Non-response in social networks: The impact of different non-response treatments on the stability of blockmodels

Discerning the essential structure of social networks is a major task. Yet, social network data usually contain different types of errors, including missing data that can wreak havoc during data analyses. Blockmodeling is one technique for delineating network structure. While we know little about its vulnerability to missing data problems, it is reasonable to expect that it is vulnerable given its positional nature. We focus on actor non-response and treatments for this. We examine their impacts on blockmodeling results using simulated and real networks. A set of ‘known’ networks are used, errors due to actor non-response are introduced and are then treated in different ways. Blockmodels are fitted to these treated networks and compared to those for the known networks. The outcome indicators are the correspondence of both position memberships and identified blockmodel structures. Both the amount and type of non-response, and considered treatments, have an impact on delineated blockmodel structures.     

Effects of missing data in social networks

We perform sensitivity analyses to assess the impact of missing data on the structural properties of social networks. The social network is conceived of as being generated by a bipartite graph, in which actors are linked together via multiple interaction contexts or affiliations. We discuss three principal missing data mechanisms: network boundary specification (non-inclusion of actors or affiliations), survey non-response, and censoring by vertex degree (fixed choice design), examining their impact on the scientific collaboration network from the Los Alamos E-print Archive as well as random bipartite graphs. The simulation results show that network boundary specification and fixed choice designs can dramatically alter estimates of network-level statistics. The observed clustering and assortativity coefficients are overestimated via omission of affiliations or fixed choice thereof, and underestimated via actor non-response, which results in inflated measurement error. We also find that social networks with multiple interaction contexts may have certain interesting properties due to the presence of overlapping cliques. In particular, assortativity by degree does not necessarily improve network robustness to random omission of nodes as predicted by current theory.     

Direct blockmodeling of valued and binary networks: a dichotomization-free approach

A long-standing open problem with direct blockmodeling is that it is explicitly intended for binary, not valued, networks. The underlying dilemma is how empirical valued blocks can be compared with ideal binary blocks, an intrinsic problem in the direct approach where partitions are solely determined through such comparisons. Addressing this dilemma, valued networks have either been dichotomized into binary versions, or novel types of ideal valued blocks have been introduced. Both these workarounds are problematic in terms of interpretability, unwanted data reduction, and the often arbitrary setting of model parameters.This paper proposes a direct blockmodeling approach that effectively bypasses the dilemma with blockmodeling of valued networks. By introducing an adaptive weighted correlation-based criteria function, the proposed approach is directly applicable to both binary and valued networks, without any form of dichotomization or transformation of the valued (or binary) data at any point in the analysis, while still using the conventional set of ideal binary blocks from structural, regular and generalized blockmodeling.The proposed approach seemingly solves two other open problems with direct blockmodeling. First, its standardized goodness-of-fit measure allows for direct comparisons across solutions, within and between networks of different sizes, value types, and notions of equivalence. Secondly, through an inherent bias of point-biserial correlations, the approach puts a premium on solutions that are closer to the mid-point density of blockmodels. This, it is argued, translates into solutions that are more intuitive and easier to interpret.The approach is demonstrated by structural, regular and generalized blockmodeling applications of six classical binary and valued networks. Finding feasible and intuitive optimal solutions in both the binary and valued examples, the approach is proposed not only as a practical, dichotomization-free heuristic for blockmodeling of valued networks but also, through its additional benefits, as an alternative to the conventional direct approach to blockmodeling.     

Notes on blockmodeling

We attempt to develop further the blockmodeling of networks, so as better to capture the network structure. For this purpose a richer structure than ordinary (valued) graphs has to be used for a model. Such structures are valued graphs with typified (complete, dominant, regular, etc.) connections. Based on the proposed formalization, the blockmodeling is cast as an optimization problem.     

