A typology of three-way interaction models: Applications and suggestions for Asian management research

To narrow our scope, we limited our search to survey studies published in APJM and six top-tiered management journals—Academy of Management Journal, Journal of Applied Psychology, Journal of Management, Strategic Management Journal, Journal of Organizational Behavior, and Journal of Occupational and Organizational Psychology. One of the authors used the search engine of each journal with the key words “three-way interaction.” The person then examined each publication and retained those that formally proposed and tested three-way interactions in their studies.

While Aiken and West’s (Aiken et al., 1991) simple slope (or pick-a-point) method is rather popular, some have criticized their choice of high and low Z based on +1 and −1 s.d. to be arbitrary (e.g., Dawson & Richter, 2006). To avoid such potential limitation, we suggest readers to consider the characteristics of Z in evaluating the significance of simple slope. When Z is dichotomous or categorical (e.g., gender), researchers can still use the pick-a-point approach to analyze whether the simple slope is significant at a particular point of Z (e.g., female). If Z is continuous, however (e.g., income), readers can adopt the Johnson-Neyman technique to evaluate the range of the value of Z in which the simple slopes are significant and whether the region of significance is consistent with researchers’ expectation (see Bauer & Curran, 2005 for explanation of the Johnson-Neyman technique and Lam, Xu, & Loi, 2018 for a recent application of such technique).

The statistical procedures in probing significance of three-way interactions in Dawson and Richter (2006) and in this paper are based on the ordinary least square (OLS) method. For interpretation and analyses of interaction terms in non-OLS regression such as logistic regression, please refer to Hoetker (2007). We thank the reviewer for making this suggestion.

As X and Z are two independent variables, they are interchangeable so that one can also state the relationship between Z and Y to be the strongest when X is high/low. Figure 5 is an illustration of how to plot joint effects in two-dimensional diagrams (see Den Hartog & Belschak, 2012 for example). An alternative is to plot joint effects of X and Z on Y on a three-dimensional space.