Testing and Interpreting Interaction Effects

Researchers often want to test whether the association between two or more variables depends on the value of a different variable. To do this, they usually test interactions, often in the form of moderated multiple regression (MMR) or its extensions. If there is an interaction effect, it means the relationship being tested does differ as the other variable (moderator) changes. While methods for determining whether an interaction exists are well established, less consensus exists about how to understand, or probe, these interactions. Many of the common methods (e.g., simple slope testing, regions of significance, use of Gardner et al.’s typology) have some reliance on post hoc significance testing, which is unhelpful much of the time, and also potentially misleading, sometimes resulting in contradictory findings. A recommended procedure for probing interaction effects involves a systematic description of the nature and size of interaction effects, considering the main effects (estimated after centering variables) as well as the size and direction of the interaction effect itself. Interaction effects can also be more usefully plotted by including both a greater range of moderator values and showing confidence bands. Although two-way linear interactions are the most common in the literature, three-way interactions and nonlinear interactions are also often found. Again, methods for testing these interactions are well known, but procedures for understanding these more complex effects have received less attention—in part because of the greater complexity of what such interpretation involves. For three-way linear interactions, the slope difference test has become a standard form of interpretation and linking the findings with theory; however, this is also prone to some of the shortcomings described for post hoc probing of two-way effects. Descriptions of three-way interactions can be improved by using some of the same principles used for two-way interactions, as well as by the appropriate use of the slope difference test. For nonlinear effects, the complexity is greater still, and a different approach is needed to explain these effects more helpfully, focusing on describing the changing shape of the effects across values of the moderator(s). Some of these principles can also be carried forward into more complex models, such as multilevel modeling, structural equation modeling, and models that involve both mediation and moderation.