Utilizing topology to generate and test theories of change.

Statistical and methodological innovations in the study of change are advancing rapidly, and visual tools have become an important component in model building and testing. Graphical representations such as path diagrams are necessary, but may be insufficient in the case of complex theories and models. Topology is a visual tool that connects theory and testable equations believed to capture the theorized patterns of change. Although some prior work has made use of topologies, these representations have often been generated as a result of the tested models. This article argues that utilizing topology a priori, when developing a theory, and applying analogous statistical models is a prudent method to conduct research. This article reviews topology by demonstrating how to build a topological representation of a theory and recover the implied equations, ultimately facilitating the transition from complex theory to testable model. Finally, topologies can guide researchers as they adjust or expand their theories in light of recent model testing. (c) 2015 APA, all rights reserved).