of the discussions depends on the degree of controversy of the subject and the intensity of personal conflict between the participants. This is in contrast to most previously studied social networks, for example networks of scientific citations, where the nature of the links is much more positive and based on similarity and collaboration rather than opposition and abuse. The work discusses also the implications of the findings for more general studies of consensus formation, where our observations of increased conflict contradict the usual assumptions that interactions between people lead to averaging of opinions and agreement."

This sounds (from the abstract) like some kind of network version of the Schelling model.

Hah!

(But at the same time, getting scooped does not feel good.)

Interesting, but so many approximations only to handle such a restricted special case!  And, of course, it assumes away homophily.

The null hypothesis, for non-contagious diseases, is IID onset times, i.e., no dependence between onset times for people near each other in the social network. So it doesn't have power against homophily on traits which affect (or even just predict!) the disease.