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.     

The Statistical Evaluation of Social Network Dynamics

A class of statistical models is proposed for longitudinal network data. The dependent variable is the changing (or evolving) relation network, represented by two or more observations of a directed graph with a fixed set of actors. The network evolution is modeled as the consequence of the actors making new choices, or withdrawing existing choices, on the basis of functions, with fixed and random components, that the actors try to maximize. Individual and dyadic exogenous variables can be used as covariates. The change in the network is modeled as the stochastic result of network effects (reciprocity, transitivity, etc.) and these covariates. The existing network structure is a dynamic constraint for the evolution of the structure itself. The models are continuous-time Markov chain models that can be implemented as simulation models. The model parameters are estimated from observed data. For estimating and testing these models, statistical procedures are proposed that are based on the method of moments. The statistical procedures are implemented using a stochastic approximation algorithm based on computer simulations of the network evolution process.     

Modeling social influence through network autocorrelation: constructing the weight matrix

Many physical and social phenomena are embedded within networks of interdependencies, the so-called ‘context’ of these phenomena. In network analysis, this type of process is typically modeled as a network autocorrelation model. Parameter estimates and inferences based on autocorrelation models, hinge upon the chosen specification of weight matrix W, the elements of which represent the influence pattern present in the network. In this paper I discuss how social influence processes can be incorporated in the specification of W. Theories of social influence center around ‘communication’ and ‘comparison’; it is discussed how these can be operationalized in a network analysis context. Starting from that, a series of operationalizations of W is discussed. Finally, statistical tests are presented that allow an analyst to test various specifications against one another or pick the best fitting model from a set of models.     

Network unfolding

Networt unfolding is a measurement model for representing relational dta by a connected and weighted graph. If the data — partial or complete rank orders — can be represented by such a graph then the complete graph yields a representation. However, our aim is to minimize the number of lines in the representation and to find a maximally reduced graph. The maximally reduced graph for a specific set of a data may not be a tree but may contain one or more cycles. THe scale level of the weights is at least that of an ordered metric scale.Four examples are provided to illustrate the model and the algorithm to find the reduce graph. The first example serves to introduce the terms and notations and represents the similarity of Apachean languages. The communication network of the second example on the network structure of exchange of positive messages as a directed graph. In the third example on the network structure of human associative memory we show by means of Monte Carlo study that the obtained reduction of the graph is larger than to be expected by chance, and infer that the structure is different from that assumed by Anderson and Bower. In the fourth example on popularity status we conceive status as a social agreement structure.We consider network unfolding to be an alternative to other models of strucuture as, e.g. multidimensional scaling, cluster, and factor analysis. Substantial theory should guid the selection among these models.     

State and Institutional Correlates of Reported Victimization and Consensual Sexual Activity in Juvenile Correctional Facilities

This article uses multi-level analysis to model the effects of both institutional and state characteristics on juvenile reported sexual behavior (both consensual and forced) in 118 juvenile correctional facilities across 36 states. Data are taken from the 2012 National Survey of Youth in Custody (NSYC). We examine three dimensions of reported sexual contact including: forced sexual contact between juveniles and other institutionalized juveniles; forced sexual contact between juveniles and staff; and alleged consensual contact between juveniles and staff. At the institutional-level, facility capacity is the most consistent significant predictor of reported sexual contact. Findings also indicate that state-level variables such as median income and state-level violent crime rates are significantly associated with some types of reported incidents. Privacy protections of the available data make it impossible to look at individual level factors; however, we suggest this as a future step in important research.     

Spectral goodness of fit for network models

We introduce a new statistic, ‘spectral goodness of fit’ (SGOF) to measure how well a network model explains the structure of the pattern of ties in an observed network. SGOF provides a measure of fit analogous to the standard R² in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied.     

Adolescents' contact with sexuality in mainstream media: a selection-based perspective

Most work on adolescents' contact with sexuality in mainstream media has been framed in terms of media effects upon the sexual self-concepts, attitudes, and behaviors of youth, even when such causality cannot be inferred. Rarely examined are the sexual characteristics of adolescents that may predict contact with sexual media. Using Steele's (1999) Media Practice Model as a foundation, we reported on these associations for 2,184 Dutch adolescents. This study emphasized sex differences in the characteristics that predict such contact, and the role of youths' critical evaluations of information about sex in the media. Correlation and regression analyses revealed several sex differences in the characteristics related to sexual media contact, with individual characteristics accounting for more variance in females and critical evaluations accounting for more variance in males. This report underscores the need for more comprehensive, longitudinal studies of adolescents' media consumption and its connections to sexual development in youth.     

Adolescents' contact with sexuality in mainstream media: A selection‐based perspective

Most work on adolescents’ contact with sexuality in mainstream media has been framed in terms of media effects upon the sexual self‐concepts, attitudes, and behaviors of youth, even when such causality cannot be inferred. Rarely examined are the sexual characteristics of adolescents that may predict contact with sexual media. Using Steele's (1999) Media Practice Model as a foundation, we reported on these associations for 2,184 Dutch adolescents. This study emphasized sex differences in the characteristics that predict such contact and the role of youths’ critical evaluations of information about sex in the media. Correlation and regression analyses revealed several sex differences in the characteristics related to sexual media contact, with individual characteristics accounting for more variance in females and critical evaluations accounting for more variance in males. This study underscores the need for more comprehensive, longitudinal studies of adolescents’ media consumption and its connections to sexual development in youth.     

