A p* primer: logit models for social networks

A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others [Holland, P.W., Leinhardt, S., 1977. Notes on the statistical analysis of social network data; Holland, P.W., Leinhardt, S., 1981. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association. 76, pp. 33–65 (with discussion); Fienberg, S.E., Wasserman, S., 1981. Categorical data analysis of single sociometric relations. In: Leinhardt, S. (Ed.), Sociological Methodology 1981, San Francisco: Jossey-Bass, pp. 156–192; Fienberg, S.E., Meyer, M.M., Wasserman, S., 1985. Statistical analysis of multiple sociometric relations. Journal of the American Statistical Association, 80, pp. 51–67; Wasserman, S., Weaver, S., 1985. Statistical analysis of binary relational data: Parameter estimation. Journal of Mathematical Psychology. 29, pp. 406–427; Wasserman, S., 1987. Conformity of two sociometric relations. Psychometrika. 52, pp. 3–18] is the very strong independence assumption made on interacting individuals or units within a network or group. This limiting assumption is no longer necessary given recent developments on models for random graphs made by Frank and Strauss [Frank, O., Strauss, D., 1986. Markov graphs. Journal of the American Statistical Association. 81, pp. 832–842] and Strauss and Ikeda [Strauss, D., Ikeda, M., 1990. Pseudolikelihood estimation for social networks. Journal of the American Statistical Association. 85, pp. 204–212]. The resulting models are extremely flexible and easy to fit to data. Although Wasserman and Pattison [Wasserman, S., Pattison, P., 1996. Logit models and logistic regressions for social networks: I. An introduction to Markov random graphs and p*. Psychometrika. 60, pp. 401–426] present a derivation and extension of these models, this paper is a primer on how to use these important breakthroughs to model the relationships between actors (individuals, units) within a single network and provides an extension of the models to multiple networks. The models for multiple networks permit researchers to study how groups are similar and/or how they are different. The models for single and multiple networks and the modeling process are illustrated using friendship data from elementary school children from a study by Parker and Asher [Parker, J.G., Asher, S.R., 1993. Friendship and friendship quality in middle childhood: Links with peer group acceptance and feelings of loneliness and social dissatisfaction. Developmental Psychology. 29, pp. 611–621].     

Some generalizations of p1: External constraints,interactions and non-binary relations

In 1977, Holland and Leinhardt introduced a new statistical approach to sociometric data analysis. The details of their approach, based on a model termed P₁, were published in 1981 in papers by Holland and Leinhardt, and Fienberg and Wasserman. Since then, many researchers have adopted this model, addressing substantive questions that were unanswerable with existing methodology. The continuing methodological research of Fienberg and Wasserman has allowed this approach to be applied to many different types of sociometric data. We carry on this research by extending p₁ to three new situations: networks of such size that it is impossible for every actor to have contact or knowledge of the other actors; networks in which actor interaction can not be adequately modeled by the simple additive main effects of expansiveness and popularity; and networks in which we measure the strength of the relationship between actors using a non-binary or multivalued relational quantity.     

Stochastic a posteriori blockmodels: Construction and assessment

In 1983, Holland, Laskey, and Leinhardt, using the ideas of Holland and Leinhardt, and Fienberg and Wasserman, introduced the notion of a stochastic blockmodel. The mathematics for stochastic a priori blockmodels, in which exogenous actor attribute data are used to partition actors independently of any statistical analysis of the available relational data, have been refined by several researchers and the resulting models used by many. Attempts to simultaneously partition actors and to perform relational data analyses using statistical methods that yield stochastic a posteriori blockmodels are still quite rare. In this paper, we discuss some old suggestions for producing such posterior blockmodels, and comment on other new suggestions based on multiple comparisons of model parameters, log-linear models for ordinal categorical data, and correspondence analysis. We also review measures for goodness-of-fit of a blockmodel, and we describe a natural approach to this problem using likelihood-ratio statistics generated from a popular model for relational data.     

REVIEWS

Gustafson, J.P., & Cooper, L. W. The modern contest: A systemic guide to the pattern that connects individual psychotherapy, family therapy, group work, teaching, organizational life, and large-scale social problesms.
Henggeler, S.W.& Borduin, C.M. Family therapy and beyond: A multisystemic approach to treating the behavior problems of children and adolescents.
Elizur, J., & Minuchin, S. Institutionalizing madness: families, therapy and society.
George, K. The adoption option: A practical handbook for prospective adoptive parents.
Landgraf, J.R.Singling: A new way to live the single life.
McCarthy, B. & McCarthy E. Couple sexual awareness.
Marlin, E. Relationships in recovery: Healing strategies for couples and families.
Miller, S., Wackman, D., Nunnally, E., & Miller, P.(1988). Connecting instrucdtor manual.
Miller, S., Wackman, D., Nunnally, E., & Miller, P.(1988). Connecting skills workbook.
Miller, S., Wackman, D., Nunnally, E., & Miller, P.(1988). Connecting with self and others.     

