Our major goal was to develop a re-parameterized regression model that captures one essential aspect of an interaction more informatively than do standard analytic approaches. If the ordinal vs. disordinal form of an interaction is crucial for distinguishing theoretical positions, our re-parameterized regression model yield more detailed information for evaluating the fit of data with theoretical predictions. With more useful tools for asking key questions, researchers can be challenged to provide more explicit hypotheses regarding predicted patterns in data. Confirming predicted patterns in data yields inductive support for the validity of a theory, but disconfirming predicted patterns points to the need to reconsider theory, measurements, or conditions to ferret out reasons for disconfirmation. Clearer predictions tested against data using more focused and definitive statistical models will provide clearer evidence regarding whether theoretical conjectures driving the research were confirmed or disconfirmed. We trust our re-parameterized equation will be yet one more tool for testing theoretical conjectures directly and strongly.
