A Mathematical Framework for the Complex System Approach to Group Dynamics: The Case of Recovery House Social Integration.

The complex system conception of group social dynamics often involves not only changing individual characteristics, but also changing within-group relationships. Recent advances in stochastic dynamic network modeling allow these interdependencies to be modeled from data. This methodology is discussed within a context of other mathematical and statistical approaches that have been or could be applied to study the temporal evolution of relationships and behaviors within small- to medium-sized groups. An example model is presented, based on a pilot study of five Oxford House recovery homes, sober living environments for individuals following release from acute substance abuse treatment. This model demonstrates how dynamic network modeling can be applied to such systems, examines and discusses several options for pooling, and shows how results are interpreted in line with complex system concepts. Results suggest that this approach (a) is a credible modeling framework for studying group dynamics even with limited data, (b) improves upon the most common alternatives, and (c) is especially well-suited to complex system conceptions. Continuing improvements in stochastic models and associated software may finally lead to mainstream use of these techniques for the study of group dynamics, a shift already occurring in related fields of behavioral science.