Network models for social selection processes

We present network models for social selection processes, based on the p¹ class of models. Social selection occurs when individuals form social relationships on the basis of certain characteristics they possess. Similarity is a common hypothesis for selection processes, but one that is usually framed dyadically. Structural balance approaches move beyond dyadic conceptualizations and require more sophisticated modeling. The two-block chain graph approach of p¹ social influence models is adapted to allow individual attribute variables to be predictors of network ties. Using a range of dependence assumptions, we present a hierarchy of increasingly complex selection models, including models for continuous attribute measures, which in their simplest form may be assumed to be linear. The models have scope, however, for more complex functional formulations so that more specific hypotheses may be investigated by postulating a particular functional form. Our empirical examples illustrate how dyadic selection may be transmuted into structural effects, and how the absence of dyadic selection may still mask a subtle higher order selection effect as individuals “position” themselves within a wider social environment. In conclusion, we discuss the links between social influence and social selection models.     

Exponential Family Models for sampled and census Network data

Much progress has been made on the development of statistical methods for network analysis in the past ten years, building on the general class of exponential family random graph (ERG) network models first introduced by Holland and Leinhardt (1981) . Recent examples include models for Markov graphs, "p*" models, and actor‐oriented models. For empirical application, these ERG models take a logistic form, and require the equivalent of a network census: data on all dyads within the network. In a largely separate stream of research, conditional log‐linear (CLL) models have been adapted for analyzing locally sampled ("egocentric") network data. While the general relation between log‐linear and logistic models is well known and has been exploited in the case of a priori blockmodels for networks, the relation for the CLL models is different due to the treatment of absent ties. For fully saturated tie independence models, CLL and ERG are equivalent and related via Bayes' rule. For other tie independence models, the two do not yield equivalent predicted values, but we show that in practice the differences are unlikely to be large. The alternate conditioning in the two models sheds light on the relationship between local and complete network data, and the role that models can play in bridging the gap between them.     

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.     

A Nash bargaining model for simple exchange networks

Starting from exogenously given negotiation networks, sociological exchange theories explain bilateral divisions of fixed surpluses (e.g., cake, dollar) as consequences of the partners’ structural embeddedness. In accordance with the available experimental evidence, we focus on simple exchange networks and present a formal model for predicting profit splits from such structures. In contrast to other approaches, we combine the generalized Nash bargaining solution from game theory with the assumption that both relational features and network positions affect exchange outcomes. The resulting point predictions for profit splits correspond closely with experimental results obtained by Cook et al. [Cook, K.S., Emerson, R.M., Gillmore, M.R., Yamagishi, T., 1983. The distribution of power in exchange networks: theory and experimental results. American Journal of Sociology 89, 275–305], Lovaglia et al. [Lovaglia, M.J., Skvoretz, J., Willer, D., Markovsky, B., 1995. Negotiated exchanges in social networks. Social Forces 74, 123–155], Markovsky et al. [Markovsky, B., Willer, D., Patton, T., 1988. Power relations in exchange networks. American Sociological Review 53, 220–236], Simpson and Willer [Simpson, B., Willer, D., 1999. A new method for finding power structures. In: Willer, D. (Ed.), Network Exchange Theory. Praeger, Westport, CT, pp. 270–284], Skvoretz and Fararo [Skvoretz, J., Fararo, T.J., 1992. Power and network exchange: an essay toward theoretical unification. Social Networks 14, 325–344], Skvoretz and Willer [Skvoretz, J., Willer, D., 1993. Exclusion and power: a test of four theories of power in exchange networks. American Sociological Review 58, 801–818] as well as Yamagishi et al. [Yamagishi, T., Gillmore, M.R., Cook, K.S., 1988. Network connections and the distribution of power in exchange networks. American Journal of Sociology 93, 833–851].     

Acyclic triplets and social structure in complete signed digraphs

This report is a study of the relationship between certain systems of signed acyclic triplets representing relationships among three actors and the properties of the graphs which they generate. It is a method of investigating macro-structure based on micro-structural properties. The motivation stems from the work of Cartwright and Harary, Davis, Leinhardt and Holland on affective ties, which we generalize. After showing the connections between our approach and theirs, we develop some new models that go beyond affect and positive sentiment.     

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.     

Spatial microsimulation for rural policy analysis in Ireland: The implications of CAP reforms for the national spatial strategy

