Linked Ego Networks: Improving estimate reliability and validity with respondent-driven sampling

Respondent-driven sampling (RDS) is currently widely used for the study of HIV/AIDS-related high risk populations. However, recent studies have shown that traditional RDS methods are likely to generate large variances and may be severely biased since the assumptions behind RDS are seldom fully met in real life. To improve estimation in RDS studies, we propose a new method to generate estimates with ego network data, which is collected by asking respondents about the composition of their personal networks, such as “what proportion of your friends are married?”. By simulations on an extracted real-world social network of gay men as well as on artificial networks with varying structural properties, we show that the precision of estimates for population characteristics is greatly improved. The proposed estimator shows superior advantages over traditional RDS estimators, and most importantly, the method exhibits strong robustness to the recruitment preference of respondents and degree reporting error, which commonly happen in RDS practice and may generate large estimate biases and errors for traditional RDS estimators. The positive results henceforth encourage researchers to collect ego network data for variables of interests by RDS, for both hard-to-access populations and general populations when random sampling is not applicable.     

Estimating network properties from snowball sampled data

This article addresses the estimation of topological network parameters from data obtained with a snowball sampling design. An approximate expression for the probability of a vertex to be included in the sample is derived. Based on this sampling distribution, estimators for the mean degree, the degree correlation, and the clustering coefficient are proposed. The performance of these estimators and their sensitivity with respect to the response rate are validated through Monte Carlo simulations on several test networks. Our approach has no complex computational requirements and is straightforward to apply to real-world survey data. In a snowball sample design, each respondent is typically enquired only once. Different from the widely used estimator for Respondent-Driven Sampling (RDS), which assumes sampling with replacement, the proposed approach relies on sampling without replacement and is thus also applicable for large sample fractions. From the simulation experiments, we conclude that the estimation quality decreases with increasing variance of the network degree distribution. Yet, if the degree distribution is not to broad, our approach results in good estimates for the mean degree and the clustering coefficient, which, moreover, are almost independent from the response rate. The estimates for the degree correlation are of moderated quality.     

AN EMPIRICAL TEST OF RESPONDENT-DRIVEN SAMPLING: POINT ESTIMATES, VARIANCE, DEGREE MEASURES, AND OUT-OF-EQUILIBRIUM DATA

This paper, which is the first large-scale application of respondent-driven sampling (RDS) to nonhidden populations, tests three factors related to RDS estimation against institutional data using two WebRDS samples of university undergraduates. First, two methods of calculating RDS point estimates are compared. RDS estimates calculated using both methods coincide closely, but variance estimation, especially for small groups, is problematic for both methods. In one method, the bootstrap algorithm used to generate confidence intervals is found to underestimate variance. In the other method, where analytical variance estimation is possible, confidence intervals tend to overestimate variance. Second, RDS estimates are found to be robust against varying measures of individual degree. Results suggest the standard degree measure currently employed in most RDS studies is among the best-performing degree measures. Finally, RDS is found to be robust against the inclusion of out-of-equilibrium data. The results show that valid point estimates can be generated with RDS analysis using real data, but that further research is needed to improve variance estimation techniques.     

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.     

A social network approach to estimating seroprevalence in the United States

Results from a representative survey of respondents in Florida are given, concerning their knowledge about members of their personal network, and specifically how many people respondents know in selected subpopulations. We employ a method known as a “network scale-up method”. By using a collection of subpopulations of known size, and also asking about one subpopulation (those who are seropositive) of unknown size, we make various estimates of personal network size and the size of the seropositive subpopulation. Our best (maximum likelihood, unbiased) estimates are 108 members of the network defined by “having been in contact with during the previous two years”, and (approximately unbiased) 1.6 million for the seropositive subpopulation. Because of the proportional over-representation of AIDS (and presumably, therefore, seropositive) in Florida, by a factor of about two, this latter estimate could be an overestimate.     

Cross-national variation in political network size,distribution, and prediction

Network size has a fundamental influence on other network properties. As studies of social network size have accumulated beyond the U.S. and Western Europe, diversity in the networks examined and methods used to construct size estimates have hindered the ability to make direct cross-national comparisons. We employ data from a summary political discussion network size measure in 17 surveys conducted in 15 countries between 2012 and 2018. We offer improved cross-national data on political network size distributions and estimate aggregate and country-specific models to understand the factors, both social and political, that predict political network size within countries.     

