Neighborhood–Based Models For Social Networks

We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of interaction and corresponds to a subset of possible network ties. In this paper, we discuss hypotheses about the form of these neighborhoods, and we present two new and theoretically plausible ways in which neighborhood–based models for networks can be constructed. In the first, we introduce the notion of a setting structure, a directly hypothesized (or observed) set of exogenous constraints on possible neighborhood forms. In the second, we propose higher–order neighborhoods that are generated, in part, by the outcome of interactive network processes themselves. Applications of both approaches to model construction are presented, and the developments are considered within a general conceptual framework of locale for social networks. We show how assumptions about neighborhoods can be cast within a hierarchy of increasingly complex models; these models represent a progressively greater capacity for network processes to "reach" across a network through long cycles or semipaths. We argue that this class of models holds new promise for the development of empirically plausible models for networks and network–based processes.     

A comparative study of social network models: Network evolution models and nodal attribute models

This paper reviews, classifies and compares recent models for social networks that have mainly been published within the physics-oriented complex networks literature. The models fall into two categories: those in which the addition of new links is dependent on the (typically local) network structure (network evolution models, NEMs), and those in which links are generated based only on nodal attributes (nodal attribute models, NAMs). An exponential random graph model (ERGM) with structural dependencies is included for comparison. We fit models from each of these categories to two empirical acquaintance networks with respect to basic network properties. We compare higher order structures in the resulting networks with those in the data, with the aim of determining which models produce the most realistic network structure with respect to degree distributions, assortativity, clustering spectra, geodesic path distributions, and community structure (subgroups with dense internal connections). We find that the nodal attribute models successfully produce assortative networks and very clear community structure. However, they generate unrealistic clustering spectra and peaked degree distributions that do not match empirical data on large social networks. On the other hand, many of the network evolution models produce degree distributions and clustering spectra that agree more closely with data. They also generate assortative networks and community structure, although often not to the same extent as in the data. The ERGM model, which turned out to be near-degenerate in the parameter region best fitting our data, produces the weakest community structure.     

Univariate and multivariate models of positive and negative networks: Liking,disliking, and bully–victim relationships

Three relations between elementary school children were investigated: networks of general dislike and bullying were related to networks of general like. These were modeled using multivariate cross-sectional (statistical) network models. Exponential random graph models for a sample of 18 classrooms, numbering 393 students, were summarized using meta-analyses. Results showed (balanced) network structures with positive ties between those who were structurally equivalent in the negative network. Moreover, essential structural parameters for the univariate network structure of positive (general like) and negative (general dislike and bullying) tie networks were identified. Different structures emerged in positive and negative networks. The results provide a starting point for further theoretical and (multiplex) empirical research about negative ties and their interplay with positive ties.     

Random errors in egocentric networks

The systematic errors that are induced by a combination of human memory limitations and common survey design and implementation have long been studied in the context of egocentric networks. Despite this, little if any work exists in the area of random error analysis on these same networks; this paper offers a perspective on the effects of random errors on egonet analysis, as well as the effects of using egonet measures as independent predictors in linear models. We explore the effects of false-positive and false-negative error in egocentric networks on both standard network measures and on linear models through simulation analysis on a ground truth egocentric network sample based on facebook-friendships. Results show that 5–20% error rates, which are consistent with error rates known to occur in ego network data, can cause serious misestimation of network properties and regression parameters.     

Logit Models for Affiliation Networks

Once confined to networks in which dyads could be reasonably assumed to be independent, the statistical analysis of network data has blossomed in recent years. New modeling and estimation strategies have made it possible to propose and evaluate very complex structures of dependency between and among ties in social networks. These advances have focused exclusively on one-mode networks—that is, networks of direct ties between actors. We generalize these models to affiliation networks, networks in which actors are tied to each other only indirectly through belonging to some group or event. We formulate models that allow us to study the (log) odds of an actor's belonging to an event (or an event including an actor) as a function of properties of the two-mode network of actors' memberships in events. We also provide illustrative analysis of some classic data sets on affiliation networks.     