A deviational approach to blockmodeling of valued networks

This article proposes a novel approach to blockmodeling of valued (one-mode) networks where the identification of (binary) block patterns in the valued relations differ from existing approaches. Rather than looking at the absolute values of relations, or examining valued ties on a per-actor basis (cf. Nordlund, 2007), the approach identifies prominent (binary) ties on the basis of deviations from expected values. By comparing the distribution of each actor's valued relations to its alters with the macro-level distributions of total in- and outdegrees, prominent (1) and non-prominent (0) ties are determined both on a per-actor-to-actor and a per-actor-from-actor basis. This allows for a direct interpretation of the underlying functional anatomy of a non-dichotomized valued network using the standard set of ideal blocks as found in generalized blockmodeling of binary networks.In addition to its applicability for direct blockmodeling, the article also suggests a novel indirect measure of deviational structural equivalence on the basis of such deviations from expected values.Exemplified with the note-sharing data in Žiberna (2007a), citations among social work journals (Baker, 1992), and total commodity trade among EU/EFTA countries as of 2010, both the direct and indirect approach produce results that are more sensitive to variations at the dyadic level than existing approaches. This is particularly evident in the case of the EU/EFTA trade network, where the indirect approach yields partitions and blockmodels in support of theories of regional trade, despite the significantly skewed valued degree distribution of the dataset.     

The magnitude and potential impact of missing data in a sexual violence campus climate survey

Abstract

Objective: Assess the impact of survey non-response and non-completion for a campus climate survey. Participants: Intended for all degree-seeking students at a large, public, midwestern university, November 2014. Methods: The survey covered sexual assault experiences and related attitudes. We identify the magnitude and potential impact of survey non-response by comparing demographic data between respondents and non-respondents, sexual assault prevalence between early and late respondents, and demographic and attitudinal data between survey completers and partial completers. Results: Demographic groups were differentially represented in the survey. Sexual assault prevalence based on survey results may be underestimated for men, overestimated for women. Sensitive questions did not increase drop-off. Students completing more of the survey differed from those completing less. Conclusions: Colleges must plan survey administration and data sensitivity analysis to reduce potential for bias. Resources for sexual assault-related needs based on estimates from campus climate surveys with high non-response will likely be misallocated.     

Missing data in networks: exponential random graph (p1) models for networks with non-respondents

Survey studies of complete social networks often involve non-respondents, whereby certain people within the “boundary” of a network do not complete a sociometric questionnaire—either by their own choice or by the design of the study—yet are still nominated by other respondents as network partners. We develop exponential random graph (p¹) models for network data with non-respondents. We model respondents and non-respondents as two different types of nodes, distinguishing ties between respondents from ties that link respondents to non-respondents. Moreover, if we assume that the non-respondents are missing at random, we invoke homogeneity across certain network configurations to infer effects as applicable to the entire set of network actors. Using an example from a well-known network dataset, we show that treating a sizeable proportion of nodes as non-respondents may still result in estimates, and inferences about structural effects, consistent with those for the entire network.If, on the other hand, the principal research focus is on the respondent-only structure, with non-respondents clearly not missing at random, we incorporate the information about ties to non-respondents as exogenous. We illustrate this model with an example of a network within and between organizational departments. Because in this second class of models the number of non-respondents may be large, values of parameter estimates may not be directly comparable to those for models that exclude non-respondents. In the context of discussing recent technical developments in exponential random graph models, we present a heuristic method based on pseudo-likelihood estimation to infer whether certain structural effects may contribute substantially to the predictive capacity of a model, thereby enabling comparisons of important effects between models with differently sized node sets.     

Generalized blockmodeling of valued networks

The paper presents several approaches to generalized blockmodeling of valued networks, where values of the ties are assumed to be measured on at least interval scale. The first approach is a straightforward generalization of the generalized blockmodeling of binary networks [Doreian, P., Batagelj, V., Ferligoj, A., 2005. Generalized Blockmodeling. Cambridge University Press, New York.] to valued blockmodeling. The second approach is homogeneity blockmodeling. The basic idea of homogeneity blockmodeling is that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values. New ideal blocks appropriate for blockmodeling of valued networks are presented together with definitions of their block inconsistencies.     

