NEW SPECIFICATIONS FOR EXPONENTIAL RANDOM GRAPH MODELS

The most promising class of statistical models for expressing structural properties of social networks observed at one moment in time is the class of exponential random graph models (ERGMs), also known as p * models. The strong point of these models is that they can represent a variety of structural tendencies, such as transitivity, that define complicated dependence patterns not easily modeled by more basic probability models. Recently, Markov chain Monte Carlo (MCMC) algorithms have been developed that produce approximate maximum likelihood estimators. Applying these models in their traditional specification to observed network data often has led to problems, however, which can be traced back to the fact that important parts of the parameter space correspond to nearly degenerate distributions, which may lead to convergence problems of estimation algorithms, and a poor fit to empirical data.
This paper proposes new specifications of exponential random graph models. These specifications represent structural properties such as transitivity and heterogeneity of degrees by more complicated graph statistics than the traditional star and triangle counts. Three kinds of statistics are proposed: geometrically weighted degree distributions, alternating k -triangles, and alternating independent two-paths. Examples are presented both of modeling graphs and digraphs, in which the new specifications lead to much better results than the earlier existing specifications of the ERGM. It is concluded that the new specifications increase the range and applicability of the ERGM as a tool for the statistical analysis of social networks.     

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.     

Advances in Exponential Random Graph (p*) Models Applied to a Large Social Network

Recent advances in statistical network analysis based on the family of exponential random graph (ERG) models have greatly improved our ability to conduct inference on dependence in large social networks (Snijders 2002, Pattison and Robins 2002, Handcock 2002, Handcock 2003, Snijders et al. 2006, Hunter et al. 2005, Goodreau et al. 2005, previous papers this issue). This paper applies advances in both model parameterizations and computational algorithms to an examination of the structure observed in an adolescent friendship network of 1,681 actors from the National Longitudinal Study of Adolescent Health (AddHealth). ERG models of social network structure are fit using the R package statnet, and their adequacy assessed through comparison of model predictions with the observed data for higher-order network statistics.For this friendship network, the commonly used model of Markov dependence leads to the problems of degeneracy discussed by Handcock (2002, 2003). On the other hand, model parameterizations introduced by Snijders et al (2006) and Hunter and Handcock (2006) avoid degeneracy and provide reasonable fit to the data. Degree-only models did a poor job of capturing observed network structure; those that did best included terms both for heterogeneous mixing on exogenous attributes (grade and self-reported race) as well as endogenous clustering. Networks simulated from this model were largely consistent with the observed network on multiple higher-order network statistics, including the number of triangles, the size of the largest component, the overall reachability, the distribution of geodesic distances, the degree distribution, and the shared partner distribution. The ability to fit such models to large datasets and to make inference about the underling processes generating the network represents a major advance in the field of statistical network analysis.     

Incorporating structural stigma into network analysis

A rich literature has explored the modeling of homophily and other forms of nonuniform mixing associated with individual-level covariates within the exponential family random graph (ERGM) framework. Such differential mixing does not fully explain phenomena such as stigma, however, which involve the active maintenance of social boundaries by ostracism of persons with out-group ties. Here, we introduce a new family of statistics that allows for such effects to be captured, making it possible to probe for the potential presence of boundary maintenance above and beyond simple differences in nomination rates. We demonstrate these statistics in the context of gender segregation in a school classroom, and introduce a framework for understanding the associated coefficients via network perturbation.     

Recent developments in exponential random graph (p*) models for social networks

This article reviews new specifications for exponential random graph models proposed by Snijders et al. [Snijders, T.A.B., Pattison, P., Robins, G.L., Handcock, M., 2006. New specifications for exponential random graph models. Sociological Methodology] and demonstrates their improvement over homogeneous Markov random graph models in fitting empirical network data. Not only do the new specifications show improvements in goodness of fit for various data sets, but they also help to avoid the problem of near-degeneracy that often afflicts the fitting of Markov random graph models in practice, particularly to network data exhibiting high levels of transitivity. The inclusion of a new higher order transitivity statistic allows estimation of parameters of exponential graph models for many (but not all) cases where it is impossible to estimate parameters of homogeneous Markov graph models. The new specifications were used to model a large number of classical small-scale network data sets and showed a dramatically better performance than Markov graph models. We also review three current programs for obtaining maximum likelihood estimates of model parameters and we compare these Monte Carlo maximum likelihood estimates with less accurate pseudo-likelihood estimates. Finally, we discuss whether homogeneous Markov random graph models may be superseded by the new specifications, and how additional elaborations may further improve model performance.     

Generalized Linear Models in Family Studies

Generalized linear models (GLMs), as defined by J. A. Nelder and R. W. M. Wedderburn (1972) , unify a class of regression models for categorical, discrete, and continuous response variables. As an extension of classical linear models, GLMs provide a common body of theory and methodology for some seemingly unrelated models and procedures, such as the logistic, Poisson, and probit models, that are increasingly used in family studies. This article provides an overview of the principle and the key components of GLMs, such as the exponential family of distributions, the linear predictor, and the link function. To illustrate the application of GLMs, this article uses Canadian national survey data to build an example focusing on the number of close friends among older adults. The article concludes with a discussion of the strengths and weaknesses of GLMs.     

