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In online social networks, it is common to use predictions of node categories to estimate measures of homophily and other relational properties. However, online social network data often lacks basic demographic information about the nodes. Researchers must rely on predicted node attributes to estimate measures of homophily, but little is known about the validity of these measures. We show that estimating homophily in a network can be viewed as a dyadic prediction problem, and that homophily estimates are unbiased when dyad-level residuals sum to zero in the network. Node-level prediction models, such as the use of names to classify ethnicity or gender, do not generally have this property and can introduce large biases into homophily estimates. Bias occurs due to error autocorrelation along dyads. Importantly, node-level classification performance is not a reliable indicator of estimation accuracy for homophily. We compare estimation strategies that make predictions at the node and dyad levels, evaluating performance in different settings. We propose a novel "ego-alter" modeling approach that outperforms standard node and dyad classification strategies. While this paper focuses on homophily, results generalize to other relational measures which aggregate predictions along the dyads in a network. We conclude with suggestions for research designs to study homophily in online networks. Code for this paper is available at https://github.com/georgeberry/autocorr., Comment: 19 pages, 4 figures, 2 tables

We consider the question of embedding nodes with similar local neighborhoods together in embedding space, commonly referred to as "role embeddings." We propose RAE, an unsupervised framework that learns role embeddings. It combines a within-node loss function and a graph neural network (GNN) architecture to place nodes with similar local neighborhoods close in embedding space. We also propose a faster way of generating negative examples called neighbor shuffling, which quickly creates negative examples directly within batches. These techniques can be easily combined with existing GNN methods to create unsupervised role embeddings at scale. We then explore role action embeddings, which summarize the non-structural features in a node's neighborhood, leading to better performance on node classification tasks. We find that the model architecture proposed here provides strong performance on both graph and node classification tasks, in some cases competitive with semi-supervised methods., Comment: 7 pages, 4 figures, 5 tables

We consider the problem of obtaining unbiased estimates of group properties in social networks when using a classifier for node labels. Inference for this problem is complicated by two factors: the network is not known and must be crawled, and even high-performance classifiers provide biased estimates of group proportions. We propose and evaluate AdjustedWalk for addressing this problem. This is a three step procedure which entails: 1) walking the graph starting from an arbitrary node; 2) learning a classifier on the nodes in the walk; and 3) applying a post-hoc adjustment to classification labels. The walk step provides the information necessary to make inferences over the nodes and edges, while the adjustment step corrects for classifier bias in estimating group proportions. This process provides de-biased estimates at the cost of additional variance. We evaluate AdjustedWalk on four tasks: the proportion of nodes belonging to a minority group, the proportion of the minority group among high degree nodes, the proportion of within-group edges, and Coleman's homophily index. Simulated and empirical graphs show that this procedure performs well compared to optimal baselines in a variety of circumstances, while indicating that variance increases can be large for low-recall classifiers., Comment: 19 pages, 6 figures, 1 table

Studies of online social influence have demonstrated that friends have important effects on many types of behavior in a wide variety of settings. However, we know much less about how influence works among relative strangers in digital public squares, despite important conversations happening in such spaces. We present the results of a study on large public Facebook pages where we randomly used two different methods--most recent and social feedback--to order comments on posts. We find that the social feedback condition results in higher quality viewed comments and response comments. After measuring the average quality of comments written by users before the study, we find that social feedback has a positive effect on response quality for both low and high quality commenters. We draw on a theoretical framework of social norms to explain this empirical result. In order to examine the influence mechanism further, we measure the similarity between comments viewed and written during the study, finding that similarity increases for the highest quality contributors under the social feedback condition. This suggests that, in addition to norms, some individuals may respond with increased relevance to high-quality comments., Comment: 10 pages, 6 figures, 2 tables

Fads, product adoption, mobs, rumors, memes, and emergent norms are diverse social contagions that have been modeled as network cascades. Empirical study of these cascades is vulnerable to what we describe as the "opacity problem": the inability to observe the critical level of peer influence required to trigger an individual's behavioral change. Even with maximal information, network cascades reveal intervals that bound critical levels of peer exposure, rather than critical values themselves. Existing practice uses interval maxima, which systematically over-estimates the social influence required for behavioral change. Simulations reveal that the over-estimation is likely common and large in magnitude. This is confirmed by an empirical study of hashtag cascades among 3.2 million Twitter users: one in five hashtag adoptions suffers critical value uncertainty due to the opacity problem. Different assumptions about these intervals lead to qualitatively different conclusions about the role of peer reinforcement in diffusion. We introduce a solution that combines identifying tightly bounded intervals with predicting uncertain critical values using node-level information., Comment: 31 pages, 7 figures, 2 tables