Change we can believe in: Comparing longitudinal network models on consistency,interpretability and predictive power

While several models for analysing longitudinal network data have been proposed, their main differences, especially regarding the treatment of time, have not been discussed extensively in the literature. However, differences in treatment of time strongly impact the conclusions that can be drawn from data. In this article we compare auto-regressive network models using the example of TERGMs – a temporal extensions of ERGMs – and process-based models using SAOMs as an example. We conclude that the TERGM has, in contrast to the ERGM, no consistent interpretation on tie-level probabilities, as well as no consistent interpretation on processes of network change. Further, parameters in the TERGM are strongly dependent on the interval length between two time-points. Neither limitation is true for process-based network models such as the SAOM. Finally, both compared models perform poorly in out-of-sample prediction compared to trivial predictive models.     

Demographic and HIV status diversities as mechanisms of social integration and segregation among Black sexual and gender minorities enrolled in a community-based social network intervention

Drawing on a social integration and intersectionality framework, this study advances a dynamic network understanding of the mechanisms that enable differential patterns of within-group social integration and segregation among Black sexual and gender minorities (BSGM). Specifically, in a cohort of BSGM (18–35 years of age, n = 340) participating in a community-based network intervention for HIV prevention, we examine how sexual, gender, age, and HIV status diversities contribute to friendship formation and maintenance patterns over the 12-month study enrollment period. We found attenuated social integration (or social activity) among non-gay-identified and older BSGM and evidence of social segregation (or homophily) on the basis of sexual identity and age similarities. Accounting for the moderating effects of the intervention revealed that the attenuated integration of non-gay-identified and older BSGM were stronger for participants who received the peer leadership training, and integration challenges were also found for transgender BSGM who received the peer leadership training. Meanwhile, BSGM living with HIV who received the peer leadership training were significantly more integrated than their counterparts in the control arm. These findings help us understand the complicated social fabric among BSGM and the dynamics that interventions for this community may have to contend with or alter.     

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.     

Initiating Sexual Experiences: How Do Young Adolescents Make Decisions Regarding Early Sexual Activity?

Understanding how young adolescents make decisions to engage in early sexual activities is vital for intervention efforts aimed at fostering positive youth development and reducing the negative outcomes of adolescent sexual behavior. In‐depth interviews with 42 suburban, mostly White, ninth‐grade adolescents (52% females, mean age=14.1, SD=.45) elicited accounts of their early sexual decisions. We adapted grounded theory methodology to build a model of sexual decision making from the adolescents' narratives. Six dominant categories emerged: contextual factors (relationship and personal characteristics), consideration of risks and benefits, boundary setting, boundary communication, the sexual experience, and evaluation. Our model of early sexual decision‐making processes, developed from the perspectives of young adolescents, highlights active consideration of health and social risks and benefits, as well as the generation of options regarding sexual activity. The model also shows that young adolescents set clear boundaries of sexual limits and evaluate sexual experiences, suggesting a dynamic process of decision making.     

What is the Point of Change? Change Point Detection in Relational Event Models

This paper presents an extension to the relational event model with change points (REM-CP) to study abrupt changes to social interaction behavior in temporal networks. A change point detection algorithm is proposed for exploring when and which network effects abruptly change, and a confirmatory approach to test the presence of a change point at a given moment. The effectiveness of the methodology was assessed with numerical simulations and NASA’s Apollo 13 mission data. The latter revealed dynamic communication behavior and identified time zones where most change points occurred, including around the time of the famous quote “Houston, we’ve had a problem.”     

A Content Analysis of Intake Paperwork: An Exploration of How Clinicians Ask About Gender,Sex, and Sexual/Affectual Orientation

In the United States, the transgender and gender nonconforming (TGNC) population has increased twofold since 2011. Although counseling professionals are called to provide competent services to TGNC clients, no empirical studies exist that examine one of the first points of contact: Intake paperwork. The authors conducted a content analysis (N = 128) of intake paperwork and assessed how and if clinicians asked for gender, sex, and sexual/affectual orientation, and whether they conflated these constructs. Findings indicate adjustments need to be made for intakes to be more inclusive of these constructs. The authors offer clinical implications and avenues for future research.     

Explaining Female Teenagers' Sexual Behavior and Outcomes: A Bivariate Probit Analysis with Selectivity Correction

Using the National Longitudinal Survey of Youth (NLSY) data, this article estimates a model of teenage childbearing. The model recognizes that teenage childbearing is conditional on earlier sexual activity and that such activity is undertaken by only a portion of the female teenage population. Consequently, rather than estimate a single equation for birth probability as much past research has done, a bivariate probit model with selectivity correction is estimated to account for the sequential nature of the process. An important result of this research suggests that AFDC benefits play a role in the decision to become sexually active as well as to become a teenage parent.     

