New methodological and software tools for probing moderation in intrinsically nonlinear models

When modeling psychological processes and relationships, intrinsically nonlinear models often enhance researchers' ability to draw useful theoretical and substantive conclusions. In addition, psychological theories frequently suggest that such processes and relationships are moderated; therefore, it is often important to test for, probe, and plot moderation. However, extant methods for assessing and visualizing moderation are largely restricted to linear models. Therefore, the goal of this paper is to develop novel analytical and software tools that enable researchers to specify and examine moderated parameters within intrinsically nonlinear models. First, methods for testing, plotting, and probing moderation are expanded in novel ways for use in nonlinear models; specifically, we present conceptual and mathematical extensions of the Johnson-Neyman (JN) technique. The JN technique is currently used to probe moderation of simple slopes within the linear modeling framework; our extensions enable its application to any moderated parameter of an intrinsically nonlinear model. Additionally, we introduce a Shiny application called CurveBuilder, which unifies the process of choosing, specifying, fitting, and visualizing intrinsically nonlinear models that may include moderated parameters and/or random effects. The application provides a code-free environment for users to complete all steps of the analysis process, including uploading data, visually choosing start values, specifying models, plotting results, and probing moderation with the extended JN technique. CurveBuilder examples are reviewed, and opportunities for future work in this area are discussed.