The same everywhere? Exploring structural homologies of national social fields using the case of journalism

Pierre Bourdieu argued for the existence of general properties and even laws of social fields. In contrast to spaces of class relations and patterns of cultural lifestyles, however, almost no systematic comparative research exists on the homologies of national social fields of a more specialised nature. Also, the large majority of research is done on Western countries, raising concerns about the relevance of the concept for less differentiated societies. Using the field of journalism as a case, typical structures of 67 national fields (n = 27,567) are in this article investigated using a reverse approach: First, the subjective spaces of journalists' experienced constraints and imperatives in their jobs are sketched as a proxy for field structure using variants of multiple correspondence analysis, and second, the distribution of the social and professional properties of journalists are used to suggest capital structures. The results suggest great stability in the fundamental organising principles of fields of journalism around the world, although with considerable variation in their autonomy.     

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.     

Covariate-defined latent space random effects model

Latent factor models are a useful and intuitive class of models; one limitation is their inability to predict links in a dynamic network. We propose a latent space random effects model with a covariate-defined social space, where the social space is a linear combination of the covariates as estimated by an MCMC algorithm. The model allows for the prediction of links in a network; it also provides an interpretable framework to explain why people connect. We fit the model using the Adolescent Health Network dataset and three simulated networks to illustrate its effectiveness in recognizing patterns in the data.     

Settings in Social Networks: A Measurement Model

A class of statistical models is proposed that aims to recover latent settings structures in social networks. Settings may be regarded as clusters of vertices. The measurement model is based on two assumptions. (1) The observed network is generated by hierarchically nested latent transitive structures, expressed by ultrametrics, and (2) the expected tie strength decreases with ultrametric distance. The approach could be described as model–based clustering with an ultrametric space as the underlying metric to capture the dependence in the observations. Bayesian methods as well as maximum–likelihood methods are applied for statistical inference. Both approaches are implemented using Markov chain Monte Carlo methods.     

A Methodological Comparison of Age‐Period‐Cohort Models: The Intrinsic Estimator and Conventional Generalized Linear Models

Age‐period‐cohort (APC) accounting models have long been objects of attention in statistical studies of human populations. It is well known that the identification problem created by the linear dependency of age, period, and cohort (Period = Age + Cohort or P = A + C) presents a major methodological challenge to APC analysis, a problem that has been widely addressed in demography, epidemiology, and statistics. This paper compares parameter estimates and model fit statistics produced by two solutions to the identification problem in age‐period‐cohort models—namely, the conventional demographic approach of constrained generalized linear models (Fienberg and Mason 1978, 1985; Mason and Smith 1985) and the intrinsic estimator method recently developed by Fu (2000; Knight and Fu 2000; Fu, Hall, and Rohan 2004). We report empirical analyses of applications of these two methods to population data on U.S. female mortality rates. Comparisons of parameter estimates suggest that both constrained generalized linear models and the intrinsic estimator method can yield similar estimates of age, period, and cohort effects, but estimates obtained by the intrinsic estimator are more direct and do not require prior information to select appropriate model identifying constraints. We also describe three statistical properties of the estimators: (1) finite‐time‐period bias, (2) relative statistical efficiency, and (3) consistency as the number of periods of observed data increases. These empirical analyses and theoretical results suggest that the intrinsic estimator may well provide a useful alternative to conventional methods for the APC analysis of demographic rates .     

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.     

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.     

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.     

Comparing Networks Across Space and Time, Size and Species

We describe and illustrate methodology for comparing networks from diverse settings. Our empirical base consists of 42 networks from four kinds of species (humans, nonhuman primates, nonprimate mammals, and birds) and covering distinct types of relations such as influence, grooming, and agonistic encounters. The general problem is to determine whether networks are similarly structured despite their surface differences. The methodology we propose is generally applicable to the characterization and comparison of network–level social structures across multiple settings, such as different organizations, communities, or social groups, and to the examination of sources of variability in network structure. We first fit a p^* model (Wasserman and Pattison 1996) to each network to obtain estimates for effects of six structural properties on the probability of the graph. We then calculate predicted tie probabilities for each network, using both its own parameter estimates and the estimates from every other network in the collection. Comparison is based on the similarity between sets of predicted tie probabilities. We then use correspondence analysis to represent the similarities among all 42 networks and interpret the resulting configuration using information about the species and relations involved. Results show that similarities among the networks are due more to the kind of relation than to the kind of animal.     

