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Statistical models for social networks as dependent variables must represent the typical network dependencies between tie variables such as reciprocity, homophily, transitivity, etc. This review first treats models for single (cross-sectionally observed) networks and then for network dynamics. For single networks, the older literature concentrated on conditionally uniform models. Various types of latent space models have been developed: for discrete, general metric, ultrametric, Euclidean, and partially ordered spaces. Exponential random graph models were proposed long ago but now are applied more and more thanks to the non-Markovian social circuit specifications that were recently proposed. Modeling network dynamics is less complicated than modeling single network observations because dependencies are spread out in time. For modeling network dynamics, continuous-time models are more fruitful. Actor-oriented models here provide a model that can represent many dependencies in a flexible way. Strong model development is now going on to combine the features of these models and to extend them to more complicated outcome spaces.

This volume provides new insights into the functioning of organizational, managerial and market societies. Multilevel analysis and social network analysis are described and the authors show how they can be combined in developing the theory, methods and empirical applications of the social sciences. This book maps out the development of multilevel reasoning and shows how it can explain behavior, through two different ways of contextualizing it. First, by identifying levels of influence on behavior and different aggregations of actors and behavior, and complex interactions between context and behavior. Second, by identifying different levels as truly different systems of agency: such levels of agency can be examined separately and jointly since the link between them is affiliation of members of one level to collective actors at the superior level. It is by combining these approaches that this work offers new insights. New case studies and datasets that explore new avenues of theorizing and new applications of methodology are presented. This book will be useful as a reference work for all social scientists, economists and historians who use network analyses and multilevel statistical analyses. Philosophers interested in the philosophy of science or epistemology will also find this book valuable

AbstractWe consider the specification of effects of numerical actor attributes, having an interval level of measurement, in statistical models for directed social networks. A fundamental mechanism is homophily or assortativity, where actors have a higher likelihood to be tied with others having similar values of the variable under study. But there are other mechanisms that may also play a role in how the attribute values of two actors influence the likelihood of a tie between them. We discuss three additional mechanisms: aspiration, the tendency to send more ties to others having high values; attachment conformity, sending more ties to others whose values are close to the "social norm"; and sociability, where those having higher values will tend to send more ties generally. These mechanisms may operate jointly, and then their effects will be confounded. We present a specification representing these effects simultaneously by a four-parameter quadratic function of the values of sender and receiver. Flexibility can be increased by a five-parameter extension. We argue that for numerical actor attributes having important effects on directed networks, these specifications may provide an improvement. An illustration is given of dependence of advice ties on academic grades, analyzed by the Stochastic Actor-oriented Model.

AbstractMultilevel models are proposed to study relational or dyadic data from multiple persons in families or other groups. The variable under study is assumed to refer to a dyadic relation between individuals in the groups. The proposed models are elaborations of the Social Relations Model. The different roles of father, mother, and child are emphasized in these models. Multilevel models provide researchers with a method to estimate the variances and correlations of the Social Relations Model and to incorporate the effects of covariates and test specialized models, even with missing observations.

We propose two complementary ways to deal with a nesting structure in the node set of a network—such a structure may be called a multilevel network, with a node set consisting of several groups. First, within‐group ties are distinguished from between‐group ties by considering them as two distinct but interrelated networks. Second, effects of nodal variables are differentiated according to the levels of the nesting structure, to prevent ecological fallacies. This is elaborated in a study of two repeated observations of a sociability network in seven villages in Senegal, analyzed using the Stochastic Actor‐oriented Model.

"Die 'neue Netzwerkforschung' argumentiert, dass große soziale Netzwerke in unterschiedlichsten Kontexten (zum Beispiel das World Wide Web, Sexualkontakte, Koautorschaften) sehr ähnliche, hocheffiziente Struktureigenschaften aufweisen ('small world' oder 'scale free' Strukturen). Darüber hinaus werden diese Strukturen als das Resultat einfachster individueller Verhaltensmechanismen gesehen, die die makroskopische Struktur als unbeabsichtigtes Nebenprodukt individueller Beziehungswahlentscheidungen erzeugen. Die Verfasser behaupten, dass diese Forschung aus Sicht der Soziologie zwei Defizite aufweist. Erstens sind die verwendeten Verhaltensmodelle soziologisch wenig plausibel. Typischerweise werden mechanistische - oftmals an physikalischen Modellen orientierte - individuelle Verhaltensregeln angenommen und die zugrundeliegenden Motive individueller Beziehungswahlen nicht explizit modelliert. Die Modelle bieten daher wenig Einsicht in die Bedingungen der behaupteten Strukturresultate. Zweitens untersuchen empirische Arbeiten üblicherweise nur, ob globale Netzwerkmerkmale in dem Bereich liegen, der durch die theoretischen Modelle vorhergesagt wird, testen aber nicht Mechanismen der Netzwerkdynamik auf der individuellen Ebene. Sie schlagen daher vor, dass soziologische 'neue Netzwerkforschung' das Instrument 'agentenbasierter Modellierung' einsetzt. Agentenbasierte Modelle beschreiben explizit die individuellen Verhaltenziele und -regeln bestenfalls beschränkt rationaler Akteure, die nur über unvollständige lokale Information verfügen. Sie zeigen an einem Beispiel auf, wie eine agentenbasierte Modellierung der Dynamik großer Netzwerke mit soziologisch plausiblen Verhaltensannahmen nicht nur die Entstehung von 'small world' und 'scale free' Strukturen erklären kann, sondern darüber hinaus auch Bedingungen identifiziert, unter denen die zugrundeliegenden Verhaltensregeln zu verschiedenen Strukturen führen. Sie gehen dann auf statistische Ansätze ein, insbesondere auf die 'actor oriented statistics', die es möglich machen, konkurrierende Verhaltenshypothesen an Netzwerkdaten zu testen." (Autorenreferat)