Gerhard G. van de Bunt

Introduction to stochastic actor-based models for network dynamics

Abstract 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. This paper gives an introduction to stochastic actor-based models for dynamics of directed networks, using only a minimum of mathematics. The focus is on understanding the basic principles of the model, understanding the results, and on sensible rules for model selection.

Friendship Networks Through Time: An Actor-Oriented Dynamic Statistical Network Model

We propose a class of actor-oriented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a data-set collected among university freshmen at 7 points in time during 1994 and 1995.

Similarity in friendship networks: Selection or influence? The effect of constraining contexts and non-visible individual attributes

Most research on similarity in friendship networks focuses on clearly visible individual attributes (i.e. attitudes and behaviors) in contexts where choices whom to befriend are relatively unconstrained. These studies often reveal that social selection rather than social influence is the dominant cause of similarity among friends. We argue that in a setting where social collaboration is crucial and friendship choices are more constrained, influence might be the main reason for similarity found among friends. In addition, we examined whether social categorization and peer control amplifies the social influence process among friends. Using a stochastic actor-based model for network dynamics, we analyzed a three-wave dataset of first year Royal Netherlands Naval College officer students on friendship formation and military discipline. The data supports our first hypothesis that students adjust their own military discipline to that of their friends. Contrary to our expectations, we did not find support for the idea that individuals adjust their discipline more to friends who are of the same military specialty, and neither more to friends who exert peer control. We elaborate on these findings in the discussion.