Relative effects at work: Bayes factors for order hypotheses

Assessing the relative importance of predictors has been of historical importance in a variety of disciplines including management, medicine, economics, and psychology. When approaching hypotheses on the relative ordering of the magnitude of predicted effects (e.g., the effects of discrimination from managers and coworkers are larger than that from clients), one quickly runs into problems within a traditional frequentist framework. Null hypothesis significance testing does not allow researchers to directly map research hypotheses on to results and suffers from a multiple testing problem that leads to low statistical power. Furthermore, all traditional structural equation modeling fit indices lose much of their suitability for model comparison, because order hypotheses are not countable in terms of degrees of freedom. To adequately tackle order hypotheses, we advocate a Bayesian method that provides a single internally consistent solution for estimation and inference. The key element in the proposed model comparison approach is the use of the Bayes factor and the incorporation of order constraints by means of a smart formulation of prior distributions. An easy-to-use software package BIEMS (Bayesian inequality and equality constrained model selection) is introduced and two empirical examples in the organizational behavior area are provided to showcase the method, both offering new findings that have implications for theory: the first on the differential impact of discrimination in the workplace from insiders and outsiders to the organization on employees’ well-being, and the second on Karasek’s stressor–strain theory about how the relative order of magnitude of the effects of job control and demands depends on the specific well-being outcome dimension.