Bayesian analysis for partially observed network data,missing ties,attributes and actors

We consider partially observed network data as defined in Handcock and Gile (2010). More specifically we introduce an elaboration of the Bayesian data augmentation scheme of Koskinen et al. (2010) that uses the exchange algorithm (Caimo and Friel, 2011) for inference for the exponential random graph model (ERGM) where tie variables are partly observed. We illustrate the generating of posteriors and unobserved tie-variables with empirical network data where 74% of the tie variables are unobserved under the assumption that some standard assumptions hold true. One of these assumptions is that covariates are fixed and completely observed. A likely scenario is that also covariates might only be partially observed and we propose a further extension of the data augmentation algorithm for missing attributes. We provide an illustrative example of parameter inference with nearly 30% of dyads affected by missing attributes (e.g. homophily effects). The assumption that all actors are known is another assumption that is liable to be violated so that there are “covert actors”. We briefly discuss various aspects of this problem with reference to the Sageman (2004) data set on suspected terrorists. We conclude by identifying some areas in need of further research.     

Covariate-defined latent space random effects model

Latent factor models are a useful and intuitive class of models; one limitation is their inability to predict links in a dynamic network. We propose a latent space random effects model with a covariate-defined social space, where the social space is a linear combination of the covariates as estimated by an MCMC algorithm. The model allows for the prediction of links in a network; it also provides an interpretable framework to explain why people connect. We fit the model using the Adolescent Health Network dataset and three simulated networks to illustrate its effectiveness in recognizing patterns in the data.     

Models,methods and network topology: Experimental design for the study of interference

How should a network experiment be designed to achieve high statistical power? Experimental treatments on networks may spread. Randomizing assignment of treatment to nodes enhances learning about the counterfactual causal effects of a social network experiment and also requires new methodology (ex. Aronow and Samii, 2017a, Bowers et al., 2013, Toulis and Kao, 2013). In this paper we show that the way in which a treatment propagates across a social network affects the statistical power of an experimental design. As such, prior information regarding treatment propagation should be incorporated into the experimental design. Our findings justify reconsideration of standard practice in circumstances where units are presumed to be independent even in simple experiments: information about treatment effects is not maximized when we assign half the units to treatment and half to control. We also present an example in which statistical power depends on the extent to which the network degree of nodes is correlated with treatment assignment probability. We recommend that researchers think carefully about the underlying treatment propagation model motivating their study in designing an experiment on a network.     

Social network analysis with respondent-driven sampling data: A study of racial integration on campus

This paper presents respondent-driven sampling (RDS) as a viable method of sampling and analyzing social networks with survey data. RDS is a network based sampling and analysis method that provides a middle ground compliment to ego-centric and saturated methods of social network analysis. The method provides survey data, similar to ego-centric approaches, on individuals who are connected by behaviorally documented ties, allowing for macro-level analysis of network structure, similar to that supported by saturated approaches. Using racial interaction of university undergraduates as an empirical example, the paper examines whether and to what extent racial diversity at the institutional level is reflected as racial integration at the interpersonal level by testing hypotheses regarding the quantity and quality of cross-race friendships. The primary goal of this article, however, is to introduce RDS to the network community and to stimulate further research toward the goal of expanding the analytical capacity of RDS. Advantages, limitations, and areas for future research to network analysis using RDS are discussed.     

Estimating network structure via random sampling: Cognitive social structures and the adaptive threshold method

This paper introduces and tests a novel methodology for measuring networks. Rather than collecting data to observe a network or several networks in full, which is typically costly or impossible, we randomly sample a portion of individuals in the network and estimate the network based on the sampled individuals’ perceptions on all possible ties. We find the methodology produces accurate estimates of social structure and network level indices in five different datasets. In order to illustrate the performance of our approach we compare its results with the traditional roster and ego network methods of data collection. Across all five datasets, our methodology outperforms these standard social network data collection methods. We offer ideas on applications of our methodology, and find it especially promising in cross-network settings.     

Network sampling coverage II: The effect of non-random missing data on network measurement

Missing data is an important, but often ignored, aspect of a network study. Measurement validity is affected by missing data, but the level of bias can be difficult to gauge. Here, we describe the effect of missing data on network measurement across widely different circumstances. In Part I of this study (Smith and Moody, 2013), we explored the effect of measurement bias due to randomly missing nodes. Here, we drop the assumption that data are missing at random: what happens to estimates of key network statistics when central nodes are more/less likely to be missing? We answer this question using a wide range of empirical networks and network measures. We find that bias is worse when more central nodes are missing. With respect to network measures, Bonacich centrality is highly sensitive to the loss of central nodes, while closeness centrality is not; distance and bicomponent size are more affected than triad summary measures and behavioral homophily is more robust than degree-homophily. With respect to types of networks, larger, directed networks tend to be more robust, but the relation is weak. We end the paper with a practical application, showing how researchers can use our results (translated into a publically available java application) to gauge the bias in their own data.     

Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models

Social network data often involve transitivity, homophily on observed attributes, community structure, and heterogeneity of actor degrees. We propose a latent cluster random effects model to represent all of these features, and we develop Bayesian inference for it. The model is applicable to both binary and non-binary network data. We illustrate the model using two real datasets: liking between monks and coreaderships between Slovenian publications. We also apply it to two simulated network datasets with very different network structure but the same highly skewed degree sequence generated from a preferential attachment process. One has transitivity and community structure while the other does not. Models based solely on degree distributions, such as scale-free, preferential attachment and power-law models, cannot distinguish between these very different situations, but the latent cluster random effects model does.     

Conditionally exponential random models for individual properties and network structures: Method and application

Exponential random models have been widely adopted as a general probabilistic framework for complex networks and recently extended to embrace broader statistical settings such as dynamic networks, valued networks or two-mode networks. Our aim is to provide a further step into the generalization of this class of models by considering sample spaces which involve both families of networks and nodal properties verifying combinatorial constraints. We propose a class of probabilistic models for the joint distribution of nodal properties (demographic and behavioral characteristics) and network structures (friendship and professional partnership). It results in a general and flexible modeling framework to account for homophily in social structures. We present a Bayesian estimation method based on the full characterization of their sample spaces by systems of linear constraints. This provides an exact simulation scheme to sample from the likelihood, based on linear programming techniques. After a detailed analysis of the proposed statistical methodology, we illustrate our approach with an empirical analysis of co-authorship of journal articles in the field of neuroscience between 2009 and 2013.     

The analysis of multiple ties in longitudinal egocentric network data: A case study on bidirectional relationships between trust and drug use

We extend multi-level models to examine single egocentric network ties to the joint analysis of paired dynamic ties. Two analytic challenges are addressed. First, inference needs to account for multiple layers of nesting: ties are nested within pairs, pairs are nested within time points, and time points are nested within egos. Second, the focus is on the relationship between two dynamic ties; specification of outcome and predictor may be difficult. Instead, we treat both ties as outcomes. Our approach is used to analyze trust and reported drug use between egos and alters over time in a Bayesian framework.     

Collecting experimental network data from interventions on critical links in workplace networks

This article describes and discusses challenges associated with interventionist network data gathering in organizational settings, with a special focus on dyadic interventions. While pointing out major risks of these approaches, we argue that collecting data in combination with dyadic network alteration methods can enable social network researchers to explore network mechanisms from a new angle and potentially benefit the members of the targeted social networks and the entire collectives, if certain research design and implementation principles are followed. We introduce a facilitated self-disclosure method for strengthening critical dyads in social networks in combination with longitudinal and retrospective network measurement. We assess the participants’ perceptions of the different stages of this process by qualitative interviews. The study illustrates that experimental network data collection includes some extra challenges in addition to the many challenges of observational network data collection but participants also reported practical benefits that would not be gained through observational network surveys alone. The results highlight the importance of early and continuous communication during the data collection process with all research participants, not just the management, and the benefits of sharing more of the preliminary results. The lessons learnt through this study can inform the design of experimental network data collection to prioritize the preferences of the participants and their benefits.     

Adolescent network positions and memory performance in adulthood: Evidence from sibling fixed effects models with sociometric network data

Although research has explored social factors influencing memory performance during adolescence, the impact of adolescent social network positions remains largely unknown. This study examines whether adolescent network position is associated with memory performance in adulthood, while also considering potential gender differences. The study used a sibling sample from the National Longitudinal Study of Adolescent to Adult Health (N = 2462) and employed sibling fixed effects models to account for unobserved family background factors, such as genetics, parental characteristics, family environment, and childhood neighborhood. Four dimensions of adolescent network position—i.e., popularity, sociality, degree centrality, and closeness centrality—were sociometrically assessed in schools. Memory performance in adulthood was measured using the Rey Auditory Verbal Learning Test. The sibling fixed effects estimates indicate that sociality, degree centrality, and closeness centrality are significantly associated with increased memory performance in adulthood, even after controlling for unobserved family heterogeneity as well as a set of individual-level covariates. In contrast, controlling for unobserved family heterogeneity attenuated the association for popularity, making it statistically insignificant. This study also provides evidence of gender differences in the association between social network position and memory performance. The associations for popularity, sociality, and degree centrality are more pronounced among men than women. This study’s findings highlight the importance of adolescent network positions as social determinants in shaping cognitive outcomes over the life course. Interventions that encourage positive peer interactions and reduce social isolation during adolescence may help improve cognitive health in the population.