Small networks and selectivity bias in the analysis of survey network data

Selectivity bias is a danger whenever observations are systematically excluded from a data set on the basis of a dependent variable, whether this exclusion is explicit or implicit. If present, the problem has severe consequences for the validity of statistical estimates of effects. The problem is of importance to the analysis of survey network data, since many network measures (such as density) are available only for persons having networks of size two or larger, while others (such as percent kin) are defined only for those having networks of size one or more. Analysts can adjust for selectivity bias by estimating the risk of exclusion (in this case, of having a network of size 0 or 1), and including the modeled risk as a control in substantive equations. Such estimates are presented for the 1985 General Social Survey network data; in the course of this results of Fischer and Phillips on social isolation are replicated. Other ways of guarding against selection bias are also discussed; at a minimum, network size should be included among the set of regressors in analyses of survey network data, as a methodological control if not as a substantive variable.     

Assessing organizational capacity for diffusion: A school-based social network analysis case study

The purposeful design of social networks is increasingly recognized as a fundamental organizational improvement strategy. In the PK-12 education sector, school-based teacher collaboration is the primary vehicle through which educators are able to gain access to essential social capital, and through which leaders promulgate diffusion of innovation and continuous organizational learning. In partnership with school administrators, the authors undertook an evaluation to examine the size, structure, and composition of school-based networks. Social network analysis (SNA) was used to measure and visualize connections (or lack thereof) of ties between teams and between educators. Isolate and disconnected network actors were revealed through visual inspection of the sociograms. Administrators used findings to reconfigure team membership to enhance teacher ability to give and receive support and collaboratively problem-solve, and to ensure greater capacity for diffusion of instructional innovation and organizational learning. This paper contributes to the field’s understanding of how evaluators and organizational leaders can use SNA to measure, visualize, and more purposefully design effective patterns of connection between people through which professional knowledge, support, and innovation will travel.     

Bridging: Locating critical connectors in a network

This paper proposes several measures for bridging in networks derived from Granovetter's (1973) insight that links which reduce distances in a network are important structural bridges. Bridging is calculated by systematically deleting links and calculating the resultant changes in network cohesion (measured as the inverse average path length). The average change for each node's links provides an individual level measure of bridging. We also present a normalized version which controls for network size and a network-level bridging index. Bridging properties are demonstrated on hypothetical networks, empirical networks, and a set of 100 randomly generated networks to show how the bridging measure correlates with existing network measures such as degree, personal network density, constraint, closeness centrality, betweenness centrality, and vitality. Bridging and the accompanying methodology provide a family of new network measures useful for studying network structure, network dynamics, and network effects on substantive behavioral phenomenon.     

Measurement error in network data: A re-classification

Research on measurement error in network data has typically focused on missing data. We embed missing data, which we term false negative nodes and edges, in a broader classification of error scenarios. This includes false positive nodes and edges and falsely aggregated and disaggregated nodes. We simulate these six measurement errors using an online social network and a publication citation network, reporting their effects on four node-level measures – degree centrality, clustering coefficient, network constraint, and eigenvector centrality. Our results suggest that in networks with more positively-skewed degree distributions and higher average clustering, these measures tend to be less resistant to most forms of measurement error. In addition, we argue that the sensitivity of a given measure to an error scenario depends on the idiosyncracies of the measure's calculation, thus revising the general claim from past research that the more ‘global’ a measure, the less resistant it is to measurement error. Finally, we anchor our discussion to commonly-used networks in past research that suffer from these different forms of measurement error and make recommendations for correction strategies.     

Variations in network boundary and type: A study of adolescent peer influences

This study compares variation in network boundary and network type on network indicators such as degree and estimates of social influences on adolescent substance use. We compare associations between individual use and peer use of tobacco and alcohol when network boundary (e.g., classroom, entire grade in school, and community) and relational type (elicited by asking whom students: (a) are friends with, (b) admire, (c) think will succeed, (d) would like to have a romantic relationship with, and (e) think are popular) are varied. Additionally, we estimate Exponential Random Graph Models (ERGMs) for 232 networks to obtain a homophily estimate for smoking and drinking. Data were collected from a cross-sectional sample of 1707 adolescents in five high schools in one school district in Los Angeles, CA. Results of logistic regression models show that associations were strongest when the boundary condition was least constrained and that associations were stronger for friendship networks than for other ones. Additionally, ERGM estimations show that grade-level friendship networks returned significant homophily effects more frequently than the classroom networks. This study validates existing theoretical approaches to the network study of social influence as well as ways to estimate them. We recommend researchers use as broad a boundary as possible when collecting network data, but observe that for some research purposes more narrow boundaries may be preferred.     

