Models for Longitudinal Network Data

Abstract

This chapter treats statistical methods for network evolution. It is argued that it is most fruitful to consider models where network evolution is represented as the result of many (usually non-observed) small changes occurring between the consecutively observed networks. Accordingly, the focus is on models where a continuous-time network evolution is assumed although the observations are made at discrete time points (two or more). Three models are considered in detail, all based on the assumption that the observed networks are outcomes of a Markov process evolving in continuous time. The independent arcs model is a trivial baseline model. The reciprocity model expresses e ects of reciprocity, but lacks other structural e ects. The actor-oriented model is based on a model of actors changing their outgoing ties as a consequence of myopic stochastic optimization of an objective function. This framework o ers the exibility to represent a variety of network e ects. An estimation algorithm is treated, based on a Markov chain Monte Carlo implementation of the method of moments.