An introduction to exponential random graph (p) models for social networks

This article provides an introductory summary to the formulation and application of exponential random graph models for social networks. The possible ties among nodes of a network are regarded as random variables, and assumptions about dependencies among these random tie variables determine the general form of the exponential random graph model for the network. Examples of different dependence assumptions and their associated models are given, including Bernoulli, dyad-independent and Markov random graph models. The incorporation of actor attributes in social selection models is also reviewed. Newer, more complex dependence assumptions are briefly outlined. Estimation procedures are discussed, including new methods for Monte Carlo maximum likelihood estimation. We foreshadow the discussion taken up in other papers in this special edition: that the homogeneous Markov random graph models of Frank and Strauss [Frank, O., Strauss, D., 1986. Markov graphs. Journal of the American Statistical Association 81, 832–842] are not appropriate for many observed networks, whereas the new model specifications of Snijders et al. [Snijders, T.A.B., Pattison, P., Robins, G.L., Handock, M. New specifications for exponential random graph models. Sociological Methodology, in press] offer substantial improvement.     

Is There a Place for Biopsychosocial Formulation in a Systemic Practice?

There is a long history of literature concerning integrative practice and how a systemic practice can fit with other models of therapy Much of this literature has focused on establishing a space for systemic therapy within the dominant medical paradigm, and exploring how the medical model can be enhanced by systemic ideas. The outcome has been better practice, especially in child and adolescent mental health. Interestingly, however, there has been less discussion of the converse: the family therapy literature has rarely considered whether or not systemic practice itself can be enhanced by ideas from the dominant medical model. This article proposes that a biopsychosocial formulation can enhance systemic practice by: (I) holding clinicians accountable for their thinking; (2) facilitating a rigour and attention to detail that may prove useful when therapy falters; (3) opening up other possibilities for intervention; and (4) providing a way to engage with the dominant medical paradigm and support clients in negotiating their way through this system. Potential problems nevertheless arise when integrating a biopsychosocial formulation into a systemic framework. This article identifies these problems and presents ideas for how they can be managed in practice.     

MODELS FOR GENERALIZED LOCATION SYSTEMS

A formal framework is introduced for a general class of assignment systems that can be used to characterize a range of social phenomena. An exponential family of distributions is developed for modeling such systems, allowing for the incorporation of both attributional and relational covariates. Methods are shown for simulation and inference using the location system model. Two illustrative applications (occupational stratification and residential settlement patterns) are presented, and simulation is employed to show the behavior of the location system model in each case; a third application, involving occupancy of positions within an organization, is used to demonstrate inference for the location system. By leveraging established results in the fields of social network analysis, spatial statistics, and statistical mechanics, it is argued that sociologists can model complex social systems without sacrificing inferential tractability.     

Imputation of attributes in networked data using Bayesian autocorrelation regression models

Misspecification in network autocorrelation models poses a challenge for parameter estimation, which is amplified by missing data. Model misspecification has been a focus of recent work in the statistics literature and new robust procedures have been developed, in particular cutting feedback. This paper shows how this helps in a misspecified network autocorrelation model. Where model misspecification is mild and the traits are fully observed, Bayesian imputation is routine. In settings with high missingness, Bayesian inference can fail, but a closely related cut model is robust. We illustrate this on a data set of graduate students using a Facebook-like messaging app.     

Family characteristics as predictors of intensity in family services

This article investigates factors influencing the number of hours families are involved with family services and uses these factors to develop a predictive model. This research began with focus groups involving family service workers who identified three key domains influencing service intensity: worker/family relationship, family motivation, and family characteristics. The family characteristics domain is the focus of this article. Influencing factors within this domain are examined through analysis of database information from 258 families who had previously accessed family services through a community services organization. Key predictors identified include the gender of main consumer, family size, and presence of issues such as family violence and physical illness. These findings are used to develop a model to predict intervention intensity for families accessing family services. The ability to estimate service intensity provides data to effectively develop innovative programs and enable better balancing of staff workloads and resources. Additionally, the capability to predict intensity helps allocate families to appropriate workers and programs.     

The Work–Family Interface: Integrating Research and Career Counseling Practice

This article addresses the work–family interface by reviewing research using Frone's ( 2003 ) bidirectional model of work–family conflict and facilitation. The review demonstrates that work–family conflict is associated with various detrimental outcomes and that work–family facilitation is positively correlated with enhanced mental and physical well‐being. After summarizing the research, the authors discuss recent models and perspectives from the field of vocational psychology, connect these models and perspectives to existing work–family literature, and propose theoretically based interventions for increasing facilitation and decreasing conflict.     

