In this chapter, we will describe a model in which Y(t) affects W(t) at each time t = 1, 2, …. The Y(t) that is involved in this model is an n × n matrix of group members' attitudes toward each other and themselves. Their Y(t) attitudes determine W(t) along with its coupled A(t); and because these attitudes are subject to interpersonal influence, W(t), together with its coupled A(t), generates a Y(t + 1) matrix of attitudes, and so on. From this process, an equilibrium matrix of attitudes, susceptibilities, and interpersonal influences may be produced in the group. The equilibrium W(∞) and A(∞) that may emerge from this process constitute a stable influence network for the group, conditioned on the matrix of initial interpersonal attitudes Y(1). Here, Y(1), in the form of a matrix of interpersonal attitudes, appears as the core construct in determining a group's influence network. The explanation of the origins of stable influence networks in groups has been a longstanding sociological issue, and this model contributes to the theoretical integration of two lines of inquiry related to it – expectation states theory and affect control theory.

Recently, there have been efforts to develop linkages between some of the major lines of work in sociological social psychology – affect control theory, expectation states theory, and social identity theory. Ridgeway and Smith-Lovin (1994) have described possible linkages between affect control theory and expectation states theory. Kalkhoff and Barnum (2000) have described possible linkages between social identity theory and expectation states theory.