Network autocorrelation models with egocentric data

Network autocorrelation models have been widely used for decades to model the joint distribution of the attributes of a network's actors. This class of models can estimate both the effect of individual characteristics as well as the network effect, or social influence, on some actor attribute of interest. Collecting data on the entire network, however, is very often infeasible or impossible if the network boundary is unknown or difficult to define. Obtaining egocentric network data overcomes these obstacles, but as of yet there has been no clear way to model this type of data and still appropriately capture the network effect on the actor attributes in a way that is compatible with a joint distribution on the full network data. This paper adapts the class of network autocorrelation models to handle egocentric data. The proposed methods thus incorporate the complex dependence structure of the data induced by the network rather than simply using ad hoc measures of the egos’ networks to model the mean structure, and can estimate the network effect on the actor attribute of interest. The vast quantities of unknown information about the network can be succinctly represented in such a way that only depends on the number of alters in the egocentric network data and not on the total number of actors in the network. Estimation is done within a Bayesian framework. A simulation study is performed to evaluate the estimation performance, and an egocentric data set is analyzed where the aim is to determine if there is a network effect on environmental mastery, an important aspect of psychological well-being.     

Analyzing event stream dynamics in two-mode networks: An exploratory analysis of private communication in a question and answer community

Information about social networks can often be collected as event stream data. However, most methods in social network analysis are defined for static network snapshots or for panel data. We propose an actor oriented Markov process framework to analyze the structural dynamics in event streams. Estimated parameters are similar to what is known from exponential random graph models or stochastic actor oriented models as implemented in SIENA. We apply the methodology on a question and answer web community and show how the relevance of different kinds of one- and two-mode network structures can be tested using a new software.     

k-means-based algorithm for blockmodeling linked networks

The paper presents a k-means-based algorithm for blockmodeling linked networks where linked networks are defined as a collection of one-mode and two-mode networks in which units from different one-mode networks are connected through two-mode networks. The reason for this is that a faster algorithm is needed for blockmodeling linked networks that can better scale to larger networks. Examples of linked networks include multilevel networks, dynamic networks, dynamic multilevel networks, and meta-networks. Generalized blockmodeling has been developed for linked/multilevel networks, yet the generalized blockmodeling approach is too slow for analyzing larger networks. Therefore, the flexibility of generalized blockmodeling is sacrificed for the speed of k-means-based approaches, thus allowing the analysis of larger networks. The presented algorithm is based on the two-mode k-means (or KL-means) algorithm for two-mode networks or matrices. As a side product, an algorithm for one-mode blockmodeling of one-mode networks is presented. The algorithm’s use on a dynamic multilevel network with more than 400 units is presented. A situation study is also conducted which shows that k-means based algorithms are superior to relocation algorithm-based methods for larger networks (e.g. larger than 800 units) and never much worse.     

The stability of exchange networks

Economic and sociological exchange theories predict divisions of exchange benefits given an assumed fixed network of exchange relations. Since network structure has been found to have a large impact on actors’ payoffs, actors have strong incentives for network change. We answer the question what happens to both the network structure and actor payoffs when myopic actors change their links in order to maximize their payoffs. We investigate the networks that are stable, the networks that are efficient or egalitarian with varying tie costs, and the occurrence of social dilemmas. Only few networks are stable over a wide range of tie costs, and all of them can be divided into two types: efficient networks consisting of only dyads and at most one isolate, and Pareto efficient and egalitarian cycles with an odd number of actors. Social dilemmas are observed in even-sized networks at low tie costs.     

Presentation matters: how mode effects in item non-response depend on the presentation of response options

Comparability of data across modes is an important issue in survey research. In this paper we discuss item non-response to attitudinal questions in telephone and web surveys. We present results from a survey experiment conducted in Italy and in Spain that compares different presentations of response options in an online setting with a benchmark telephone survey. In line with earlier studies we find that (A), the share of non substantial answers in the online survey depends on how the response option is presented. Comparing different presentations in an online survey to the standard approach of telephone surveys using propensity score matching, we find that (B), the share and pattern of non substantial answers, is most similar across the two modes in the online survey when the it is captured in an instruction on each screen for the online survey. Our findings are of particular relevance for the design of multiple mode or mix-mode surveys of attitudinal questions using online and telephone modes.     