Heating up the debate? Measuring fragmentation and polarisation in a German climate change hyperlink network

Research into polarisation on the internet has so far primarily focused on contentious issues and yielded contradictory results. Shifting the focus to a non-contentious setting, this article combines community detection with brokerage analysis and exponential random graph models to assess the degree of polarisation at different levels of a German hyperlink network on climate change. Although homophily accounts for a moderate degree of polarisation at the top level of the network, the communities reveal that other factors prove more decisive in shaping its structure and the article thus contributes to a more refined understanding of the nature of online polarisation.     

Assessment in Marriage and Family Therapy: A Review of Clinical Updates for Family Therapists

This article presents information from an integrative literature review that examined assessment processes presented to marriage and family therapists in Clinical Updates for Family Therapists, Volumes 1 (2005), 2 (2006), and 3 (2007). The study was based on the concern that marriage and family therapy is losing its systemic relational focus as practitioners must comply with diagnosis models using the Diagnostic and Statistical Manual of Mental Disorders. Using integrative literature review methods, similar to qualitative research, 54 articles were deconstructed to identify assessment tools and diagnostic processes being presented as best practice. Of the 54 articles, 96% identified the importance of having a family or couple relational perspective for working with individuals with mental disorders; however, only 54% provided any explanation to how this could be accomplished. These findings suggest a need to increase the identification of unique, relational assessment practices in articles that offer best practice techniques in marriage and family therapy.     

Dyadic regression in the presence of heteroscedasticity—An assessment of alternative approaches

Although the problem of heteroscedasticity has been the subject of much discussion in other areas of applied statistics the problem has received scant attention in the social network literature. This study attempts to remedy this situation by considering how traditional methods for significance testing in dyadic regression models, such as standard QAP tests, perform under conditions of heteroscedasticity. Moreover, the article presents two alternative methods to deal with heteroscedasticity that are both shown to perform rather well with typical social network data under conditions of both heteroscedasticity and homoscedasticity. Overall, the results of the study suggest that applied researchers using regression techniques to study dyadic data are well advised to correct for heteroscedasticity, by either of the two methods discussed here, whenever there is a reason to suspect heteroscedasticity.     

Home‐based Telework,Gender, and the Synchronization of Work and Family: Perspectives of Teleworkers and their Co‐residents

This article explores the relationship between work–family roles and boundaries, and gender, among home‐based teleworkers and their families. Previous literature suggests two alternative models of the implications of home‐based work for gendered experiences of work and family: the new opportunities for flexibility model and the exploitation model. Drawing on the findings of a qualitative study of home‐based workers and their co‐residents, we argue that these models are not mutually exclusive. We explore the gendered processes whereby teleworking can simultaneously enhance work–life balance while perpetuating traditional work and family roles.     

BEHAVIORAL ECONOMICS AND DRINKING BEHAVIOR: PRELIMINARY RESULTS FROM AN IRISH COLLEGE STUDY

This article examines the results of single-equation regression models of the determinants of alcohol consumption patterns among college students modeling a rich variety of covariates including gender, family and peer drinking, tenure, personality, risk perception, time preferences, and age of drinking onset. The results demonstrate very weak income effects and very strong effects of personality, peer drinking (in particular closest friend), time preferences, and other substance use. The task of future research is to verify these results and assess causality using more detailed methods ( JEL D12, I31).     

Predictors and outcomes of social network compositions: A compositional structural equation modeling approach

Proportions of a total, including social network compositions (proportions of partner, family, friends, etc.) lie in a restricted space, which challenges statistical analysis. Network compositions can be both dependent and explanatory variables and are usually measured with error by survey instruments. Structural equation models make it possible to correct measurement error bias. Coenders et al. (2011) fitted a factor analysis model to transformed network compositions. In this article, we use another transformation called an isometric log-ratio and we extend the model to include predictors and outcomes. The findings and hypotheses in the literature can be reformulated with isometric log-ratios in a more interpretable manner. For instance, we find relationships of gender with partner support, of education and extraversion with friend support, and of family support with tie multiplexity and closeness.     

The effects of family therapies for adolescent delinquency and substance abuse: a meta-analysis

This meta-analysis summarizes results from k = 24 studies comparing either Brief Strategic Family Therapy, Functional Family Therapy, Multidimensional Family Therapy, or Multisystemic Therapy to either treatment-as-usual, an alternative therapy, or a control group in the treatment of adolescent substance abuse and delinquency. Additionally, the authors reviewed and applied three advanced meta-analysis methods including influence analysis, multivariate meta-analysis, and publication bias analyses. The results suggested that as a group the four family therapies had statistically significant, but modest effects as compared to treatment-as-usual (d = 0.21; k = 11) and as compared to alternative therapies (d = 0.26; k = 11). The effect of family therapy compared to control was larger (d = 0.70; k = 4) but was not statistically significant probably because of low power. There was insufficient evidence to determine whether the various models differed in their effectiveness relative to each other. Influence analyses suggested that three studies had a large effect on aggregate effect sizes and heterogeneity statistics. Moderator and multivariate analyses were largely underpowered but will be useful as this literature grows.