Methodology and Statistics
International Conference, 17 - 19 September 2001
FDV, Ljubljana, Slovenia


Tom A.B. Snijders
Department of Statistics and Measurement Theory / ICS
University of Groningen
Grote Kruisstraat 2/1, NL-9712 TS Groningen
The Netherlands

Social networks are structures of relations between individuals. The most common representation of a social network is a directed graph, in which the arcs indicate for each of the ordered pairs of individuals whether the relation in question (e.g., friendship) is present or not.

Repeated measures on social networks represent a complicated data structure, and few probability models and statistical methods have been proposed for such data. Computer simulation offers fruitful possibilities here, because it greatly expands the scope of modeling beyond the models for which likelihood and other functions can be analytically calculated. Continuous-time models are more appropriate for modeling longitudinal social network data than discrete-time models because of the endogenous feedback processes involved in network evolution.

The probability models for the evolution of social networks proposed here are based on the idea of actor-oriented modeling: the vertices in the network represent actors who change their relations in a process of optimizing their "utility function". This function includes a random component to represent unexplained change. The resulting model constitutes a continuous-time Markov chain, and can be simulated in a straightforward manner. It can be applied also when the actor-oriented interpretation is not so obvious. The change in the network is modeled as the stochastic result of network effects (reciprocity, transitivity, etc.) and effects of covariates.

The main parameters of this model are weights in the utility function, representing these various effects. The parameters can be estimated using a stochastic version of the method of moments, implemented by a Robbins-Monro-type algorithm.

An example is given of the evolution of the friendship network in a group of university freshmen students.

Key words: simulation, evolution