Introduction to stochastic actor-based models for network dynamics

Stochastic actor-based models are models for network dynamics that can represent a wide variety of influences on network change, and allow to estimate parameters expressing such influences, and test corresponding hypotheses. The nodes in the network represent social actors, and the collection of ties represents a social relation. The assumptions posit that the network evolves as a stochastic process ‘driven by the actors’, i.e., the model lends itself especially for representing theories about how actors change their outgoing ties. The probabilities of tie changes are in part endogenously determined, i.e., as a function of the current network structure itself, and in part exogenously, as a function of characteristics of the nodes (‘actor covariates’) and of characteristics of pairs of nodes (‘dyadic covariates’). In an extended form, stochastic actor-based models can be used to analyze longitudinal data on social networks jointly with changing attributes of the actors: dynamics of networks and behavior.     

Combined physical and psychosexual therapy for provoked vestibulodynia-an evaluation of a multidisciplinary treatment model

Our objective is to standardize and evaluate a combined physical and psychosexual therapy for women with provoked vestibulodynia. Twenty-four patients underwent the treatment program. Sessions with a psychosexual counselor included issues on sexual functioning, psychological adjustments, and stress elimination. Exercises for mucosal desensitization and reestablishment of pelvic floor function were supervised by a midwife. A questionnaire was used for evaluation at a minimum of 6 months after the treatment. The mean number of appointments to the counselor was 12 (4-24) and 15 (9-26) to the midwife during a mean period of 53 weeks (19-92). Nineteen women (79%) considered themselves to be cured or having greatly improved. Intercourse frequency was increased (p = 0.001) and coital pain was reduced (p = 0.02) after completing the treatment. Improvements in sexual functioning and coping strategies for psychological impairment and stress were reported. Women with provoked vestibulodynia benefit from a multidisciplinary treatment model including desensitization of the vestibular mucosa, rehabilitation of the pelvic floor, and psychosexual adjustments.     

Bayesian model selection for exponential random graph models

Exponential random graph models are a class of widely used exponential family models for social networks. The topological structure of an observed network is modelled by the relative prevalence of a set of local sub-graph configurations termed network statistics. One of the key tasks in the application of these models is which network statistics to include in the model. This can be thought of as statistical model selection problem. This is a very challenging problem—the posterior distribution for each model is often termed “doubly intractable” since computation of the likelihood is rarely available, but also, the evidence of the posterior is, as usual, intractable. The contribution of this paper is the development of a fully Bayesian model selection method based on a reversible jump Markov chain Monte Carlo algorithm extension of Caimo and Friel (2011) which estimates the posterior probability for each competing model.     

Sexual Satisfaction and Marital Satisfaction During the Early Years of Chinese Marriage: A Three-Wave,Cross-Lagged,Actor–Partner Interdependence Model

Sexuality is an integral component of many intimate relationships, and research has consistently demonstrated a positive association between sexual and marital satisfaction. However, the temporal dynamics of this association remain controversial and understudied with rigorous longitudinal dyadic approaches, and empirical efforts examining this association in non-Western samples remain sparse. Based on three annual waves of data from 268 Chinese couples during the early years of marriage, this study tested a cross-lagged, actor–partner interdependence model examining the association between sexual and marital satisfaction. Results indicated that (a) across three waves, husbands’ earlier sexual satisfaction predicted their later marital satisfaction, rather than the reverse; (b) from Wave 1 to Wave 2, wives’ earlier marital satisfaction predicted their later sexual satisfaction, rather than the reverse, but no association between wives’ sexual and marital satisfaction was found from Wave 2 to Wave 3; and (c) four longitudinal indirect associations linking sexual and marital satisfaction were identified, including three actor associations and one partner association. Such findings shed light on the complexity inherent within the dynamic association between sexual and marital satisfaction over the early years of marriage in the Chinese cultural context.     

Measuring structural HIV stigma

Despite the progress in pharmaceutical and epidemiological tools for combating HIV spread, HIV stigma remains a significant social barrier impeding treatment and prevention efforts, potentially reducing the effectiveness of interventions to reduce HIV transmission. In this paper, we propose a novel approach to defining and estimating HIV stigmatization through the structure of sexual relations, as opposed to attitudes. We conceptualize structural stigma as arising from two mechanisms: (1) a reduced propensity towards HIV serodiscordant partnerships (exclusion); and (2) a reduced propensity towards partnerships with seroconcordant individuals who themselves have serodiscordant partnerships (ostracism). Both mechanisms can be assessed from observed partnership network data using exponential family random graph models (ERGMs). We demonstrate our approach on a sexual contact network of black men who have sex with men in the South Side of Chicago. We find a tendency for serodiscordant sexual relationships to be suppressed in the network ($\theta$ = −0.69, p $<$ .05), as well as a suppressive tendency for HIV negative YBMSM to have sex with other HIV negative people in serodiscordant relationships ($\theta$ = −0.96, p $<$ .05) suggesting that structural HIV stigma is present in this network. Potential relationships with attitudinal stigma and implications for epidemiological strategies for reducing HIV stigma are discussed.