Comparison of methods for positional analysis: Structural and general equivalences

This paper explores the conceptualization and measurement of social position in relational data. It is argued that social positions are evidenced in the interactions among individuals, which are encoded in measured social relations. Given a set of measured relations the task is to reveal social positions which consist of groups of individuals wth similar patterns of relations. Methods based on two alternative approaches are discussed. The first set of approaches is based on structural equivalence, and locates groups of similar individuals based on the extent to which they share identical ties with identical others. A second set of approaches, here called general equivalences, locates groups of similar individuals based on their sharing of “types” of ties with “types” of others. Procedures based on these different approaches are described and applied to actual data and to a constructed example. Results suggest that these different approaches identify different kinds of social groups. It is argued that structural equivalence is an unsuitable basis for analysis of relational data if the goal is detection of social positions.