Bias decomposition and estimator performance in respondent-driven sampling

Respondent-Driven Sampling (RDS) is a method of network sampling that is used to sample hard-to-reach populations. The resultant sample is non-random, but different weighting methods can account for the over-sampling of (1) high-degree individuals and (2) homophilous groups that recruit members more effectively. While accounting for degree-bias is almost universally agreed upon, accounting for recruitment-bias has been debated as it can further increase estimate variance without substantially reducing bias. Simulation-based research has examined which weighting procedures perform best given underlying population network structures, group recruitment differences, and sampling processes. Yet, in the field, analysts do not have a priori knowledge of the network they are sampling. We show that the RDS sample data itself can determine whether a degree-based estimator is sufficient. Formulas derived from the decomposition of a ‘dual-component’ estimator can approximate the ‘recruitment component’ (RC) and ‘degree component’ (DC) of a sample’s bias. Simulations show that RC and DC values can predict the performance of different classes of estimators. Samples with extreme ‘RC’ values, a consequence of network homophily and differential recruitment, are better served by a classical estimator. The use of sample data to improve estimator selection is a promising innovation for RDS, as the population network features that should guide estimator selection are typically unknown.     

Respondent-Driven Sampling: An Assessment of Current Methodology

Respondent-Driven Sampling (RDS) employs a variant of a link-tracing network sampling strategy to collect data from hard-to-reach populations. By tracing the links in the underlying social network, the process exploits the social structure to expand the sample and reduce its dependence on the initial (convenience) sample.The current estimators of population averages make strong assumptions in order to treat the data as a probability sample. We evaluate three critical sensitivities of the estimators: to bias induced by the initial sample, to uncontrollable features of respondent behavior, and to the without-replacement structure of sampling.Our analysis indicates: (1) that the convenience sample of seeds can induce bias, and the number of sample waves typically used in RDS is likely insufficient for the type of nodal mixing required to obtain the reputed asymptotic unbiasedness; (2) that preferential referral behavior by respondents leads to bias; (3) that when a substantial fraction of the target population is sampled the current estimators can have substantial bias.This paper sounds a cautionary note for the users of RDS. While current RDS methodology is powerful and clever, the favorable statistical properties claimed for the current estimates are shown to be heavily dependent on often unrealistic assumptions. We recommend ways to improve the methodology.     

Exploring variation in active network size: Constraints and ego characteristics

Studies of active personal networks have primarily focused on providing reliable estimates of the size of the network. In this study, we examine how compositional properties of the network and ego characteristics are related to variation in network size. There was a negative relationship between mean emotional closeness and network size, for both related and unrelated networks. Further, there was a distinct upper bound on total network size. These results suggest that there are constraints both on the absolute number of individuals that ego can maintain in the network, and also on the emotional intensity of the relationships that ego can maintain with those individuals.     

A sexual affiliation network of swingers,heterosexuals practicing risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach

Using the example of the sexual affiliation networks of swingers, this paper examines how the analysis of sexual affiliation networks can contribute to the development of sexually transmitted infection (STI) prevention strategies. Two-mode network methodology and ERGMs are applied to describe the structural composition of the affiliation network and analyse attribute effects. Swingers were found to recruit their sex partners through one large, moderately cohesive network component. Swingers who used drugs or had a longer history of swinging tended to frequent websites instead of clubs. This study confirms the relevance of studying sexual affiliation networks and its additional value for STI epidemiology.     

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.     

Random sampling of alters from networks: A promising direction in egocentric network research

The social network perspective has great potential for advancing knowledge of social mechanisms in many fields. However, collecting egocentric (i.e., personal) network data is costly and places a heavy burden on respondents. This is especially true of the task used to elicit information on ties between network members (i.e., alter-alter ties or density matrix), which grows exponentially in length as network size increases. While most existing national surveys circumvent this problem by capping the number of network members that can be named, this strategy has major limitations. Here, we apply random sampling of network members to reduce cost, respondent burden, and error in network studies. We examine the effectiveness and reliability of random sampling in simulated and real-world egocentric network data. We find that in estimating sample/population means of network measures, randomly selecting a small number of network members produces only minor errors, regardless of true network size. For studies that use network measures in regressions, randomly selecting the mean number of network members (e.g., randomly selecting 10 alters when mean network size is 10) is enough to recover estimates of network measures that correlate close to 1 with those of the full sample. We conclude with recommendations for best practices that will make this versatile but resource intensive methodology accessible to a wider group of researchers without sacrificing data quality.     

Unpacking Burt’s constraint measure

Burt (1992) proposed two principal measures of structural holes, effective size and constraint. However, the formulas describing the measures are somewhat opaque and have led to a certain amount of confusion. Borgatti (1997) showed that, for binary data, the effective size formula could be written very simply as degree (ego network size) minus average degree of alters within the ego network. The present paper presents an analogous reformulation of the constraint measure. We also derive minima and maxima for constraint, showing that, for small ego networks, constraint can be larger than one, and for larger ego networks, constraint cannot get as large as one. We also show that for networks with more than seven alters, the maximum constraint does not occur in a maximally dense or closed network, but rather in a relatively sparse “shadow ego network”, which is a network that contains an alter (the shadow ego) that is connected to every other alter, and where no other alter-alter ties exist.     

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.