Models of Network Structure

TLDR: The actor-status epistemic linkage is thus logically isomorphic with the in-icator-concept epistemic correlation as discussed by the authors, and the well developed statistics of multiple indicator structural equation models (e.g. Bielby & Hauser 1 977) can be used to test hypotheses regarding the status /role set duality.

Abstract: relational pattern translated into relations between actors. This means that all abstract models of social structure are quantitatively linked to observed relations. Models abstracting role-sets among statuses from observed relations among actors are at all times subject to empirical test as descriptions of observed relational patterns. 2. Analysis of network and covariance structures merges in a natural and' useful manner. Actors jointly occupying a status provide inter­ changeable representations of the role-set defining the status and accord­ ingly provide interchangeable indicators of distance to the status. The actor-status epistemic linkage is thus logically isomorphic with the in­ dicator-concept epistemic correlation. As a result of this isomorphism, the well developed statistics of multiple indicator structural equation models (e.g. Bielby & Hauser 1 977) can be used to test hypotheses regarding the status /role-set duality. Used in equations 1 5 and 16 to test structural equivalence as a statistical hypothesis, this isomorphism is also 29In contrast to Lewin's ( 1936) discussion of a psychological topology as interrelated sets of perceptions, a social topology refers to relational patterns in a system. An argument can be made for synthesizing the two via symbolic interaction and ethnomethodology since perceptions are intimately connected to relational patterns (e.g. Burt 1 980b); however, it is difficult to match psychological with social topologies since the latter are stated with considerably more rigor than the former.