When "It depends" amounts to more than simple contingent relationships: Three canonical forms of inversions. (23rd February 2016) - Cavarretta, Fabrice L.; Trinchera, Laura; Choi, Dong Ook; Hannah, Sean T.
Summary: Organizational behavior theories can be subject to potential inversions in the nature of the effects expected or described (i.e. an effect inverts from positive to negative or vice versa). Yet, inversions are rarely considered or assessed. We explore three possible canonical inversions: the maximum or minimum point in a quadratic regression model, the point of intersection in disordinal interactions, and the change of slope in a moderated regression model. We describe both the motivation for, and the theoretical and empirical importance of, considering such inversions in theory‐building and testing. We consider common situations in which inversions are misinterpreted empirically and present methods to conduct explorations for potential inversions. Two different cases of errors concerning inversions can occur. In the first case entailing omission, an inversion is occurring but is not observed in the sample. In the second case, researchers wrongly assume an inversion is occurring in their model, yet the prospective inversion would actually occur out of the range of possible values on the focal variable(s), and is thus not significant. We illustrate different types of inversions using simulated examples. Ultimately, we seek to encourage and equip management researchers to identify important theoretical boundary conditions imposed by inversions. Copyright © 2016 John Wiley & Sons, Ltd.