Networks containing negative ties

Social network analysts have often collected data on negative relations such as dislike, avoidance, and conflict. Most often, the ties are analyzed in such a way that the fact that they are negative is of no consequence. For example, they have often been used in blockmodeling analyses where many different kinds of ties are used together and all ties are treated the same, regardless of meaning. However, sometimes we may wish to apply other network analysis concepts, such as centrality or cohesive subgroups. The question arises whether all extant techniques are applicable to negative tie data. In this paper, we consider in a systematic way which standard techniques are applicable to negative ties and what changes in interpretation have to be made because of the nature of the ties. We also introduce some new techniques specifically designed for negative ties. Finally we show how one of these techniques for centrality can be extended to networks with both positive and negative ties to give a new centrality measure (PN centrality) that is applicable to directed valued data with both positive and negative ties.     

Structural effects of network sampling coverage I: Nodes missing at random

Network measures assume a census of a well-bounded population. This level of coverage is rarely achieved in practice, however, and we have only limited information on the robustness of network measures to incomplete coverage. This paper examines the effect of node-level missingness on 4 classes of network measures: centrality, centralization, topology and homophily across a diverse sample of 12 empirical networks. We use a Monte Carlo simulation process to generate data with known levels of missingness and compare the resulting network scores to their known starting values. As with past studies (0035 and 0135), we find that measurement bias generally increases with more missing data. The exact rate and nature of this increase, however, varies systematically across network measures. For example, betweenness and Bonacich centralization are quite sensitive to missing data while closeness and in-degree are robust. Similarly, while the tau statistic and distance are difficult to capture with missing data, transitivity shows little bias even with very high levels of missingness. The results are also clearly dependent on the features of the network. Larger, more centralized networks are generally more robust to missing data, but this is especially true for centrality and centralization measures. More cohesive networks are robust to missing data when measuring topological features but not when measuring centralization. Overall, the results suggest that missing data may have quite large or quite small effects on network measurement, depending on the type of network and the question being posed.     

Approaches to blockmodeling dynamic networks: A Monte Carlo simulation study

Blockmodeling refers to a variety of statistical methods for reducing and simplifying large and complex networks. While methods for blockmodeling networks observed at one time point are well established, it is only recently that researchers have proposed several methods for analysing dynamic networks (i.e., networks observed at multiple time points). The considered approaches are based on k-means or stochastic blockmodeling, with different ways being used to model time dependency among time points. Their novelty means they have yet to be extensively compared and evaluated and the paper therefore aims to compare and evaluate them using Monte Carlo simulations. Different network characteristics are considered, including whether tie formation is random or governed by local network mechanisms. The results show the Dynamic Stochastic Blockmodel (Matias and Miele 2017) performs best if the blockmodel does not change; otherwise, the Stochastic Blockmodel for Multipartite Networks (Bar-Hen et al. 2020) does.     

Fragments and Links: Organizational Actor‐World of the Harry Potter Phenomenon

The article seeks to develop an Actor‐Network Theory perspective on the relationship between organization and literature by focusing on the Harry Potter phenomenon. The latter is seen as an example of how contemporary popular literature does not stop at itself, but rather supersedes itself by spinning its own truly impressive organizational actor‐network. This industrious industrial entanglement challenges what may be called the ‘disembodied’ conceptualization of literature—the conceptualization that is centred on the contents of works of fiction alone. When the contents of the literary texts are decentred in that they are taken as but one (however important) actor of the actor‐world that comes to be known by their name, other actors become more visible that help to conceptualize Harry Potter as an organizational, as much as a literary, phenomenon.     

Assessing the missing data problem in criminal network analysis using forensic DNA data

Missing data is pertinent to criminal networks due to the hidden nature of crime. Generally, researchers evaluate the impact of incomplete network data by extracting or adding nodes and/or edges from a known network. Statistics on this reduced or completed network are then compared with statistics from the known network. In this study, we integrate police data on known offenders with DNA data on unknown offenders. Statistics from the integrated dataset (‘known network’) are compared with statistics from the police data (‘reduced network’). Networks with both known and unknown offenders are bigger but also have a different structure to networks with only known offenders.     

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.