Chapter 2: Reverse Arrow Dynamics: Feedback Loops and Formative Measurement

This chapter is about two types of special covariance structure models where some arrows (paths) point backwards compared with more standard models. The first kind is nonrecursive structural models with feedback loops where sets of variables are specified as causes and effects of each other in a cross-sectional design. An example of a feedback loop is the specification V1 ⇄ V2 where V1 is presumed to affect V2 and vice versa; that is, there is feedback. It is relatively easy to think of several real world causal processes, especially dynamic ones that may be based on cycles of mutual influence, including the relation between parental behavior and child behavior, rates of incarceration and crime rates, and violence on the part of protestors and police. In standard, or recursive, structural models estimated in cross-sectional designs, all presumed causal effects are specified as unidirectional only so that no two variables are causes of each other. Thus, it is impossible to estimate feedback effects when analyzing recursive structural models in cross-sectional designs. For example, a recursive model for such a design could include either the path V1 → V2 or the path V2 ← V1, but not both.