Chapter 9 demonstrates how RIO facilitates a field-theoretic approach to regression models. The chapter draws parallels between the data representations made possible by turning regression models inside out and the geometric data analysis (GDA) that is central to field theoretic approaches to social research.

Whereas previous chapters have focused on networks as conduits through which important resources and influences flow, this chapter provides a more in-depth account of the positional approach to networks. In doing so, we move away from conceptualizing social structures as more or less cohesive and integrated groups, cliques, communities, etc., toward a view of social structures as comprised of role structures. To use the baseball analogy, in moving toward a more positional view of networks, we shift from seeing teams as interacting individual players with relations with one another to seeing players as enacting the game through an interrelated set of positions on the field that come with role expectations. Thus, as depicted in our view of social structure in Figure 2.3, we begin to move upward and to the right – that is, toward higher levels of structure and greater levels of conceptual abstraction. Doing so requires a different set of methods, which we introduce in this chapter.