Canonical correlation analysis: Assessing links between multiplex networks

Ignoring the multiplex nature of social networks might result in sets of empirical findings that are misleading or contradictory. It would be helpful to adapt a variety of multivariate statistical techniques to handle network-oriented data. A canonical correlation analysis (CCA) makes a particularly interesting example since it is the most general form of the general linear model. In an example involving 317 banks, a CCA is applied to two multiplex networks: interdependence and cooperative alliances. Four significant patterns of association (orthogonal linear functions) are identified.     

ANOTHER LOOK AT THE STRATIFICATION OF EDUCATIONAL TRANSITIONS: THE LOGISTIC RESPONSE MODEL WITH PARTIAL PROPORTIONALITY CONSTRAINTS

In this paper we reanalyze Robert D. Mare's highly influential work on educational transitions among American men born in the first half of the 20th century. Contrary to previous belief, Mare found that the effects of socioeconomic background variables decline regularly across educational transitions in conditional logistic regression analyses. We have reconfirmed Mare's findings and tested them by introducing a modified logistic response model that constrains selected social background effects to vary proportionally across educational transitions. We refer to our preferred model as the logistic response model with partial proportionality constraints (LRPPC). The model can easily be estimated in Stata or using other standard statistical software. Partial proportionality constraints may also prove useful in interpopulation comparisons based on other linear models.     

Expectations About Single Event Probabilities in the First Year of Life: The Influence of Perceptual and Statistical Information

Recent evidence suggests that infants can generate expectations about future events from a sample of probabilistic data. However, little is known about the conditions that support the development of this ability. Three experiments tested the prediction that 8‐ and 12‐month‐olds respond to base rates as well as perceptual cues when they generate expectations from a sample of probabilistic data. Results revealed that 12‐month‐olds were sensitive to the statistical and perceptual properties of the evidence depending on the distribution of high‐to‐low base rate items in the sample. Specifically, 12‐month‐olds focused on perceptual features of the evidence when a sample was large and more skewed (e.g., 6:1), whereas they attended to statistical properties when the sample was smaller and less skewed (e.g., 4:1). In contrast, eight‐month‐olds always focused on the perceptual features of the evidence. Neither group generated expectations from a small, less skewed sample (e.g., 2:1). These results suggest that the ability to generate expectations about future events is mediated by specific features of the available evidence and undergoes significant change during the first year of life.     

Interregionalism in Transnational Interest Networks: Euro-Asian Civil Society and the EU–ASEAN Free Trade Agreement

The study of interest groups is still a relatively small field of political science. The process of globalization has brought about the evolution of interest networks from national organizations to regional and transnational networks. This article uses the modes of political participation framework created by Jayasuriya and Rodan, in order to study the created spaces used by public interest networks at an interregional level. The empirical case study relates to Asia-Europe Meeting: the Europe-Asian interregional institution, and the work of public interest networks stemming from the civil society organizations that shadow it in opposing the EU–Association of Southeast Asian Nations (ASEAN) free trade agreement (FTA). We find that the ‘modes of political participation’ model explains quite accurately the political spaces created by civil society in the EU–ASEAN FTA. We extend the framework by adding a fifth space, lobbying, which appears out of isomorphism. This concept represents the adoption by organizations of practices carried by other institutions they interact with. In this case, public interest networks have adopted the practice of directly influencing policy-makers that was the prerogative of private interest groups.     

INFERENCE USING QUALITATIVE AND QUANTITATIVE INFORMATION WITH AN APPLICATION TO MONETARY POLICY

I propose a framework for drawing inferences about an unobserved variable using qualitative and quantitative information. Using this framework, I study the timing and persistence of monetary policy regimes and compute probabilistic measures of the qualitative indicator's reliability. These estimates suggest that (1) it is over one and one-half times more likely that monetary policy is not restrictive at any point in time, (2) Boschen and Mills's [1995] policy index is a reliable indicator of the stance of monetary policy, and (3) certain qualitative indicators of monetary policy improve interest rate forecasts that are based on linear forecasting models. (JEL C22, E52)