Microsimulation attempts to describe economic and social events by modelling the behaviour of individual agents. These models have proved useful in evaluating the impact of policy changes at the micro level. Spatial microsimulation models contain geographic information and allow for a regional or local approach to policy analysis. This paper builds on previous work on urban systems by employing similar modelling techniques for the analysis of rural areas [Birkin, M., Clarke, M., 1988. SYNTHESIS—a synthetic spatial information system for urban and regional analysis: methods and examples. Environment and Planning A 20, 1645–1671; Ballas, D. et al., 1999. Exploring microsimulation methodologies for the estimation of household attributes. The Fourth International Conference on GeoComputation, 25–28 July 1999, Fredericksburg, Virginia, USA (paper presentation); Ballas, D, Clarke, G. P., 2000. GIS and microsimulation for local labour market policy analysis. Computers, Environment and Urban Systems 24, 305–330; Ballas, D., Clarke, G. P., 2001a. Modelling the local impacts of national social policies: a spatial microsimulation approach. Environment and Planning C: Government and Policy 19, 587–606; Ballas, D., Clarke, G. P., 2001b. Towards local implications of major job transformations in the city: a spatial microsimulation approach. Geographical Analysis 33, 291–311]. It describes the development of the simulation model for the Irish local economy (SMILE) model. SMILE is a static and dynamic spatial microsimulation designed to analyse the impact of policy change and economic development on rural areas in Ireland. This paper focuses on the static model. First, we describe the European and Irish policy environment and indicate the importance of building spatial models to analyse change in rural Ireland. Second, we review existing literature on regional and local modelling techniques and the use of spatial models as tools for policy analysis. Third, we describe the SMILE static model. The model generates synthetic spatially referenced population for the Irish Republic at the small area level—the population micro data is produced for district electoral divisions (DEDs). Finally, we show how data from other sources can be linked to the static model output. We link data from the Irish National Farm Survey on farm system, income and off-farm employment of operator to the SMILE static model. We use this example to show its potential as a tool for policy analysis.     

Network inference,error, and informant (in)accuracy: a Bayesian approach

Much, if not most, social network data is derived from informant reports; past research, however, has indicated that such reports are in fact highly inaccurate representations of social interaction. In this paper, a family of hierarchical Bayesian models is developed which allows for the simultaneous inference of informant accuracy and social structure in the presence of measurement error and missing data. Posterior simulation for these models using Markov Chain Monte Carlo methods is outlined. Robustness of the models to structurally correlated error rates, implications of the Bayesian modeling framework for improved data collection strategies, and the validity of the criterion graph are also discussed.     

MEASUREMENT ERROR IN MACROECONOMIC DATA AND ECONOMICS RESEARCH: DATA REVISIONS,GROSS DOMESTIC PRODUCT,AND GROSS DOMESTIC INCOME

We use a preanalysis plan to analyze the effect of measurement error on economics research using the fact that the Bureau of Economic Analysis both revises its gross domestic product (GDP) data and also publishes a second, theoretically identical estimate of U.S. output that only differs from GDP due to measurement error: gross domestic income (GDI). Using a sample of 23 models published in top economics journals, we find that reestimating models using revised GDP always gives the same qualitative result as the original publication. Estimating models using GDI instead of GDP gives a different qualitative result for three of 23 models (13%). (JEL C80, C82, E01)     

Anatomie von Kommunikationsrollen

The identification of generalizable roles in social systems has been one of the most central issues in social science ever since. Particularly in the field of interpersonal communication, the notion of communication roles has been used to describe and better understand the complex processes in social groups and society. This contribution identifies the theoretical and methodological concepts that have to be considered when roles in directed networks are operationalized. Based on a network analytic approach and critically evaluating the shortcomings of some widely used models, this study aims to propose new concepts for the operationalization of communication roles. These concepts can be divided into two distinctive approaches. One possibility is to use microstructures like dyadic and triadic communication roles as basic units. For this approach, different aggregation rules are discussed which are necessary for their application in more complex networks. The second approach takes the overall structure of a network into account and identifies different roles by applying centrality measures, blockmodelling or hierarchical structure analysis tools. For illustrative reasons, this study limits its focus on the operationalization of communication roles as a prominent object in social science research. The concepts presented, however, are applicable for directed graphs in general.     

A Dyadic Approach to Understanding the Link Between Sexual Functioning and Sexual Satisfaction in Heterosexual Couples

Researchers have demonstrated that several dimensions of sexual functioning (e.g., sexual desire, arousal, orgasm) are associated with the sexual satisfaction of individuals in a committed mixed-sex (male–female) relationship. We extended this research by comparing a dyadic model that included both own (i.e., actor effect) and partner (i.e., partner effect) domains of sexual functioning to an individual model that included only actor effects. Participants were 124 mixed-sex couples who completed online measures of sexual functioning and sexual satisfaction. Data analysis using the actor–partner interdependence model (APIM) and structural equation modeling (SEM) indicated that the dyadic model had a better fit than the individual model. Women’s sexual desire and orgasm and men’s erectile functioning were significant positive predictors of both own and partner’s sexual satisfaction. These results are discussed in terms of the importance of taking a dyadic approach to research and clinical work related to sexual satisfaction.     

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.     

African Americans,U.S. Poverty,and International Law

ABSTRACT

Statistical rates of poverty among African Americans often hide the cultural and historical nature of their intended consequences. Unfavorable outcomes for social change can occur when viewing poverty among African Americans in isolation from their unique historical and cultural experiences and U.S. social, political, and capitalistic influences. While pressures to subordinate African Americans continue, African Americans also exert pressure (e.g., social movements) as human agents in their efforts toward self-determination. In order to understand and/or ameliorate poverty in the US, policy makers, researchers, and educators must first deal with the cultural hegemony undergirding it.