SAOMs

SAOMs, or stochastic actor-oriented models, are a class of statistical models for longitudinal network data that treat network evolution as a dynamic process driven by actor decisions. Time is conceptualized as continuous, with networks observed at discrete waves as snapshots of an underlying continuous-time Markov process; actors update ties and covariates at random times according to an objective function. Each actor is assumed to act to optimize a utility function that depends on network structure (such as reciprocity and transitivity) and actor attributes.

Parameters in SAOMs are estimated from data using simulation-based methods, typically Monte Carlo maximum likelihood. The estimation approach uses simulated network trajectories to approximate the likelihood and infer parameters. Software such as RSiena implements these procedures, supplying tools for estimation, hypothesis testing, and model assessment.

Data requirements include longitudinal network data across multiple waves, with measured actor attributes. SAOMs can handle directed or undirected networks and can incorporate multiple networks or covariates. Outputs typically include estimated effects for specified network statistics (for example, reciprocity, popularity, transitivity, homophily by attributes), along with standard errors, confidence intervals, and goodness-of-fit diagnostics.

Applications span social and organizational networks, collaboration networks, political networks, and online platforms, wherever ties evolve over time and actors make decisions that shape the network. The framework can help disentangle selection effects (actors forming ties with similar others) from influence effects (attributes changing as a result of ties), given appropriate model specifications.

Key assumptions include a Markovian decision process, time-homogeneous dynamics between observed waves, and correct specification of the included statistics. Limitations include computational intensity, sensitivity to time intervals and model specification, and potential identifiability issues. SAOMs provide a coherent, dynamic perspective on network change and related behavioral processes.