Extrapolation in congruence research: A conceptual framework and diagnostic strategy

Polynomial regression analysis (PRA) has played a central role in recent advances in congruence theory and research. Yet, the potential of PRA depends on careful management of extrapolation. We organize extrapolation around two broad uses of PRA in congruence research: theory development and theory application. In theory development, extrapolation concerns drawing inferences (conclusions) about theorized response-surface features beyond regions supported by the observed data. In theory application, extrapolation concerns making predictions beyond the observed data range. Within theory development, we further distinguish inadvertent and purposeful extrapolation. We conceptualize inadvertent extrapolation not as a merely methodological artifact but as a symptom of deeper misalignment among theory, method, and data. To manage theory development extrapolation, we propose a five-step strategy that can be routinely applied in PRA studies: (1) contextualize theory, (2) design for full-range sampling, (3) examine empirical support in the joint predictor space, (4) restrict interpretation to empirically supported regions, and (5) leverage purposeful extrapolation to guide theory building and future research. We also introduce Convex Hull, an app that visually distinguishes observed from extrapolated regions in the joint predictor space. Using empirical illustrations and simulations, we demonstrate both the risks of inadvertent extrapolation and the benefits of our strategy. This approach strengthens theoretical precision, empirical transparency, and cumulative theory development in congruence research and beyond. (PsycInfo Database Record (c) 2026 APA, all rights reserved).