When “It depends” amounts to more than simple contingent relationships: Three canonical forms of inversions

• Published date: 01 August 2016
• Author: Fabrice L. Cavarretta,Laura Trinchera,Sean T. Hannah,Dong Ook Choi
• Date: 01 August 2016
• DOI: http://doi.org/10.1002/job.2093

When “It depends”amounts to more than simple

contingent relationships: Three canonical forms of

inversions

FABRICE L. CAVARRETTA

1

*, LAURA TRINCHERA

2

, DONG OOK CHOI

3

AND

SEAN T. HANNAH

4

1

Management Department, ESSEC Business School, Cergy Pontoise Cédex, France

2

NEOMA Business School, Mont-Saint-Aignan, France

3

Korea Development Institute, Sejong-si, South Korea

4

School of Business, Wake Forest University, Winston Salem, NC, U.S.A.

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, con-

sidering 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 dif-

ferent cases of errors concerning inversions can occur. In the first case entailing omission, an inversion is oc-

curring 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 impor-

tant theoretical boundary conditions imposed by inversions. Copyright © 2016 John Wiley & Sons, Ltd.

Keywords: inversion; moderation; interaction; ordinal; disordinal; curvilinearity

Organizational behavior theories often include curvilinear or moderation effects to describe contingencies among

construct relationships. Identifying contingent effects is critical, as they answer questions such as when,where,or

under what conditions an independent variable (IV or X) will, or will more or less, influence a given dependent var-

iable (DV or Y). These contingencies have significant theoretical and practical implications to scholars and organi-

zations alike. A simple relationship might be specified as being contingent on a third variable—hence a moderated

specification. For example, research had commonly shown that team empowerment was strongly related to team per-

formance (e.g. Kirkman & Rosen, 1999). Yet, Kirkman, Rosen, Tesluk, and Gibson (2004) subsequently found that

this relationship was moderated by team interaction, such that the positive main effect of empowerment on team per-

formance was only significant for virtual teams that rarely (versus frequently) met face to face. Curvilinear theoret-

ical specifications, conversely, start from a simple relationship of an independent factor influencing an outcome, then

consider the possibility that the influence might increase (or decrease) disproportionally across different levels of the

factor. For example, one might theorize and test that team empowerment enhances team performance up to a certain

level, and then tapers off.

*Correspondence to: Fabrice L. Cavarretta, Management Department, ESSEC Business School, 3 av. B. Hirsch CS 50105 Cergy, 95021 Cergy

Pontoise Cédex, France. E-mail: Cavarretta@essec.edu

Correspondence regarding the R code used in this article should be addressed to Laura Trinchera, Neoma Business School, 1 Rue du Maréchal

Juin, 76130 Mont-Saint-Aignan, France. Laura.TRINCHERA@neoma-bs.fr

Copyright © 2016 John Wiley & Sons, Ltd. Received 08 January2016, Accepted 18 January 2016

Journal of Organizational Behavior, J. Organiz. Behav. 37, 933–945 (2016)

Published online 23 February 2016 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/job.2093

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