Stochastic actor‐oriented models for network change

TLDR

The models are grounded in methodological individualism, where actors use heuristics to pursue individual goals within constraints that include the existing network structure. The authors introduce a class of continuous‑time Markov chain models for longitudinal network data and propose statistical methods for estimating and testing them. These models combine purposeful change driven by actors’ goals with random change, are implemented as simulation models, and their parameters are estimated via a method‑of‑moments approach using simulation and a Robbins‑Monro stochastic approximation. The estimation procedures also apply to other simulation models, and the authors illustrate their use on Newcomb’s fraternity data, capturing reciprocity and balance.

Abstract

A class of models is proposed for longitudinal network data. These models are along the lines of methodological individualism: actors use heuristics to try to achieve their individual goals, subject to constraints. The current network structure is among these constraints. The models are continuous time Markov chain models that can be implemented as simulation models. They incorporate random change in addition to the purposeful change that follows from the actors' pursuit of their goals, and include parameters that must be estimated from observed data. Statistical methods are proposed for estimating and testing these models. These methods can also be used for parameter estimation for other simulation models. The statistical procedures are based on the method of moments, and use computer simulation to estimate the theoretical moments. The Robbins‐Monro process is used to deal with the stochastic nature of the estimated theoretical moments. An example is given for Newcomb's fraternity data, using a model that expresses reciprocity and balance.